diff --git a/collects/frtime/frtime.scrbl b/collects/frtime/frtime.scrbl
index 383d9c3ce0..0c874f2422 100644
--- a/collects/frtime/frtime.scrbl
+++ b/collects/frtime/frtime.scrbl
@@ -318,7 +318,7 @@ the current state of the text field.}
                                           'vertical-label 'horizontal-label 
                                           'deleted)) 
                         '(vertical)]
-                 [selection nonnegative-exact-integer? 0]
+                 [selection exact-nonnegative-integer? 0]
                  [font (is-a?/c font%) normal-control-font]
                  [enabled any/c #t]
                  [vert-margin (integer-in 0 1000) 2]
@@ -345,7 +345,7 @@ the currently selected element in the radio box.}
                  [style (listof (one-of/c 'horizontal-label 'vertical-label
                                           'deleted)) 
                    null]
-                 [selection nonnegative-exact-integer? 0]
+                 [selection exact-nonnegative-integer? 0]
                  [font (is-a?/c font%) @scheme[normal-control-font]]
                  [enabled any/c #t]
                  [vert-margin (integer-in 0 1000) 2]
@@ -373,7 +373,7 @@ the currently selected element in the choice control.}
                                           'vertical-label 'horizontal-label 
                                           'deleted)) 
                         '(single)]
-                 [selection (or/c nonnegative-exact-integer? false/c) #f]
+                 [selection (or/c exact-nonnegative-integer? false/c) #f]
                  [font (is-a?/c font%) @scheme[view-control-font]]
                  [label-font (is-a?/c font%) @scheme[normal-control-font]]
                  [enabled any/c #t]
diff --git a/collects/games/cards/cards.scrbl b/collects/games/cards/cards.scrbl
index c76f7fda56..7eda556041 100644
--- a/collects/games/cards/cards.scrbl
+++ b/collects/games/cards/cards.scrbl
@@ -12,8 +12,8 @@ module provides a toolbox for creating cards games.}
 @section{Creating Tables and Cards}
 
 @defproc[(make-table [title string? "Cards"] 
-                     [w nonnegative-exact-integer? 7]
-                     [h nonnegative-exact-integer? 3])
+                     [w exact-nonnegative-integer? 7]
+                     [h exact-nonnegative-integer? 3])
          table<%>]{
 
 Returns a table.  The table is named by @scheme[title], and it is
@@ -153,7 +153,7 @@ Create an instance with @scheme[make-table].
 @defmethod[(add-cards [cards (listof (is-a?/c card<%>))]
                       [x real?]
                       [y real?]
-                      [offset-proc (nonnegative-exact-integer? 
+                      [offset-proc (exact-nonnegative-integer? 
                                     . -> . (values real? real?))
                                    (lambda (i) (values 0 0))])
             void?]{
@@ -196,7 +196,7 @@ Removes @scheme[card] from the table.}
 @defmethod[(move-cards [cards (listof (is-a?/c card<%>))]
                        [x real?]
                        [y real?]
-                       [offset-proc (nonnegative-exact-integer? . -> . (values real? real?))
+                       [offset-proc (exact-nonnegative-integer? . -> . (values real? real?))
                                     (lambda (i) (values 0 0))])
             void?]{
 
@@ -251,8 +251,8 @@ Removes @scheme[card] from the table.}
  Returns a list of all cards on the table in stacking order from front
  to back.}
 
-@defmethod*[([(table-width) nonnegative-exact-integer?]
-             [(table-height) nonnegative-exact-integer?])]{
+@defmethod*[([(table-width) exact-nonnegative-integer?]
+             [(table-height) exact-nonnegative-integer?])]{
 
  Returns the width/height of the table in pixels.}
 
@@ -382,12 +382,12 @@ Removes @scheme[card] from the table.}
 
 Create instances with @scheme[make-deck] or @scheme[make-card].
 
-@defmethod[(card-width) nonnegative-exact-integer?]{
+@defmethod[(card-width) exact-nonnegative-integer?]{
 
  Returns the width of the card in pixels.  All cards have the same
  width.}
 
-@defmethod[(card-height) nonnegative-exact-integer?]{
+@defmethod[(card-height) exact-nonnegative-integer?]{
 
  Returns the height of the card in pixels. All cards have the same
  height.}
diff --git a/collects/mzlib/scribblings/pregexp.scrbl b/collects/mzlib/scribblings/pregexp.scrbl
index c5fb04d3b9..ba79806c52 100644
--- a/collects/mzlib/scribblings/pregexp.scrbl
+++ b/collects/mzlib/scribblings/pregexp.scrbl
@@ -16,8 +16,8 @@ The library also re-exports: @scheme[pregexp], and it re-exports
 @deftogether[(
 @defproc[(pregexp-match [pattern (or/c string? bytes? regexp? byte-regexp?)]
                        [input (or/c string? bytes? input-port?)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                        [output-port (or/c output-port? false/c) #f])
          (or/c (listof (or/c (cons (or/c string? bytes?)
                                    (or/c string? bytes?))
@@ -25,17 +25,17 @@ The library also re-exports: @scheme[pregexp], and it re-exports
                false/c)]
 @defproc[(pregexp-match-positions [pattern (or/c string? bytes? regexp? byte-regexp?)]
                         [input (or/c string? bytes? input-port?)]
-                        [start-pos nonnegative-exact-integer? 0]
-                        [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                        [start-pos exact-nonnegative-integer? 0]
+                        [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                         [output-port (or/c output-port? false/c) #f])
-          (or/c (listof (or/c (cons nonnegative-exact-integer?
-                                    nonnegative-exact-integer?)
+          (or/c (listof (or/c (cons exact-nonnegative-integer?
+                                    exact-nonnegative-integer?)
                               false/c))
                 false/c)]
 @defproc[(pregexp-split [pattern (or/c string? bytes? regexp? byte-regexp?)]
                        [input (or/c string? bytes? input-port?)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos (or/c nonnegative-exact-integer? false/c) #f])
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos (or/c exact-nonnegative-integer? false/c) #f])
          (listof (or/c string? bytes?))]
 @defproc[(pregexp-replace [pattern (or/c string? bytes? regexp? byte-regexp?)]
                          [input (or/c string? bytes?)]
diff --git a/collects/net/scribblings/tcp.scrbl b/collects/net/scribblings/tcp.scrbl
index 610ea9d28f..0bbd37886d 100644
--- a/collects/net/scribblings/tcp.scrbl
+++ b/collects/net/scribblings/tcp.scrbl
@@ -26,9 +26,9 @@ See also @scheme[tcp-redirect] and @scheme[make-ssl-tcp@].
 
 @defsignature[tcp^ ()]{
 
-@defproc[(tcp-listen [port-no (and/c nonnegative-exact-integer?
+@defproc[(tcp-listen [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
-                     [max-allow-wait nonnegative-exact-integer? 4]
+                     [max-allow-wait exact-nonnegative-integer? 4]
                      [reuse? any/c #f]
                      [hostname (or/c string? false/c) #f]) 
          #, @sigelem[tcp^ tcp-listener?]]{
@@ -36,10 +36,10 @@ See also @scheme[tcp-redirect] and @scheme[make-ssl-tcp@].
 Like @scheme[tcp-listen] from @schememodname[scheme/tcp].}
 
 @defproc[(tcp-connect [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
                       [local-hostname (or/c string? false/c) #f]
-                      [local-port-no (or/c (and/c nonnegative-exact-integer?
+                      [local-port-no (or/c (and/c exact-nonnegative-integer?
                                                   (integer-in 1 65535))
                                            false/c)
                                      #f])
@@ -48,10 +48,10 @@ Like @scheme[tcp-listen] from @schememodname[scheme/tcp].}
 Like @scheme[tcp-connect] from @schememodname[scheme/tcp].}
 
 @defproc[(tcp-connect/enable-break [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
                       [local-hostname (or/c string? false/c) #f]
-                      [local-port-no (or/c (and/c nonnegative-exact-integer?
+                      [local-port-no (or/c (and/c exact-nonnegative-integer?
                                                   (integer-in 1 65535))
                                            false/c)])
           (values input-port? output-port?)]{
diff --git a/collects/openssl/openssl.scrbl b/collects/openssl/openssl.scrbl
index cc6a5f03a5..49166ece87 100644
--- a/collects/openssl/openssl.scrbl
+++ b/collects/openssl/openssl.scrbl
@@ -126,7 +126,7 @@ Returns @scheme[#t] if @scheme[v] is a value produced by
 
 @defproc[(ssl-listen
 	  (port-no (integer-in 1 65535))
-	  [queue-k nonnegative-exact-integer?]
+	  [queue-k exact-nonnegative-integer?]
 	  [reuse? any/c #f]
 	  [hostname-or-#f (or/c string? false/c) #f]
 	  [server-protocol
diff --git a/collects/readline/readline.scrbl b/collects/readline/readline.scrbl
index 8e6c26e51c..dbfa8a50ec 100644
--- a/collects/readline/readline.scrbl
+++ b/collects/readline/readline.scrbl
@@ -110,7 +110,7 @@ The default value of this parameter is therefore @scheme[#t], making
 it mimic plain I/O interactions.}
 
 
-@defparam[max-history n nonnegative-exact-integer?]{
+@defparam[max-history n exact-nonnegative-integer?]{
 
 A parameter that determines the number of history entries to save,
 defaults to @scheme[100].}
@@ -194,7 +194,7 @@ the user via the up-arrow key.}
 Adds the given byte string to the @|readline| history, which is
 accessible to the user via the up-arrow key.}
 
-@defproc[(history-length) nonnegative-exact-integer?]{
+@defproc[(history-length) exact-nonnegative-integer?]{
 
 Returns the length of the history list.}
 
diff --git a/collects/scribblings/foreign/misc.scrbl b/collects/scribblings/foreign/misc.scrbl
index c950cf25d1..cf5dd3d4f2 100644
--- a/collects/scribblings/foreign/misc.scrbl
+++ b/collects/scribblings/foreign/misc.scrbl
@@ -56,7 +56,7 @@ Like @scheme[list->cblock], but for Scheme vectors.}
 
 @declare-exporting[scribblings/foreign/unsafe-foreign]
 
-@defproc[(cblock->list [cblock any/c][type ctype?][length nonnegative-exact-integer?])
+@defproc[(cblock->list [cblock any/c][type ctype?][length exact-nonnegative-integer?])
          list?]{
 
 Converts C @scheme[cblock], which is a vector of @scheme[type]s, to a
@@ -65,7 +65,7 @@ Scheme list.  The arguments are the same as in the
 there is no way to know where the block ends.}
 
 
-@defproc[(cblock->vector [cblock any/c][type ctype?][length nonnegative-exact-integer?])
+@defproc[(cblock->vector [cblock any/c][type ctype?][length exact-nonnegative-integer?])
          vector?]{
 
 Like @scheme[cblock->vector], but for Scheme vectors.}
diff --git a/collects/scribblings/foreign/pointers.scrbl b/collects/scribblings/foreign/pointers.scrbl
index 07d64c70cc..1dc0ed1314 100644
--- a/collects/scribblings/foreign/pointers.scrbl
+++ b/collects/scribblings/foreign/pointers.scrbl
@@ -127,20 +127,20 @@ easily lead to a segmentation fault or memory corruption.}
 
 @defproc*[([(memmove [cptr cpointer?]
                      [src-cptr cpointer?]
-                     [count nonnegative-exact-integer?]
+                     [count exact-nonnegative-integer?]
                      [type ctype? _byte])
             void?]
            [(memmove [cptr cpointer?]
                      [offset exact-integer?]
                      [src-cptr cpointer?]
-                     [count nonnegative-exact-integer?]
+                     [count exact-nonnegative-integer?]
                      [type ctype? _byte])
             void?]
            [(memmove [cptr cpointer?]
                      [offset exact-integer?]
                      [src-cptr cpointer?]
                      [src-offset exact-integer?]
-                     [count nonnegative-exact-integer?]
+                     [count exact-nonnegative-integer?]
                      [type ctype? _byte])
             void?])]{
 
@@ -153,20 +153,20 @@ instances when supplied.}
 
 @defproc*[([(memcpy [cptr cpointer?]
                     [src-cptr cpointer?]
-                    [count nonnegative-exact-integer?]
+                    [count exact-nonnegative-integer?]
                     [type ctype? _byte])
             void?]
            [(memcpy [cptr cpointer?]
                     [offset exact-integer?]
                     [src-cptr cpointer?]
-                    [count nonnegative-exact-integer?]
+                    [count exact-nonnegative-integer?]
                     [type ctype? _byte])
             void?]
            [(memcpy [cptr cpointer?]
                     [offset exact-integer?]
                     [src-cptr cpointer?]
                     [src-offset exact-integer?]
-                    [count nonnegative-exact-integer?]
+                    [count exact-nonnegative-integer?]
                     [type ctype? _byte])
             void?])]{
 
@@ -175,13 +175,13 @@ and source overlap.}
 
 @defproc*[([(memset [cptr cpointer?]
                     [byte byte?]
-                    [count nonnegative-exact-integer?]
+                    [count exact-nonnegative-integer?]
                     [type ctype? _byte])
             void?]
            [(memset [cptr cpointer?]
                     [offset exact-integer?]
                     [byte byte?]
-                    [count nonnegative-exact-integer?]
+                    [count exact-nonnegative-integer?]
                     [type ctype? _byte])
             void?])]{
 
diff --git a/collects/scribblings/foreign/types.scrbl b/collects/scribblings/foreign/types.scrbl
index 6195fa80ca..d9b0d5d370 100644
--- a/collects/scribblings/foreign/types.scrbl
+++ b/collects/scribblings/foreign/types.scrbl
@@ -32,14 +32,14 @@ Returns @scheme[#t] if @scheme[v] is a @tech{C type}, @scheme[#f]
 otherwise.}
 
 
-@defproc*[([(ctype-sizeof [type ctype?]) nonnegative-exact-integer?]
-           [(ctype-alignof [ctype ctype?]) nonnegative-exact-integer?])]{
+@defproc*[([(ctype-sizeof [type ctype?]) exact-nonnegative-integer?]
+           [(ctype-alignof [ctype ctype?]) exact-nonnegative-integer?])]{
 
 Returns the size or alignment of a given @scheme[type] for the current
 platform.}
 
 
-@defproc[(compiler-sizeof [sym symbol?]) nonnegative-exact-integer?]{
+@defproc[(compiler-sizeof [sym symbol?]) exact-nonnegative-integer?]{
 
 Possible values for @scheme[symbol] are @scheme['int], @scheme['char],
 @scheme['short], @scheme['long], @scheme['*], @scheme['void],
diff --git a/collects/scribblings/framework/text.scrbl b/collects/scribblings/framework/text.scrbl
index ffae4f29a6..2970b0d8b8 100644
--- a/collects/scribblings/framework/text.scrbl
+++ b/collects/scribblings/framework/text.scrbl
@@ -149,7 +149,7 @@
     See
     @method[text:basic<%> set-styles-fixed].
   }
-  @defmethod*[#:mode augment (((after-insert (start nonnegative-exact-integer?) (len nonnegative-exact-integer?)) void))]{
+  @defmethod*[#:mode augment (((after-insert (start exact-nonnegative-integer?) (len exact-nonnegative-integer?)) void))]{
 
     See
     @method[text:basic<%> set-styles-fixed].
@@ -209,7 +209,7 @@
     Starts an edit-sequence by calling
     @method[editor<%> begin-edit-sequence].
   }
-  @defmethod*[#:mode augment (((after-insert (start nonnegative-exact-integer?) (len nonnegative-exact-integer?)) void))]{
+  @defmethod*[#:mode augment (((after-insert (start exact-nonnegative-integer?) (len exact-nonnegative-integer?)) void))]{
 
     Replaces all non-breaking space characters
     @scheme[(integer->char 160)]
@@ -255,10 +255,10 @@
     @scheme[keymap:get-search]
   }
 
-  @defmethod[#:mode augment (after-insert [start nonnegative-exact-integer?][len nonnegative-exact-integer?]) void?]{
+  @defmethod[#:mode augment (after-insert [start exact-nonnegative-integer?][len exact-nonnegative-integer?]) void?]{
     Re-does any search now that the contents of the window have changed.
   }
-  @defmethod[#:mode augment (after-delete [start nonnegative-exact-integer?][len nonnegative-exact-integer?]) void?]{
+  @defmethod[#:mode augment (after-delete [start exact-nonnegative-integer?][len exact-nonnegative-integer?]) void?]{
     Re-does any search now that the contents of the window have changed.
   }
 
@@ -512,7 +512,7 @@
     @scheme[top-level-window<%>]
     as the frame.
   }
-  @defmethod*[#:mode augment (((after-insert (start nonnegative-exact-integer?) (len nonnegative-exact-integer?)) void))]{
+  @defmethod*[#:mode augment (((after-insert (start exact-nonnegative-integer?) (len exact-nonnegative-integer?)) void))]{
 
     Calls the
     @method[frame:text-info<%> editor-position-changed]
@@ -522,7 +522,7 @@
     @scheme[top-level-window<%>]
     as the frame.
   }
-  @defmethod*[#:mode augment (((after-delete (start nonnegative-exact-integer?) (len nonnegative-exact-integer?)) void))]{
+  @defmethod*[#:mode augment (((after-delete (start exact-nonnegative-integer?) (len exact-nonnegative-integer?)) void))]{
 
     Calls the
     @method[frame:text-info<%> editor-position-changed]
diff --git a/collects/scribblings/gui/bitmap-class.scrbl b/collects/scribblings/gui/bitmap-class.scrbl
index 2c3f1c580a..6e4f8a350a 100644
--- a/collects/scribblings/gui/bitmap-class.scrbl
+++ b/collects/scribblings/gui/bitmap-class.scrbl
@@ -61,7 +61,7 @@ the bitmap is selected into another DC, attached as a button label, etc.).
 }
 
 @defmethod[(get-depth)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Gets the color depth of the bitmap. See also @method[bitmap%
 is-color?].
diff --git a/collects/scribblings/gui/choice-class.scrbl b/collects/scribblings/gui/choice-class.scrbl
index ba154348c9..356013f9ea 100644
--- a/collects/scribblings/gui/choice-class.scrbl
+++ b/collects/scribblings/gui/choice-class.scrbl
@@ -25,7 +25,7 @@ See also
                  [style (listof (one-of/c 'horizontal-label 'vertical-label
                                           'deleted)) 
                    null]
-                 [selection nonnegative-exact-integer? 0]
+                 [selection exact-nonnegative-integer? 0]
                  [font (is-a?/c font%) normal-control-font]
                  [enabled any/c #t]
                  [vert-margin (integer-in 0 1000) 2]
diff --git a/collects/scribblings/gui/dc-intf.scrbl b/collects/scribblings/gui/dc-intf.scrbl
index 2c71db065b..14a73d9b27 100644
--- a/collects/scribblings/gui/dc-intf.scrbl
+++ b/collects/scribblings/gui/dc-intf.scrbl
@@ -364,7 +364,7 @@ See also @method[dc<%> set-smoothing] for information on the
                       [x real?]
                       [y real?]
                       [combine? any/c #f]
-                      [offset nonnegative-exact-integer? 0]
+                      [offset exact-nonnegative-integer? 0]
                       [angle real? 0])
            void?]{
 
@@ -557,7 +557,7 @@ set-text-background].
 @defmethod[(get-text-extent [string string?]
                             [font (or/c (is-a?/c font%) false/c) #f]
                             [combine? any/c #f]
-                            [offset nonnegative-exact-integer? 0])
+                            [offset exact-nonnegative-integer? 0])
            (values nonnegative-real? 
                    nonnegative-real?
                    nonnegative-real? 
diff --git a/collects/scribblings/gui/dialog-funcs.scrbl b/collects/scribblings/gui/dialog-funcs.scrbl
index 4629b2b0bb..906a0cb73c 100644
--- a/collects/scribblings/gui/dialog-funcs.scrbl
+++ b/collects/scribblings/gui/dialog-funcs.scrbl
@@ -377,9 +377,9 @@ If @scheme[style] includes @scheme['password], the dialog's text field
                                 [message (or/c string? false/c)]
                                 [choices (listof string?)]
                                 [parent (or/c (is-a?/c frame%) (is-a?/c dialog%) false/c) #f]
-                                [init-choices (listof nonnegative-exact-integer?) null]
+                                [init-choices (listof exact-nonnegative-integer?) null]
                                 [style (listof (one-of/c 'single 'multiple 'extended)) '(single)])
-         (or/c (listof nonnegative-exact-integer?) false/c)]{
+         (or/c (listof exact-nonnegative-integer?) false/c)]{
 
 Gets a list box selection from the user via a modal dialog, using
  @scheme[parent] as the parent window if it is specified. The dialog's
diff --git a/collects/scribblings/gui/editor-data-class-list-intf.scrbl b/collects/scribblings/gui/editor-data-class-list-intf.scrbl
index ca258fed57..ce2ea11dbb 100644
--- a/collects/scribblings/gui/editor-data-class-list-intf.scrbl
+++ b/collects/scribblings/gui/editor-data-class-list-intf.scrbl
@@ -25,12 +25,12 @@ Finds a snip data class from the list with the given name, returning
 }
 
 @defmethod[(find-position [class (is-a?/c editor-data-class%)])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 Returns an index into the list for the specified class.
 
 }
 
-@defmethod[(nth [n nonnegative-exact-integer?])
+@defmethod[(nth [n exact-nonnegative-integer?])
            (or/c (is-a?/c editor-data-class%) false/c)]{
 Returns the @scheme[n]th class in the list (counting from 0), returning
  @scheme[#f] if the list has @scheme[n] or less classes.
@@ -38,7 +38,7 @@ Returns the @scheme[n]th class in the list (counting from 0), returning
 }
 
 @defmethod[(number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of editor data classes in the list.
 
diff --git a/collects/scribblings/gui/editor-funcs.scrbl b/collects/scribblings/gui/editor-funcs.scrbl
index d9801f7344..5764e33da7 100644
--- a/collects/scribblings/gui/editor-funcs.scrbl
+++ b/collects/scribblings/gui/editor-funcs.scrbl
@@ -209,8 +209,8 @@ Opens @scheme[filename] (in @scheme['binary] mode) and checks whether it looks
 }
 
 @defproc[(open-input-text-editor [text-editor (is-a?/c text%)]
-                                 [start-position nonnegative-exact-integer? 0]
-                                 [end-position (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
+                                 [start-position exact-nonnegative-integer? 0]
+                                 [end-position (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
                                  [snip-filter ((is-a?/c snip%) . -> . any/c) (lambda (s) s)]
                                  [port-name any/c @scheme[text-editor]]
                                  [expect-to-read-all? any/c #f])
@@ -257,7 +257,7 @@ The result port must not be used if @scheme[text-editor] changes in any
 }
 
 @defproc[(open-output-text-editor [text-editor (is-a?/c text%)]
-                                  [start-position (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
+                                  [start-position (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
                                   [special-filter (any/c . -> . any/c) (lambda (x) x)]
                                   [port-name any/c @scheme[text-editor]])
          output-port]{
diff --git a/collects/scribblings/gui/editor-intf.scrbl b/collects/scribblings/gui/editor-intf.scrbl
index aaee110855..3b4cff2df2 100644
--- a/collects/scribblings/gui/editor-intf.scrbl
+++ b/collects/scribblings/gui/editor-intf.scrbl
@@ -543,7 +543,7 @@ The first snip in a text editor is the one at @techlink{position}
 }
 
 @defmethod[(find-scroll-line [location real?])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Maps a vertical @techlink{location} within the editor to a vertical
  scroll position.
@@ -1215,7 +1215,7 @@ The @scheme[localx], @scheme[localy], @scheme[width], and @scheme[height]
 
 
 @defmethod[(num-scroll-lines)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Reports the number of scroll positions available within the editor.
 
@@ -2206,7 +2206,7 @@ Setting the height is disallowed when the editor is internally locked
 }
 
 
-@defmethod[(set-max-undo-history [count (or/c nonnegative-exact-integer? (one/of 'forever))])
+@defmethod[(set-max-undo-history [count (or/c exact-nonnegative-integer? (one/of 'forever))])
            void?]{
 
 Sets the maximum number of undoables that will be remembered by the
diff --git a/collects/scribblings/gui/editor-snip-class.scrbl b/collects/scribblings/gui/editor-snip-class.scrbl
index 9d8182eb49..f4a58c32fd 100644
--- a/collects/scribblings/gui/editor-snip-class.scrbl
+++ b/collects/scribblings/gui/editor-snip-class.scrbl
@@ -11,14 +11,14 @@ An @scheme[editor-snip%] object is a @scheme[snip%] object that
 
 @defconstructor[([editor (or/c (is-a?/c text%) false/c) #f]
                  [with-border? any/c #t]
-                 [left-margin nonnegative-exact-integer? 5]
-                 [top-margin nonnegative-exact-integer? 5]
-                 [right-margin nonnegative-exact-integer? 5]
-                 [bottom-margin nonnegative-exact-integer? 5]
-                 [left-inset nonnegative-exact-integer? 1]
-                 [top-inset nonnegative-exact-integer? 1]
-                 [right-inset nonnegative-exact-integer? 1]
-                 [bottom-inset nonnegative-exact-integer? 1]
+                 [left-margin exact-nonnegative-integer? 5]
+                 [top-margin exact-nonnegative-integer? 5]
+                 [right-margin exact-nonnegative-integer? 5]
+                 [bottom-margin exact-nonnegative-integer? 5]
+                 [left-inset exact-nonnegative-integer? 1]
+                 [top-inset exact-nonnegative-integer? 1]
+                 [right-inset exact-nonnegative-integer? 1]
+                 [bottom-inset exact-nonnegative-integer? 1]
                  [min-width (or/c (and/c real? (not/c negative?)) (one/of 'none)) 'none]
                  [max-width (or/c (and/c real? (not/c negative?)) (one/of 'none)) 'none]
                  [min-height (or/c (and/c real? (not/c negative?)) (one/of 'none)) 'none]
@@ -120,10 +120,10 @@ If the editor is a text editor, then @scheme[1] is normally subtracted
 }
 
 
-@defmethod[(get-inset [l (box/c nonnegative-exact-integer?)]
-                      [t (box/c nonnegative-exact-integer?)]
-                      [r (box/c nonnegative-exact-integer?)]
-                      [b (box/c nonnegative-exact-integer?)])
+@defmethod[(get-inset [l (box/c exact-nonnegative-integer?)]
+                      [t (box/c exact-nonnegative-integer?)]
+                      [r (box/c exact-nonnegative-integer?)]
+                      [b (box/c exact-nonnegative-integer?)])
            void?]{
 
 Gets the current border insets for the snip. The inset sets how much space
@@ -137,10 +137,10 @@ is left between the edge of the snip and the border.
 }
 
 
-@defmethod[(get-margin [l (box/c nonnegative-exact-integer?)]
-                       [t (box/c nonnegative-exact-integer?)]
-                       [r (box/c nonnegative-exact-integer?)]
-                       [b (box/c nonnegative-exact-integer?)])
+@defmethod[(get-margin [l (box/c exact-nonnegative-integer?)]
+                       [t (box/c exact-nonnegative-integer?)]
+                       [r (box/c exact-nonnegative-integer?)]
+                       [b (box/c exact-nonnegative-integer?)])
            void?]{
 
 Gets the current margins for the snip. The margin sets how much space
@@ -244,10 +244,10 @@ When an @scheme[editor-snip%] object is not inserted in an editor, it
 
 }
 
-@defmethod[(set-inset [l nonnegative-exact-integer?]
-                      [t nonnegative-exact-integer?]
-                      [r nonnegative-exact-integer?]
-                      [b nonnegative-exact-integer?])
+@defmethod[(set-inset [l exact-nonnegative-integer?]
+                      [t exact-nonnegative-integer?]
+                      [r exact-nonnegative-integer?]
+                      [b exact-nonnegative-integer?])
            void?]{
 
 Sets the current border insets for the snip. The inset sets how much
@@ -256,10 +256,10 @@ Sets the current border insets for the snip. The inset sets how much
 }
 
 
-@defmethod[(set-margin [l nonnegative-exact-integer?]
-                       [t nonnegative-exact-integer?]
-                       [r nonnegative-exact-integer?]
-                       [b nonnegative-exact-integer?])
+@defmethod[(set-margin [l exact-nonnegative-integer?]
+                       [t exact-nonnegative-integer?]
+                       [r exact-nonnegative-integer?]
+                       [b exact-nonnegative-integer?])
            void?]{
 
 Sets the current margins for the snip. The margin sets how much space
diff --git a/collects/scribblings/gui/editor-stream-in-base-class.scrbl b/collects/scribblings/gui/editor-stream-in-base-class.scrbl
index e550144921..fd336631e4 100644
--- a/collects/scribblings/gui/editor-stream-in-base-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-in-base-class.scrbl
@@ -22,7 +22,7 @@ Returns @scheme[#t] if there has been an error reading from the
 }
 
 @defmethod[(read [data (and/c bytes? (not/c immutable?))])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Reads characters to fill the supplied vector. The return value is the
  number of characters read, which may be less than the number
@@ -33,14 +33,14 @@ Reads characters to fill the supplied vector. The return value is the
 }
 
 
-@defmethod[(seek [pos nonnegative-exact-integer?])
+@defmethod[(seek [pos exact-nonnegative-integer?])
            void?]{
 
 Moves to the specified absolute position in the stream.
 
 }
 
-@defmethod[(skip [n nonnegative-exact-integer?])
+@defmethod[(skip [n exact-nonnegative-integer?])
            void?]{
 
 Skips past the next @scheme[n] characters in the stream.
@@ -48,7 +48,7 @@ Skips past the next @scheme[n] characters in the stream.
 }
 
 @defmethod[(tell)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the current stream position.
 
diff --git a/collects/scribblings/gui/editor-stream-in-class.scrbl b/collects/scribblings/gui/editor-stream-in-class.scrbl
index 76fd40b606..25f0e9647b 100644
--- a/collects/scribblings/gui/editor-stream-in-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-in-class.scrbl
@@ -30,7 +30,7 @@ Reading from a bad stream always gives @scheme[0].
 }
 
 
-@defmethod[(get-bytes [len (or/c (box/c nonnegative-exact-integer?) false/c) #f])
+@defmethod[(get-bytes [len (or/c (box/c exact-nonnegative-integer?) false/c) #f])
            (or/c bytes? false/c)]{
 
 Like @method[editor-stream-in% get-unterminated-bytes], but the last
@@ -69,7 +69,7 @@ Returns the next floating-point value in the stream.
 
 }
 
-@defmethod[(get-unterminated-bytes [len (or/c (box/c nonnegative-exact-integer?) false/c) #f])
+@defmethod[(get-unterminated-bytes [len (or/c (box/c exact-nonnegative-integer?) false/c) #f])
            (or/c bytes? false/c)]{
 
 Returns the next byte string from the stream.  Reading from a bad
@@ -83,7 +83,7 @@ Note that when @method[editor-stream-out% put] is not given a byte
 
 }
 
-@defmethod[(jump-to [pos nonnegative-exact-integer?])
+@defmethod[(jump-to [pos exact-nonnegative-integer?])
            void?]{
 
 Jumps to a given position in the stream.
@@ -105,7 +105,7 @@ See @method[editor-stream-in% set-boundary].
 
 }
 
-@defmethod[(set-boundary [n nonnegative-exact-integer?])
+@defmethod[(set-boundary [n exact-nonnegative-integer?])
            void?]{
 
 Sets a file-reading boundary at @scheme[n] bytes past the current
@@ -122,7 +122,7 @@ Boundaries help keep a subroutine from reading too much data leading
 }
 
 
-@defmethod[(skip [n nonnegative-exact-integer?])
+@defmethod[(skip [n exact-nonnegative-integer?])
            void?]{
 
 Skips past the next @scheme[n] bytes in the stream.
@@ -130,7 +130,7 @@ Skips past the next @scheme[n] bytes in the stream.
 }
 
 @defmethod[(tell)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the current stream position.
 
diff --git a/collects/scribblings/gui/editor-stream-out-base-class.scrbl b/collects/scribblings/gui/editor-stream-out-base-class.scrbl
index a93f7eca34..fa05dc5da7 100644
--- a/collects/scribblings/gui/editor-stream-out-base-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-out-base-class.scrbl
@@ -22,7 +22,7 @@ Returns @scheme[#t] if there has been an error writing to the stream,
 
 }
 
-@defmethod[(seek [pos nonnegative-exact-integer?])
+@defmethod[(seek [pos exact-nonnegative-integer?])
            void?]{
 
 Moves to the specified absolute position in the stream.
@@ -30,7 +30,7 @@ Moves to the specified absolute position in the stream.
 }
 
 @defmethod[(tell)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the current stream position.
 
diff --git a/collects/scribblings/gui/editor-stream-out-class.scrbl b/collects/scribblings/gui/editor-stream-out-class.scrbl
index 57e54dd267..2499f448a3 100644
--- a/collects/scribblings/gui/editor-stream-out-class.scrbl
+++ b/collects/scribblings/gui/editor-stream-out-class.scrbl
@@ -18,7 +18,7 @@ An out-stream base---possibly an
 
 }
 
-@defmethod[(jump-to [pos nonnegative-exact-integer?])
+@defmethod[(jump-to [pos exact-nonnegative-integer?])
            void?]{
 Jumps to a given position in the stream.
 
@@ -49,7 +49,7 @@ This method is called by @scheme[write-editor-global-header].
 
 }
 
-@defmethod*[([(put [n nonnegative-exact-integer?]
+@defmethod*[([(put [n exact-nonnegative-integer?]
                    [v bytes?])
               (is-a?/c editor-stream-out%)]
              [(put [v bytes?])
@@ -90,7 +90,7 @@ Numbers written to a stream with @method[editor-stream-out% put-fixed]
 }
 
 @defmethod[(tell)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the current stream position.
 
diff --git a/collects/scribblings/gui/global-draw-funcs.scrbl b/collects/scribblings/gui/global-draw-funcs.scrbl
index 89b663f5f4..98006f2014 100644
--- a/collects/scribblings/gui/global-draw-funcs.scrbl
+++ b/collects/scribblings/gui/global-draw-funcs.scrbl
@@ -13,14 +13,14 @@ Under X and Mac OS X, flushes pending display messages such that the
 }
 
 @defproc[(get-display-depth)
-         nonnegative-exact-integer?]{
+         exact-nonnegative-integer?]{
 
 Returns the depth of the main display (a value of 1 denotes a monochrome display).
 
 }
 
 @defproc[(get-display-left-top-inset [avoid-bars? bool @scheme[#f]])
-         (values nonnegative-exact-integer? nonnegative-exact-integer?)]{
+         (values exact-nonnegative-integer? exact-nonnegative-integer?)]{
 
 When the optional argument is @scheme[#f] (the default), this function
  returns the offset of the main screen's origin from the
@@ -36,7 +36,7 @@ When the optional argument is true, this function returns the amount
 }
 
 @defproc[(get-display-size [full-screen? bool @scheme[#f]])
-         (values nonnegative-exact-integer? nonnegative-exact-integer?)]{
+         (values exact-nonnegative-integer? exact-nonnegative-integer?)]{
 
 @index["screen resolution"]{Gets} the physical size of the display in
  pixels.  Under Windows, this size does not include the task bar by
diff --git a/collects/scribblings/gui/list-box-class.scrbl b/collects/scribblings/gui/list-box-class.scrbl
index c9600c83d8..486872ec9a 100644
--- a/collects/scribblings/gui/list-box-class.scrbl
+++ b/collects/scribblings/gui/list-box-class.scrbl
@@ -32,7 +32,7 @@ See also @scheme[choice%].
                                           'vertical-label 'horizontal-label 
                                           'deleted)) 
                         '(single)]
-                 [selection (or/c nonnegative-exact-integer? false/c) #f]
+                 [selection (or/c exact-nonnegative-integer? false/c) #f]
                  [font (is-a?/c font%) view-control-font]
                  [label-font (is-a?/c font%) normal-control-font]
                  [enabled any/c #t]
@@ -110,7 +110,7 @@ See also @xmethod[list-control<%> append].
 }
 
 
-@defmethod[(delete [n nonnegative-exact-integer?])
+@defmethod[(delete [n exact-nonnegative-integer?])
            void?]{
 
 Deletes the item indexed by @scheme[n]. @|lbnumnote| If @scheme[n] is equal
@@ -121,7 +121,7 @@ Selected items that are not deleted remain selected, and no other
 
 }
 
-@defmethod[(get-data [n nonnegative-exact-integer?])
+@defmethod[(get-data [n exact-nonnegative-integer?])
            any/c]{
 
 Returns the data for the item indexed by @scheme[n], or @scheme[#f]
@@ -135,7 +135,7 @@ See also @method[list-box% append] and @method[list-box% set-data].
 
 
 @defmethod[(get-first-visible-item)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Reports the index of the item currently scrolled to the top of the
  list box. @|lbnumnote|
@@ -151,7 +151,7 @@ Returns the font used for the control's label, which is optionally
 }
 
 @defmethod[(get-selections)
-           (listof nonnegative-exact-integer?)]{
+           (listof exact-nonnegative-integer?)]{
 
 Returns a list of indices for all currently selected items.
  @|lbnumnote|
@@ -162,7 +162,7 @@ For single-selection lists, the result is always either @scheme[null] or
 }
 
 
-@defmethod[(is-selected? [n nonnegative-exact-integer?])
+@defmethod[(is-selected? [n exact-nonnegative-integer?])
            boolean?]{
 
 Returns @scheme[#t] if the item index by @scheme[n] is selected,
@@ -175,7 +175,7 @@ Returns @scheme[#t] if the item index by @scheme[n] is selected,
 }
 
 @defmethod[(number-of-visible-items)
-           positive-exact-integer?]{
+           exact-positive-integer?]{
 
 Returns the maximum number of items in the list box that are visible
  to the user with the control's current size (rounding down if the
@@ -183,7 +183,7 @@ Returns the maximum number of items in the list box that are visible
 
 }
 
-@defmethod[(select [n nonnegative-exact-integer?]
+@defmethod[(select [n exact-nonnegative-integer?]
                    [select? any/c #t])
            void?]{
 
@@ -212,7 +212,7 @@ Clears the list box and installs a new list of items.
 }
 
 
-@defmethod[(set-data [n nonnegative-exact-integer?]
+@defmethod[(set-data [n exact-nonnegative-integer?]
                      [data any/c])
            void?]{
 
@@ -225,7 +225,7 @@ See also @method[list-box% append].
 }
 
 
-@defmethod[(set-first-visible-item [n nonnegative-exact-integer?])
+@defmethod[(set-first-visible-item [n exact-nonnegative-integer?])
            void?]{
 
 Scrolls the list box so that the item indexed by @scheme[n] is at the
@@ -238,7 +238,7 @@ Scrolls the list box so that the item indexed by @scheme[n] is at the
 }
 
 
-@defmethod[(set-string [n nonnegative-exact-integer?]
+@defmethod[(set-string [n exact-nonnegative-integer?]
                        [label label-string?])
            void?]{
 
diff --git a/collects/scribblings/gui/list-control-intf.scrbl b/collects/scribblings/gui/list-control-intf.scrbl
index 4320e4d264..c04e1e34b2 100644
--- a/collects/scribblings/gui/list-control-intf.scrbl
+++ b/collects/scribblings/gui/list-control-intf.scrbl
@@ -37,7 +37,7 @@ Removes all user-selectable items from the control.
 }
 
 @defmethod[(find-string [s string])
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 Finds a user-selectable item matching the given string. If no matching
  choice is found, @scheme[#f] is returned, otherwise the index of the
  matching choice is returned (items are indexed from @scheme[0]).
@@ -45,14 +45,14 @@ Finds a user-selectable item matching the given string. If no matching
 }
 
 @defmethod[(get-number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 Returns the number of user-selectable items in the control (which is
  also one more than the greatest index in the list control).
 
 }
 
 @defmethod[(get-selection)
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 Returns the index of the currently selected item (items are indexed
  from @scheme[0]). If the choice item currently contains no choices or no
  selections, @scheme[#f] is returned.  If multiple selections are
@@ -61,7 +61,7 @@ Returns the index of the currently selected item (items are indexed
 
 }
 
-@defmethod[(get-string [n nonnegative-exact-integer?])
+@defmethod[(get-string [n exact-nonnegative-integer?])
            (and/c immutable? label-string?)]{
 
 Returns the item for the given index (items are indexed from
@@ -79,7 +79,7 @@ Returns the currently selected item.  If the control currently
 
 }
 
-@defmethod[(set-selection [n nonnegative-exact-integer?])
+@defmethod[(set-selection [n exact-nonnegative-integer?])
            void?]{
 Selects the item specified by the given index (items are indexed from
  @scheme[0]). If the given index larger than the greatest index in the
diff --git a/collects/scribblings/gui/miscwin-funcs.scrbl b/collects/scribblings/gui/miscwin-funcs.scrbl
index c68b468485..1f5f871e4a 100644
--- a/collects/scribblings/gui/miscwin-funcs.scrbl
+++ b/collects/scribblings/gui/miscwin-funcs.scrbl
@@ -188,8 +188,8 @@ See also @scheme[write-resource].}
 @defproc[(get-window-text-extent [string string]
                                  [font (is-a?/c font%)]
                                  [combine? any/c #f])
-         (values nonnegative-exact-integer?
-                 nonnegative-exact-integer?)]{
+         (values exact-nonnegative-integer?
+                 exact-nonnegative-integer?)]{
 
 Returns the pixel size of a string drawn as a window's label or value
 when drawn with the given font. The optional @scheme[combine?]
diff --git a/collects/scribblings/gui/ps-setup-class.scrbl b/collects/scribblings/gui/ps-setup-class.scrbl
index fbd4e4c6ca..fd0f49b9a4 100644
--- a/collects/scribblings/gui/ps-setup-class.scrbl
+++ b/collects/scribblings/gui/ps-setup-class.scrbl
@@ -168,8 +168,8 @@ Sets the printer command used to print a file under X. See
 
 }
 
-@defmethod[(set-editor-margin [h nonnegative-exact-integer?]
-                              [v nonnegative-exact-integer?])
+@defmethod[(set-editor-margin [h exact-nonnegative-integer?]
+                              [v exact-nonnegative-integer?])
            void?]{
 
 Sets the horizontal and vertical margins used when printing an editor
diff --git a/collects/scribblings/gui/radio-box-class.scrbl b/collects/scribblings/gui/radio-box-class.scrbl
index fbea90c5d4..323b38e990 100644
--- a/collects/scribblings/gui/radio-box-class.scrbl
+++ b/collects/scribblings/gui/radio-box-class.scrbl
@@ -28,7 +28,7 @@ Whenever the user changes the selected radio button, the radio box's
                                           'vertical-label 'horizontal-label 
                                           'deleted)) 
                         '(vertical)]
-                 [selection nonnegative-exact-integer? 0]
+                 [selection exact-nonnegative-integer? 0]
                  [font (is-a?/c font%) normal-control-font]
                  [enabled any/c #t]
                  [vert-margin (integer-in 0 1000) 2]
@@ -75,7 +75,7 @@ By default, the first radio button is initially selected. If
 @defmethod*[#:mode override 
             ([(enable [enable? any/c])
               void?]
-             [(enable [n nonnegative-exact-integer?]
+             [(enable [n exact-nonnegative-integer?]
                       [enable? any/c])
               void?])]{
 
@@ -90,7 +90,7 @@ If two arguments are provided, then if @scheme[enable?] is
 }
 
 
-@defmethod[(get-item-label [n nonnegative-exact-integer?])
+@defmethod[(get-item-label [n exact-nonnegative-integer?])
            string?]{
 
 Gets the label of a radio button by position. Radio buttons are
@@ -99,7 +99,7 @@ Gets the label of a radio button by position. Radio buttons are
 
 }
 
-@defmethod[(get-item-plain-label [n nonnegative-exact-integer?])
+@defmethod[(get-item-plain-label [n exact-nonnegative-integer?])
            string?]{
 
 Like @method[radio-box% get-item-label], except that the label must be
@@ -108,14 +108,14 @@ a string and @litchar{&}s in the label are removed.
 }
 
 @defmethod[(get-number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of radio buttons in the radio box.
 
 }
 
 @defmethod[(get-selection)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Gets the position of the selected radio button. Radio buttons are
 numbered from @scheme[0].
@@ -125,7 +125,7 @@ numbered from @scheme[0].
 @defmethod*[#:mode override 
             ([(is-enabled?)
               boolean?]
-             [(is-enabled? [n nonnegative-exact-integer?])
+             [(is-enabled? [n exact-nonnegative-integer?])
               boolean?])]{
 
 If no arguments are provided, the enable state of the entire radio box
@@ -139,7 +139,7 @@ box, @|MismatchExn|.
 
 }
 
-@defmethod[(set-selection [n nonnegative-exact-integer?])
+@defmethod[(set-selection [n exact-nonnegative-integer?])
            void?]{
 
 Sets the selected radio button by position. (The control's callback
diff --git a/collects/scribblings/gui/readable-snip-intf.scrbl b/collects/scribblings/gui/readable-snip-intf.scrbl
index c497e3a23c..71e96005cc 100644
--- a/collects/scribblings/gui/readable-snip-intf.scrbl
+++ b/collects/scribblings/gui/readable-snip-intf.scrbl
@@ -10,9 +10,9 @@ A @scheme[readable-snip<%>] object is treated specially by the port
  generate the read result for the snip.
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 The arguments are the same as the arguments to a procedure returned by
diff --git a/collects/scribblings/gui/snip-class-list-intf.scrbl b/collects/scribblings/gui/snip-class-list-intf.scrbl
index b2d3f9c887..17b8134f7b 100644
--- a/collects/scribblings/gui/snip-class-list-intf.scrbl
+++ b/collects/scribblings/gui/snip-class-list-intf.scrbl
@@ -27,13 +27,13 @@ Finds a snip class from the list with the given name, returning
 }
 
 @defmethod[(find-position [class (is-a?/c snip-class%)])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns an index into the list for the specified class.
 
 }
 
-@defmethod[(nth [n nonnegative-exact-integer?])
+@defmethod[(nth [n exact-nonnegative-integer?])
            (or/c (is-a?/c snip-class%) false/c)]{
 
 Returns the @scheme[n]th class in the list, or @scheme[#f] if
@@ -42,7 +42,7 @@ Returns the @scheme[n]th class in the list, or @scheme[#f] if
 }
 
 @defmethod[(number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of snip classes in the list.
 
diff --git a/collects/scribblings/gui/snip-class.scrbl b/collects/scribblings/gui/snip-class.scrbl
index d8f94577d2..50a7c764b0 100644
--- a/collects/scribblings/gui/snip-class.scrbl
+++ b/collects/scribblings/gui/snip-class.scrbl
@@ -214,7 +214,7 @@ Draws nothing.
 
 
 @defmethod[(find-scroll-step [y real?])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 @methspec{
 
@@ -361,7 +361,7 @@ following symbols:
 
 
 @defmethod[(get-num-scroll-steps)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 @methspec{
 
@@ -378,7 +378,7 @@ Returns @scheme[1].
 }}
 
 
-@defmethod[(get-scroll-step-offset [offset nonnegative-exact-integer?])
+@defmethod[(get-scroll-step-offset [offset exact-nonnegative-integer?])
            (and/c real? (not/c negative?))]{
 
 @methspec{
@@ -414,8 +414,8 @@ Returns the snip's style. See also @method[snip% set-style].
 }
 
 
-@defmethod[(get-text [offset nonnegative-exact-integer?]
-                     [num nonnegative-exact-integer?]
+@defmethod[(get-text [offset exact-nonnegative-integer?]
+                     [num exact-nonnegative-integer?]
                      [flattened? any/c #f])
            string?]{
 @methspec{
@@ -439,10 +439,10 @@ Returns @scheme[""].
 }}
 
 
-@defmethod[(get-text! [buffer mutable string]
-                      [offset nonnegative-exact-integer?]
-                      [num nonnegative-exact-integer?]
-                      [buffer-offset nonnegative-exact-integer?])
+@defmethod[(get-text! [buffer (and/c string? (not/c immutable?))]
+                      [offset exact-nonnegative-integer?]
+                      [num exact-nonnegative-integer?]
+                      [buffer-offset exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -617,7 +617,7 @@ Does nothing.
 @defmethod[(partial-offset [dc (is-a?/c dc<%>)]
                            [x real?]
                            [y real?]
-                           [len nonnegative-exact-integer?])
+                           [len exact-nonnegative-integer?])
            real?]{
 @methspec{
 
@@ -807,7 +807,7 @@ Does nothing.
 }}
 
 
-@defmethod[(split [position nonnegative-exact-integer?]
+@defmethod[(split [position exact-nonnegative-integer?]
                   [first (box/c (is-a?/c snip%))]
                   [second (box/c (is-a?/c snip%))])
            void?]{
diff --git a/collects/scribblings/gui/string-snip-class.scrbl b/collects/scribblings/gui/string-snip-class.scrbl
index 96dad1b9ab..38baf6f48d 100644
--- a/collects/scribblings/gui/string-snip-class.scrbl
+++ b/collects/scribblings/gui/string-snip-class.scrbl
@@ -8,7 +8,7 @@ An instance of @scheme[string-snip%] is created automatically when
  on-new-string-snip].
 
 
-@defconstructor*/make[(([allocsize nonnegative-exact-integer? 0])
+@defconstructor*/make[(([allocsize exact-nonnegative-integer? 0])
                        ([s string?]))]{
 
 Creates a string snip whose initial content is @scheme[s], if
@@ -20,8 +20,8 @@ Creates a string snip whose initial content is @scheme[s], if
 
 
 @defmethod[(insert [s string?]
-                   [len nonnegative-exact-integer?]
-                   [pos nonnegative-exact-integer? 0])
+                   [len exact-nonnegative-integer?]
+                   [pos exact-nonnegative-integer? 0])
            void?]{
 
 Inserts @scheme[s] (with length @scheme[len]) into the snip at relative
@@ -30,7 +30,7 @@ Inserts @scheme[s] (with length @scheme[len]) into the snip at relative
 }
 
 
-@defmethod[(read [len nonnegative-exact-integer?]
+@defmethod[(read [len exact-nonnegative-integer?]
                  [f (is-a?/c editor-stream-in%)])
            void?]{
 
diff --git a/collects/scribblings/gui/style-list-class.scrbl b/collects/scribblings/gui/style-list-class.scrbl
index b8cc48ca7e..b9eef1351f 100644
--- a/collects/scribblings/gui/style-list-class.scrbl
+++ b/collects/scribblings/gui/style-list-class.scrbl
@@ -91,7 +91,7 @@ notify-on-change].
 }
 
 
-@defmethod[(index-to-style [i nonnegative-exact-integer?])
+@defmethod[(index-to-style [i exact-nonnegative-integer?])
            (or/c (is-a?/c style<%>) false/c)]{
 
 Returns the style associated with the given index, or @scheme[#f] for
@@ -136,7 +136,7 @@ The return value from @method[style-list% notify-on-change] is an
 
 
 @defmethod[(number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of styles in the list.
 
@@ -152,7 +152,7 @@ Like @method[style-list% new-named-style], except that if the name is
 }
 
 @defmethod[(style-to-index [style (is-a?/c style<%>)])
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 
 Returns the index for a particular style. The index for a style's base
  style (and shift style, if it is a join style) is guaranteed to be
diff --git a/collects/scribblings/gui/tab-panel-class.scrbl b/collects/scribblings/gui/tab-panel-class.scrbl
index f82e86e83e..6743928c7f 100644
--- a/collects/scribblings/gui/tab-panel-class.scrbl
+++ b/collects/scribblings/gui/tab-panel-class.scrbl
@@ -66,7 +66,7 @@ The label string @scheme[choice] can contain @litchar{&}, which (in
 
 }
 
-@defmethod[(delete [n nonnegative-exact-integer?])
+@defmethod[(delete [n exact-nonnegative-integer?])
            void?]{
 
 Deletes an existing tab. If @scheme[n] is equal to or larger than the
@@ -74,7 +74,7 @@ Deletes an existing tab. If @scheme[n] is equal to or larger than the
 
 }
 
-@defmethod[(get-item-label [n nonnegative-exact-integer?])
+@defmethod[(get-item-label [n exact-nonnegative-integer?])
            string?]{
 
 Gets the label of a tab by position. Tabs are numbered from @scheme[0].
@@ -84,14 +84,14 @@ If @scheme[n] is equal to or larger than the number of tabs in the panel,
 }
 
 @defmethod[(get-number)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of tabs on the panel.
 
 }
 
 @defmethod[(get-selection)
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 
 Returns the index (counting from 0) of the currently selected tab.  If
  the panel has no tabs, the result is @scheme[#f].
@@ -106,7 +106,7 @@ Removes all tabs from the panel and installs tabs with the given
 
 }
 
-@defmethod[(set-item-label [n nonnegative-exact-integer?]
+@defmethod[(set-item-label [n exact-nonnegative-integer?]
                            [label label-string?])
            string?]{
 
@@ -115,7 +115,7 @@ Set the label for tab @scheme[n] to @scheme[label]. If @scheme[n] is equal to
 
 }
 
-@defmethod[(set-selection [n nonnegative-exact-integer?])
+@defmethod[(set-selection [n exact-nonnegative-integer?])
            void?]{
 
 Sets the currently selected tab by index (counting from 0).
diff --git a/collects/scribblings/gui/text-class.scrbl b/collects/scribblings/gui/text-class.scrbl
index a80d59cb5f..a66ba7d02e 100644
--- a/collects/scribblings/gui/text-class.scrbl
+++ b/collects/scribblings/gui/text-class.scrbl
@@ -33,8 +33,8 @@ A new @scheme[style-list%] object is created for the new editor.  See
 
 
 @defmethod[#:mode pubment 
-           (after-change-style [start nonnegative-exact-integer?]
-                               [len nonnegative-exact-integer?])
+           (after-change-style [start exact-nonnegative-integer?]
+                               [len exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -56,8 +56,8 @@ Does nothing.
 }}
 
 @defmethod[#:mode pubment 
-           (after-delete [start nonnegative-exact-integer?]
-                         [len nonnegative-exact-integer?])
+           (after-delete [start exact-nonnegative-integer?]
+                         [len exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -84,8 +84,8 @@ Does nothing.
 }}
 
 @defmethod[#:mode pubment 
-           (after-insert [start nonnegative-exact-integer?]
-                         [len nonnegative-exact-integer?])
+           (after-insert [start exact-nonnegative-integer?]
+                         [len exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -111,7 +111,7 @@ Does nothing.
 }}
 
 @defmethod[#:mode pubment 
-           (after-merge-snips [pos nonnegative-exact-integer?])
+           (after-merge-snips [pos exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -177,7 +177,7 @@ Does nothing.
 
 
 @defmethod[#:mode pubment 
-           (after-split-snip [pos nonnegative-exact-integer?])
+           (after-split-snip [pos exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -195,8 +195,8 @@ Does nothing.
 
 }}
 
-@defmethod[(call-clickback [start nonnegative-exact-integer?]
-                           [end nonnegative-exact-integer?])
+@defmethod[(call-clickback [start exact-nonnegative-integer?]
+                           [end exact-nonnegative-integer?])
            void?]{
 
 Simulates a user click that invokes a clickback, if the given range of
@@ -206,8 +206,8 @@ Simulates a user click that invokes a clickback, if the given range of
 }
 
 @defmethod[#:mode pubment 
-           (can-change-style? [start nonnegative-exact-integer?]
-                              [len nonnegative-exact-integer?])
+           (can-change-style? [start exact-nonnegative-integer?]
+                              [len exact-nonnegative-integer?])
            boolean?]{
 
 @methspec{
@@ -232,8 +232,8 @@ Returns @scheme[#t].
 }
 
 @defmethod[#:mode pubment 
-           (can-delete? [start nonnegative-exact-integer?]
-                        [len nonnegative-exact-integer?])
+           (can-delete? [start exact-nonnegative-integer?]
+                        [len exact-nonnegative-integer?])
            boolean?]{
 @methspec{
 
@@ -261,8 +261,8 @@ Returns @scheme[#t].
 }}
 
 @defmethod[#:mode pubment 
-           (can-insert? [start nonnegative-exact-integer?]
-                        [len nonnegative-exact-integer?])
+           (can-insert? [start exact-nonnegative-integer?]
+                        [len exact-nonnegative-integer?])
            boolean?]{
 @methspec{
 
@@ -325,13 +325,13 @@ See also @method[text% hide-caret].
 
 @defmethod*[#:mode extend
             ([(change-style [delta (or/c (is-a?/c style-delta%) false/c)]
-                            [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                            [end (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
+                            [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                            [end (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
                             [counts-as-mod? any/c #t])
               void?]
              [(change-style [style (or/c (is-a?/c style<%>) false/c)]
-                            [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                            [end (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
+                            [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                            [end (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
                             [counts-as-mod? any/c #t])
               void?])]{
 
@@ -352,8 +352,8 @@ When @scheme[style] is provided: @InStyleListNote[]
 @defmethod[#:mode extend
            (copy [extend? any/c]
                  [time (and/c exact? integer?)]
-                 [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                 [end (or/c nonnegative-exact-integer? (one/of 'end)) 'end])
+                 [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                 [end (or/c exact-nonnegative-integer? (one/of 'end)) 'end])
            void?]{
 
 Copies specified range of text into the clipboard. If @scheme[extend?] is
@@ -383,8 +383,8 @@ In addition to the default @xmethod[editor<%> copy-self-to] work,
 @defmethod[#:mode override
            (cut [extend? any/c]
                 [time (and/c exact? integer?)]
-                [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                [end (or/c nonnegative-exact-integer? (one/of 'end)) 'end])
+                [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                [end (or/c exact-nonnegative-integer? (one/of 'end)) 'end])
            void?]{
 
 Copies and then deletes the specified range. If @scheme[extend?] is not
@@ -399,8 +399,8 @@ See @|timediscuss| for a discussion of the @scheme[time] argument. If
 }
 
 
-@defmethod*[([(delete [start (or/c nonnegative-exact-integer? (one/of 'start))]
-                      [end (or/c nonnegative-exact-integer? (one/of 'back)) 'back]
+@defmethod*[([(delete [start (or/c exact-nonnegative-integer? (one/of 'start))]
+                      [end (or/c exact-nonnegative-integer? (one/of 'back)) 'back]
                       [scroll-ok? any/c #t])
               void?]
              [(delete)
@@ -422,8 +422,8 @@ Deletes the specified range or the currently selected text (when no
 
 }
 
-@defmethod[(do-copy [start nonnegative-exact-integer?]
-                    [end nonnegative-exact-integer?]
+@defmethod[(do-copy [start exact-nonnegative-integer?]
+                    [end exact-nonnegative-integer?]
                     [time (and/c exact? integer?)]
                     [extend? any/c])
            void?]{
@@ -446,7 +446,7 @@ Copy the data from @scheme[start] to @scheme[end], extending the current
 }}
 
 
-@defmethod[(do-paste [start nonnegative-exact-integer?]
+@defmethod[(do-paste [start exact-nonnegative-integer?]
                      [time (and/c exact? integer?)])
            void?]{
 @methspec{
@@ -467,7 +467,7 @@ Pastes into the @techlink{position} @scheme[start].
 }}
 
 
-@defmethod[(do-paste-x-selection [start nonnegative-exact-integer?]
+@defmethod[(do-paste-x-selection [start exact-nonnegative-integer?]
                                  [time (and/c exact? integer?)])
            void?]{
 @methspec{
@@ -501,7 +501,7 @@ See also @method[text% delete].
 
 @defmethod[(find-line [y real?]
                       [on-it? (or/c (box/c any/c) false/c) #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Given a @techlink{location} in the editor, returns the line at the
  @techlink{location}. @|LineNumbering|
@@ -533,7 +533,7 @@ Given a snip, returns the next snip in the editor (after the given
                           [at-eol? (or/c (box/c any/c) false/c) #f]
                           [on-it? (or/c (box/c any/c) false/c) #f]
                           [edge-close? (or/c (box/c real?) false/c) #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Given a @techlink{location} in the editor, returns the @techlink{position} at the
  @techlink{location}.
@@ -555,12 +555,12 @@ See @|ateoldiscuss| for a discussion of the @scheme[at-eol?] argument.
 }
 
 
-@defmethod[(find-position-in-line [line nonnegative-exact-integer?]
+@defmethod[(find-position-in-line [line exact-nonnegative-integer?]
                                   [x real?]
                                   [at-eol? (or/c (box/c any/c) false/c) #f]
                                   [on-it? (or/c (box/c any/c) false/c) #f]
                                   [edge-close? (or/c (box/c real?) false/c) #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Given a @techlink{location} within a line of the editor, returns the
  @techlink{position} at the @techlink{location}. @|LineNumbering|
@@ -577,9 +577,9 @@ See @method[text% find-position] for a discussion of
 }
 
 
-@defmethod[(find-snip [pos nonnegative-exact-integer?]
+@defmethod[(find-snip [pos exact-nonnegative-integer?]
                       [direction (one-of/c 'before-or-none 'before 'after 'after-or-none)]
-                      [s-pos (or/c (box/c nonnegative-exact-integer?) false/c) #f])
+                      [s-pos (or/c (box/c exact-nonnegative-integer?) false/c) #f])
            (or/c (is-a?/c snip%) false/c)]{
 
 Returns the snip at a given @techlink{position}, or @scheme[#f] if an appropriate
@@ -611,11 +611,11 @@ can be any of the following:
 
 @defmethod[(find-string [str string?]
                         [direction (one-of/c 'forward 'backward) 'forward]
-                        [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                        [end (or/c nonnegative-exact-integer? (one/of 'eof)) 'eof]
+                        [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                        [end (or/c exact-nonnegative-integer? (one/of 'eof)) 'eof]
                         [get-start? any/c #t]
                         [case-sensitive? any/c #t])
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 
 Finds an exact-match string in the editor and returns its @techlink{position}. 
  If the string is not found, @scheme[#f] is returned.
@@ -643,11 +643,11 @@ If @scheme[case-sensitive?] is @scheme[#f], then an uppercase and lowercase
 
 @defmethod[(find-string-all [str string?]
                             [direction (one-of/c 'forward 'backward) 'forward]
-                            [start (or/c nonnegative-exact-integer? (one/of 'start)) 'start]
-                            [end (or/c nonnegative-exact-integer? (one/of 'eof)) 'eof]
+                            [start (or/c exact-nonnegative-integer? (one/of 'start)) 'start]
+                            [end (or/c exact-nonnegative-integer? (one/of 'eof)) 'eof]
                             [get-start? any/c #t]
                             [case-sensitive any/c #t])
-           (listof nonnegative-exact-integer?)]{
+           (listof exact-nonnegative-integer?)]{
 
 Finds all occurrences of a string using @method[text% find-string]. If
  no occurrences are found, the empty list is returned.  The arguments
@@ -656,8 +656,8 @@ Finds all occurrences of a string using @method[text% find-string]. If
 }
 
 
-@defmethod[(find-wordbreak [start (or/c (box/c nonnegative-exact-integer?) false/c)]
-                           [end (or/c (box/c nonnegative-exact-integer?) false/c)]
+@defmethod[(find-wordbreak [start (or/c (box/c exact-nonnegative-integer?) false/c)]
+                           [end (or/c (box/c exact-nonnegative-integer?) false/c)]
                            [reason (one-of/c 'caret 'line 'selection 'user1 'user2)])
            void?]{
 
@@ -711,11 +711,11 @@ Turns off the hiliting and shows the normal selection range again; see
 }
 
 
-@defmethod[(flash-on [start nonnegative-exact-integer?]
-                     [end nonnegative-exact-integer?]
+@defmethod[(flash-on [start exact-nonnegative-integer?]
+                     [end exact-nonnegative-integer?]
                      [at-eol? any/c #f]
                      [scroll? any/c #t]
-                     [timeout nonnegative-exact-integer? 500])
+                     [timeout exact-nonnegative-integer? 500])
            void?]{
 
 Temporarily hilites a region in the editor without changing the
@@ -754,7 +754,7 @@ See also @method[text% set-between-threshold].
 }
 
 
-@defmethod[(get-character [start nonnegative-exact-integer?])
+@defmethod[(get-character [start exact-nonnegative-integer?])
            char?]{
 
 Returns the character following the @techlink{position}
@@ -768,7 +768,7 @@ If @scheme[start] is greater than or equal to the last
 
 
 @defmethod[(get-end-position)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the ending @techlink{position} of the current selection. See
  also @method[text% get-position].
@@ -804,8 +804,8 @@ Returns @scheme[#t] if the editor is in overwrite mode, @scheme[#f]
 }
 
 
-@defmethod[(get-position [start (or/c (box/c nonnegative-exact-integer?) false/c)]
-                         [end (or/c (box/c nonnegative-exact-integer?) false/c) #f])
+@defmethod[(get-position [start (or/c (box/c exact-nonnegative-integer?) false/c)]
+                         [end (or/c (box/c exact-nonnegative-integer?) false/c) #f])
            void?]{
 
 Returns the current selection range in @techlink{position}s.  If
@@ -821,8 +821,8 @@ and @method[text% get-end-position].
 }
 
 
-@defmethod[(get-region-data [start nonnegative-exact-integer?]
-                            [end nonnegative-exact-integer?])
+@defmethod[(get-region-data [start exact-nonnegative-integer?]
+                            [end exact-nonnegative-integer?])
            (or/c (is-a?/c editor-data%) false/c)]{
 
 Gets extra data associated with a given region. See
@@ -854,7 +854,7 @@ Returns an inexact number that increments every time the editor is
 
 
 @defmethod[(get-snip-position [snip (is-a?/c snip%)])
-           (or/c nonnegative-exact-integer? false/c)]{
+           (or/c exact-nonnegative-integer? false/c)]{
 
 Returns the starting @techlink{position} of a given snip or
  @scheme[#f] if the snip is not in this editor.
@@ -862,7 +862,7 @@ Returns the starting @techlink{position} of a given snip or
 }
 
 @defmethod[(get-snip-position-and-location [snip (is-a?/c snip%)]
-                                           [pos (or/c (box/c nonnegative-exact-integer?) false/c)]
+                                           [pos (or/c (box/c exact-nonnegative-integer?) false/c)]
                                            [x (or/c (box/c real?) false/c) #f]
                                            [y (or/c (box/c real?) false/c) #f])
            boolean?]{
@@ -881,7 +881,7 @@ When @techlink{location} information is requested: @|OVD| @|FCA|
 
 
 @defmethod[(get-start-position)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the starting @techlink{position} of the current selection. See also
  @method[text% get-position].
@@ -911,7 +911,7 @@ See also @method[text% set-styles-sticky].
 }
 
 
-@defmethod[(get-tabs [length (or/c (box/c nonnegative-exact-integer?) false/c) #f]
+@defmethod[(get-tabs [length (or/c (box/c exact-nonnegative-integer?) false/c) #f]
                      [tab-width (or/c (box/c real?) false/c) #f]
                      [in-units (or/c (box/c any/c) false/c) #f])
            (listof real?)]{
@@ -931,8 +931,8 @@ See also
 }
 
 
-@defmethod[(get-text [start nonnegative-exact-integer? 0]
-                     [end (or/c nonnegative-exact-integer? (one/of 'eof)) 'eof]
+@defmethod[(get-text [start exact-nonnegative-integer? 0]
+                     [end (or/c exact-nonnegative-integer? (one/of 'eof)) 'eof]
                      [flattened? any/c #f]
                      [force-cr? any/c #f])
            string?]{
@@ -964,8 +964,8 @@ Returns the distance from the top of the editor to the alignment
 }
 
 
-@defmethod[(get-visible-line-range [start (or/c (box/c nonnegative-exact-integer?) false/c)]
-                                   [end (or/c (box/c nonnegative-exact-integer?) false/c)]
+@defmethod[(get-visible-line-range [start (or/c (box/c exact-nonnegative-integer?) false/c)]
+                                   [end (or/c (box/c exact-nonnegative-integer?) false/c)]
                                    [all? any/c #t])
            void?]{
 
@@ -985,8 +985,8 @@ If the editor is displayed by multiple canvases and @scheme[all?] is
 }
 
 
-@defmethod[(get-visible-position-range [start (or/c (box/c nonnegative-exact-integer?) false/c)]
-                                       [end (or/c (box/c nonnegative-exact-integer?) false/c)]
+@defmethod[(get-visible-position-range [start (or/c (box/c exact-nonnegative-integer?) false/c)]
+                                       [end (or/c (box/c exact-nonnegative-integer?) false/c)]
                                        [all? any/c #t])
            void?]{
 
@@ -1032,24 +1032,24 @@ See also @method[text% caret-hidden?] and @method[editor<%> lock].
 
 @defmethod*[#:mode override 
             ([(insert [str string?]
-                      [start nonnegative-exact-integer?]
-                      [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+                      [start exact-nonnegative-integer?]
+                      [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                       [scroll-ok? any/c #t])
               void?]
-             [(insert [n nonnegative-exact-integer?]
+             [(insert [n exact-nonnegative-integer?]
                       [str string?]
-                      [start nonnegative-exact-integer?]
-                      [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+                      [start exact-nonnegative-integer?]
+                      [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                       [scroll-ok? any/c #t])
               void?]
              [(insert [str string?])
               void?]
-             [(insert [n nonnegative-exact-integer?]
+             [(insert [n exact-nonnegative-integer?]
                       [str string?])
               void?]
              [(insert [snip (is-a?/c snip%)]
-                      [start nonnegative-exact-integer?]
-                      [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+                      [start exact-nonnegative-integer?]
+                      [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                       [scroll-ok? any/c #t])
               void?]
              [(insert [snip (is-a?/c snip%)])
@@ -1057,8 +1057,8 @@ See also @method[text% caret-hidden?] and @method[editor<%> lock].
              [(insert [char char?])
               void?]
              [(insert [char char?]
-                      [start nonnegative-exact-integer?]
-                      [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same])
+                      [start exact-nonnegative-integer?]
+                      [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same])
               void?])]{
 
 Inserts text or a snip into @this-obj[] at @techlink{position}
@@ -1101,8 +1101,8 @@ See also @method[text% get-styles-sticky].
             ([(kill [time (and/c exact? integer?) 0])
               void?]
              [(kill [time (and/c exact? integer?)]
-                    [start nonnegative-exact-integer?]
-                    [end nonnegative-exact-integer?])
+                    [start exact-nonnegative-integer?]
+                    [end exact-nonnegative-integer?])
               void?])]{
 
 Cuts the text in the given region. If @scheme[start] and @scheme[end]
@@ -1118,7 +1118,7 @@ See @|timediscuss| for a discussion of the @scheme[time] argument. If
 
 
 @defmethod[(last-line)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of the last line in the editor. Lines are numbered
  starting with @scheme[0], so this is one less than the number of lines
@@ -1131,7 +1131,7 @@ Returns the number of the last line in the editor. Lines are numbered
 
 
 @defmethod[(last-paragraph)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the number of the last paragraph in the editor. Paragraphs are
  numbered starting with @scheme[0], so this is one less than the
@@ -1142,16 +1142,16 @@ Returns the number of the last paragraph in the editor. Paragraphs are
 }
 
 @defmethod[(last-position)
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the last selection @techlink{position} in the editor. This is
  also the number of @techlink{item}s in the editor.
 
 }
 
-@defmethod[(line-end-position [line nonnegative-exact-integer?]
+@defmethod[(line-end-position [line exact-nonnegative-integer?]
                               [visible? any/c #t])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the last @techlink{position} of a given line. @|LineNumbering|
 
@@ -1171,8 +1171,8 @@ If the line ends with invisible @techlink{item}s (such as a carriage
 }
 
 
-@defmethod[(line-length [i nonnegative-exact-integer?])
-           nonnegative-exact-integer?]{
+@defmethod[(line-length [i exact-nonnegative-integer?])
+           exact-nonnegative-integer?]{
 
 Returns the number of @techlink{item}s in a given
 line. @|LineNumbering|
@@ -1182,7 +1182,7 @@ line. @|LineNumbering|
 }
 
 
-@defmethod[(line-location [line nonnegative-exact-integer?]
+@defmethod[(line-location [line exact-nonnegative-integer?]
                           [top? any/c #t])
            real?]{
 
@@ -1198,8 +1198,8 @@ If @scheme[top?] is not @scheme[#f], the @techlink{location} for the
 
 }
 
-@defmethod[(line-paragraph [start nonnegative-exact-integer?])
-           nonnegative-exact-integer?]{
+@defmethod[(line-paragraph [start exact-nonnegative-integer?])
+           exact-nonnegative-integer?]{
 
 Returns the paragraph number of the paragraph containing the line.
  @|LineNumbering| @|ParagraphNumbering|
@@ -1208,9 +1208,9 @@ Returns the paragraph number of the paragraph containing the line.
 
 }
 
-@defmethod[(line-start-position [line nonnegative-exact-integer?]
+@defmethod[(line-start-position [line exact-nonnegative-integer?]
                                 [visible? any/c #t])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the first @techlink{position} of the given line. @|LineNumbering|
 
@@ -1285,8 +1285,8 @@ See also @method[text% set-position].
 
 
 @defmethod[#:mode pubment 
-           (on-change-style [start nonnegative-exact-integer?]
-                            [len nonnegative-exact-integer?])
+           (on-change-style [start exact-nonnegative-integer?]
+                            [len exact-nonnegative-integer?])
            void?]{
 
 @methspec{
@@ -1363,8 +1363,8 @@ Tracks clicks on a clickback (see @method[text% set-clickback]) of
 
 
 @defmethod[#:mode pubment 
-           (on-delete [start nonnegative-exact-integer?]
-                      [len nonnegative-exact-integer?])
+           (on-delete [start exact-nonnegative-integer?]
+                      [len exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -1394,8 +1394,8 @@ Does nothing.
 
 
 @defmethod[#:mode pubment 
-           (on-insert [start nonnegative-exact-integer?]
-                      [len nonnegative-exact-integer?])
+           (on-insert [start exact-nonnegative-integer?]
+                      [len exact-nonnegative-integer?])
            void?]{
 @methspec{
 
@@ -1493,8 +1493,8 @@ Does nothing.
 }}
 
 
-@defmethod[(paragraph-end-line [paragraph nonnegative-exact-integer?])
-           nonnegative-exact-integer?]{
+@defmethod[(paragraph-end-line [paragraph exact-nonnegative-integer?])
+           exact-nonnegative-integer?]{
 
 Returns the ending line of a given paragraph. @|ParagraphNumbering| @|LineNumbering|
 
@@ -1503,9 +1503,9 @@ Returns the ending line of a given paragraph. @|ParagraphNumbering| @|LineNumber
 }
 
 
-@defmethod[(paragraph-end-position [paragraph nonnegative-exact-integer?]
+@defmethod[(paragraph-end-position [paragraph exact-nonnegative-integer?]
                                    [visible? any/c #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the ending @techlink{position} of a given paragraph. @|ParagraphNumbering|
 
@@ -1520,8 +1520,8 @@ If the paragraph ends with invisible @techlink{item}s (such as a carriage
 }
 
 
-@defmethod[(paragraph-start-line [paragraph nonnegative-exact-integer?])
-           nonnegative-exact-integer?]{
+@defmethod[(paragraph-start-line [paragraph exact-nonnegative-integer?])
+           exact-nonnegative-integer?]{
 
 Returns the starting line of a given paragraph. @|ParagraphNumbering| @|LineNumbering|
 
@@ -1530,9 +1530,9 @@ Returns the starting line of a given paragraph. @|ParagraphNumbering| @|LineNumb
 }
 
 
-@defmethod[(paragraph-start-position [paragraph nonnegative-exact-integer?]
+@defmethod[(paragraph-start-position [paragraph exact-nonnegative-integer?]
                                      [visible? any/c #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the starting @techlink{position} of a given paragraph. @|ParagraphNumbering|
 
@@ -1548,8 +1548,8 @@ If the paragraph starts with invisible @techlink{item}s and @scheme[visible?] is
 
 @defmethod[#:mode override
            (paste [time (and/c exact? integer?)]
-                  [start (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
-                  [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same])
+                  [start (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
+                  [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same])
            void?]{
 
 Pastes into the specified range. If @scheme[start] is @scheme['end], then
@@ -1586,8 +1586,8 @@ If the previous operation on the editor was not a paste, calling
 
 @defmethod[#:mode override
            (paste-x-selection [time (and/c exact? integer?)]
-                              [start (or/c nonnegative-exact-integer? (one/of 'end)) 'end]
-                              [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same])
+                              [start (or/c exact-nonnegative-integer? (one/of 'end)) 'end]
+                              [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same])
            void?]{
 
 Pastes into the specified range. If @scheme[start] is @scheme['end], then
@@ -1600,9 +1600,9 @@ See @|timediscuss| for a discussion of the @scheme[time] argument. If
 
 }
 
-@defmethod[(position-line [start nonnegative-exact-integer?]
+@defmethod[(position-line [start exact-nonnegative-integer?]
                           [at-eol? any/c #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 Returns the line number of the line containing a given @techlink{position}. @|LineNumbering|
 
@@ -1615,7 +1615,7 @@ See @|ateoldiscuss| for a discussion of @scheme[at-eol?].
 }
 
 
-@defmethod[(position-location [start nonnegative-exact-integer?]
+@defmethod[(position-location [start exact-nonnegative-integer?]
                               [x (or/c (box/c real?) false/c) #f]
                               [y (or/c (box/c real?) false/c) #f]
                               [top? any/c #t]
@@ -1646,7 +1646,7 @@ maximum bottom @techlink{location} for the whole line is returned in @scheme[y].
 }
 
 
-@defmethod[(position-locations [start nonnegative-exact-integer?]
+@defmethod[(position-locations [start exact-nonnegative-integer?]
                                [top-x (or/c (box/c real?) false/c) #f]
                                [top-y (or/c (box/c real?) false/c) #f]
                                [bottom-x (or/c (box/c real?) false/c) #f]
@@ -1662,9 +1662,9 @@ and ``bottom'' results at once.
 
 }
 
-@defmethod[(position-paragraph [start nonnegative-exact-integer?]
+@defmethod[(position-paragraph [start exact-nonnegative-integer?]
                                [at-eol? any/c #f])
-           nonnegative-exact-integer?]{
+           exact-nonnegative-integer?]{
 
 See @|ateoldiscuss| for a discussion of @scheme[at-eol?].
 
@@ -1675,7 +1675,7 @@ Returns the paragraph number of the paragraph containing a given @techlink{posit
 
 @defmethod[#:mode extend
            (read-from-file [stream (is-a?/c editor-stream-in%)]
-                           [start (or/c nonnegative-exact-integer? (one/of 'start))]
+                           [start (or/c exact-nonnegative-integer? (one/of 'start))]
                            [overwrite-styles? any/c #t])
            boolean?]{
 
@@ -1685,8 +1685,8 @@ New data is inserted at the @techlink{position} indicated by @scheme[start], or
 }
 
 
-@defmethod[(remove-clickback [start nonnegative-exact-integer?]
-                             [end nonnegative-exact-integer?])
+@defmethod[(remove-clickback [start exact-nonnegative-integer?]
+                             [end exact-nonnegative-integer?])
            void?]{
 
 Removes all clickbacks installed for exactly the range @scheme[start]
@@ -1695,9 +1695,9 @@ Removes all clickbacks installed for exactly the range @scheme[start]
 }
 
 
-@defmethod[(scroll-to-position [start nonnegative-exact-integer?]
+@defmethod[(scroll-to-position [start exact-nonnegative-integer?]
                                [at-eol? any/c #f]
-                               [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+                               [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                                [bias (one-of/c 'start 'end 'none) 'none])
            boolean?]{
 
@@ -1784,11 +1784,11 @@ See also
 }
 
 
-@defmethod[(set-clickback [start nonnegative-exact-integer?]
-                          [end nonnegative-exact-integer?]
+@defmethod[(set-clickback [start exact-nonnegative-integer?]
+                          [end exact-nonnegative-integer?]
                           [f ((is-a?/c text% 
-                                       nonnegative-exact-integer?
-                                       nonnegative-exact-integer?)
+                                       exact-nonnegative-integer?
+                                       exact-nonnegative-integer?)
                               . -> . any)]
                           [hilite-delta (or/c (is-a?/c style-delta%) false/c) #f]
                           [call-on-down? any/c #f])
@@ -1852,7 +1852,7 @@ Enables or disables overwrite mode. See @method[text%
 }
 
 
-@defmethod[(set-paragraph-alignment [paragraph nonnegative-exact-integer?]
+@defmethod[(set-paragraph-alignment [paragraph exact-nonnegative-integer?]
                                     [alignment (one-of/c 'left 'center 'right)])
            void?]{
 
@@ -1870,7 +1870,7 @@ Sets a paragraph-specific horizontal alignment. The alignment is only
 }
 
 
-@defmethod[(set-paragraph-margins [paragraph nonnegative-exact-integer?]
+@defmethod[(set-paragraph-margins [paragraph exact-nonnegative-integer?]
                                   [first-left (and/c real? (not/c negative?))]
                                   [left (and/c real? (not/c negative?))]
                                   [right (and/c real? (not/c negative?))])
@@ -1891,8 +1891,8 @@ The first line of the paragraph is indented by @scheme[first-left] points
 }
 
 
-@defmethod[(set-position [start nonnegative-exact-integer?]
-                         [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+@defmethod[(set-position [start exact-nonnegative-integer?]
+                         [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                          [at-eol? any/c #f]
                          [scroll? any/c #t]
                          [seltype (one-of/c 'default 'x 'local) 'default])
@@ -1935,8 +1935,8 @@ See also @scheme[editor-set-x-selection-mode].
 
 
 @defmethod[(set-position-bias-scroll [bias (one-of/c 'start-only 'start 'none 'end 'end-only)]
-                                     [start nonnegative-exact-integer?]
-                                     [end (or/c nonnegative-exact-integer? (one/of 'same)) 'same]
+                                     [start exact-nonnegative-integer?]
+                                     [end (or/c exact-nonnegative-integer? (one/of 'same)) 'same]
                                      [ateol? any/c #f]
                                      [scroll? any/c #t]
                                      [seltype (one-of/c 'default 'x 'local) 'default])
@@ -1958,8 +1958,8 @@ See also @method[text% scroll-to-position].
 }
 
 
-@defmethod[(set-region-data [start nonnegative-exact-integer?]
-                            [end nonnegative-exact-integer?]
+@defmethod[(set-region-data [start exact-nonnegative-integer?]
+                            [end exact-nonnegative-integer?]
                             [data (is-a?/c editor-data%)])
            void?]{
 
@@ -2010,8 +2010,8 @@ Setting tabs is disallowed when the editor is internally locked for
 }
 
 
-@defmethod[(set-wordbreak-func [f ((is-a?/c text%) (or/c (box/c nonnegative-exact-integer?) false/c)
-                                                   (or/c (box/c nonnegative-exact-integer?) false/c)
+@defmethod[(set-wordbreak-func [f ((is-a?/c text%) (or/c (box/c exact-nonnegative-integer?) false/c)
+                                                   (or/c (box/c exact-nonnegative-integer?) false/c)
                                                    symbol?
                                    . -> . any)])
            void?]{
@@ -2048,7 +2048,7 @@ If @scheme[map] is @scheme[#f], then the standard map
 }
 
 
-@defmethod[(split-snip [pos nonnegative-exact-integer?])
+@defmethod[(split-snip [pos exact-nonnegative-integer?])
            void?]{
 
 Given a @techlink{position}, splits the snip that includes the
@@ -2064,8 +2064,8 @@ Splitting a snip is disallowed when the editor is internally locked
 
 @defmethod[#:mode extend
            (write-to-file [stream (is-a?/c editor-stream-out%)]
-                          [start nonnegative-exact-integer? 0]
-                          [end (or/c nonnegative-exact-integer? (one/of 'eof)) 'eof])
+                          [start exact-nonnegative-integer? 0]
+                          [end (or/c exact-nonnegative-integer? (one/of 'eof)) 'eof])
            boolean?]{
 
 If @scheme[start] is 0 and @scheme[end] is @scheme['eof] negative,
diff --git a/collects/scribblings/gui/wxme.scrbl b/collects/scribblings/gui/wxme.scrbl
index 2837aaf9df..626562cfa3 100644
--- a/collects/scribblings/gui/wxme.scrbl
+++ b/collects/scribblings/gui/wxme.scrbl
@@ -185,9 +185,9 @@ An interface to be implemented by values returned from a snip reader.
 The only method is @method[readable<%> read-special].
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 Like @method[readable-snip<%> read-special], but for non-graphical
@@ -413,9 +413,9 @@ No data is available.
 }
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 Generates a special comment using @scheme[make-special-comment]. The
@@ -446,9 +446,9 @@ Returns @scheme[#t] if whitespace is elimited from the contained XML
 literal, @scheme[#f] otherwise.}
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 Generates a @scheme[quasiquote] S-expression that enclosed the XML,
@@ -480,9 +480,9 @@ Returns @scheme[#t] if the box corresponds to a splicing unquote,
 @scheme[#f] for a non-splicing unquote.}
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 Generates an S-expression for the code in the box.}
@@ -511,9 +511,9 @@ mode.
 No data is available.}
 
 @defmethod[(read-special [source any/c]
-                         [line (or/c nonnegative-exact-integer? false/c)]
-                         [column (or/c nonnegative-exact-integer? false/c)]
-                         [position (or/c nonnegative-exact-integer? false/c)])
+                         [line (or/c exact-nonnegative-integer? false/c)]
+                         [column (or/c exact-nonnegative-integer? false/c)]
+                         [position (or/c exact-nonnegative-integer? false/c)])
            any/c]{
 
 Generates a string containing the text.}
diff --git a/collects/scribblings/reference/bytes.scrbl b/collects/scribblings/reference/bytes.scrbl
index 7e76676f08..d6cdf50595 100644
--- a/collects/scribblings/reference/bytes.scrbl
+++ b/collects/scribblings/reference/bytes.scrbl
@@ -423,15 +423,15 @@ Closes the given converter, so that it can no longer be used with
 
 @defproc[(bytes-convert [converter bytes-converter?]
                         [src-bstr bytes?]
-                        [src-start-pos nonnegative-exact-integer? 0]
-                        [src-end-pos nonnegative-exact-integer? (bytes-length src-bstr)]
+                        [src-start-pos exact-nonnegative-integer? 0]
+                        [src-end-pos exact-nonnegative-integer? (bytes-length src-bstr)]
                         [dest-bstr (or/c bytes? false/c) #f]
-                        [dest-start-pos nonnegative-exact-integer? 0]
-                        [dest-end-pos (or/c nonnegative-exact-integer? false/c)
+                        [dest-start-pos exact-nonnegative-integer? 0]
+                        [dest-end-pos (or/c exact-nonnegative-integer? false/c)
                                       (and dest-bstr
                                            (bytes-length dest-bstr))])
-          (values (or/c bytes? nonnegative-exact-integer?)
-                  nonnegative-exact-integer?
+          (values (or/c bytes? exact-nonnegative-integer?)
+                  exact-nonnegative-integer?
                   (one-of 'complete 'continues 'aborts 'error))]{
 
 Converts the bytes from @scheme[src-start-pos] to @scheme[src-end-pos]
@@ -499,11 +499,11 @@ sequence and reset the converter, use @scheme[bytes-convert-end].}
 
 @defproc[(bytes-convert-end [converter bytes-converter?]
                             [dest-bstr (or/c bytes? false/c) #f]
-                            [dest-start-pos nonnegative-exact-integer? 0]
-                            [dest-end-pos (or/c nonnegative-exact-integer? false/c)
+                            [dest-start-pos exact-nonnegative-integer? 0]
+                            [dest-end-pos (or/c exact-nonnegative-integer? false/c)
                                           (and dest-bstr
                                                (bytes-length dest-bstr))])
-          (values (or/c bytes? nonnegative-exact-integer?)
+          (values (or/c bytes? exact-nonnegative-integer?)
                   (one-of 'complete 'continues))]{
 
 Like @scheme[bytes-convert], but instead of converting bytes, this
diff --git a/collects/scribblings/reference/class.scrbl b/collects/scribblings/reference/class.scrbl
index 6770203cb5..45192b8f4b 100644
--- a/collects/scribblings/reference/class.scrbl
+++ b/collects/scribblings/reference/class.scrbl
@@ -1627,7 +1627,7 @@ methods whose names are local (i.e., declared with
 @scheme[define-local-member-names]).}
 
 
-@defproc[(object-method-arity-includes? [object object?][sym symbol?][cnt nonnegative-exact-integer?])
+@defproc[(object-method-arity-includes? [object object?][sym symbol?][cnt exact-nonnegative-integer?])
          boolean?]{
 
 Returns @scheme[#t] if @scheme[object] has a method named @scheme[sym]
@@ -1662,10 +1662,10 @@ K%
 
 @defproc[(class-info [class class?])
          (values symbol?
-                 nonnegative-exact-integer?
+                 exact-nonnegative-integer?
                  (listof symbol?)
-                 (any/c nonnegative-exact-integer? . -> . any/c)
-                 (any/c nonnegative-exact-integer? any/c . -> . any/c)
+                 (any/c exact-nonnegative-integer? . -> . any/c)
+                 (any/c exact-nonnegative-integer? any/c . -> . any/c)
                  (or/c class? false/c)
                  boolean?)]{
 
diff --git a/collects/scribblings/reference/contracts.scrbl b/collects/scribblings/reference/contracts.scrbl
index e565c7e9b6..267b8fe1c6 100644
--- a/collects/scribblings/reference/contracts.scrbl
+++ b/collects/scribblings/reference/contracts.scrbl
@@ -145,7 +145,7 @@ between @scheme[j] and @scheme[k], inclusive.}
 A flat contract that requires the input to be an exact non-negative integer.}
 
 
-@defproc[(string-len/c [len nonnegative-exact-integer?]) flat-contract?]{
+@defproc[(string-len/c [len exact-nonnegative-integer?]) flat-contract?]{
 
 Returns a flat contract that recognizes strings that have fewer than
 @scheme[len] characters.}
diff --git a/collects/scribblings/reference/custodians.scrbl b/collects/scribblings/reference/custodians.scrbl
index a5e784c5dd..459e5bb270 100644
--- a/collects/scribblings/reference/custodians.scrbl
+++ b/collects/scribblings/reference/custodians.scrbl
@@ -56,7 +56,7 @@ which is the main variant of PLT Scheme, and not normally available in
 PLT Scheme CGC.}}
 
 @defproc[(custodian-require-memory [limit-cust custodian?]
-                                   [need-amt nonnegative-exact-integer?]
+                                   [need-amt exact-nonnegative-integer?]
                                    [stop-cust custodian?]) void?]{
 
 Registers a require check if PLT Scheme is compiled with support for
@@ -69,7 +69,7 @@ garbage collection (see @secref["gc-model"]) where allocating
 tigger some shutdown, then @scheme[stop-cust] is shut down.}
 
 @defproc[(custodian-limit-memory [limit-cust custodian?]
-                                 [limit-amt nonnegative-exact-integer?]
+                                 [limit-amt exact-nonnegative-integer?]
                                  [stop-cust custodian? limit-cust]) void?]{
 
 Registers a limit check if PLT Scheme is compiled with support for
diff --git a/collects/scribblings/reference/custom-ports.scrbl b/collects/scribblings/reference/custom-ports.scrbl
index 11a0e79d04..af57077794 100644
--- a/collects/scribblings/reference/custom-ports.scrbl
+++ b/collects/scribblings/reference/custom-ports.scrbl
@@ -11,31 +11,31 @@ written.
 
 @defproc[(make-input-port [name any/c]
                           [read-in (bytes? 
-                                    . -> . (one-of/c nonnegative-exact-integer?
+                                    . -> . (one-of/c exact-nonnegative-integer?
                                                      eof-object?
                                                      procedure?
                                                      evt?))]
-                          [peek (bytes? nonnegative-exact-integer? (or/c evt? false/c)
-                                        . -> . (one-of/c nonnegative-exact-integer?
+                          [peek (bytes? exact-nonnegative-integer? (or/c evt? false/c)
+                                        . -> . (one-of/c exact-nonnegative-integer?
                                                          eof-object?
                                                          procedure?
                                                          evt?
                                                          false/c))]
                           [close (-> any)]
                           [get-progress-evt (or/c (-> evt?) false/c) #f]
-                          [commit (or/c (positive-exact-integer? evt? evt? . -> . any)
+                          [commit (or/c (exact-positive-integer? evt? evt? . -> . any)
                                         false/c) 
                                   #f]
                           [get-location (or/c 
                                          (() 
                                           . ->* . 
-                                          ((or/c positive-exact-integer? false/c)
-                                           (or/c nonnegative-exact-integer? false/c)
-                                           (or/c positive-exact-integer? false/c)))
+                                          ((or/c exact-positive-integer? false/c)
+                                           (or/c exact-nonnegative-integer? false/c)
+                                           (or/c exact-positive-integer? false/c)))
                                          false/c)
                                         #f]
                           [count-lines! (-> any) void]
-                          [init-position positive-exact-integer? 1]
+                          [init-position exact-positive-integer? 1]
                           [buffer-mode (or/c (case-> ((one-of/c 'block 'none) . -> . any)
                                                      (-> (one-of/c 'block 'none #f)))
                                              false/c)
@@ -653,12 +653,12 @@ s
 
 @defproc[(make-output-port [name any/c]
                            [evt evt?]
-                           [write-out (bytes? nonnegative-exact-integer?
-                                              nonnegative-exact-integer?
+                           [write-out (bytes? exact-nonnegative-integer?
+                                              exact-nonnegative-integer?
                                               boolean?
                                               boolean?
                                               . -> .
-                                              (or/c nonnegative-exact-integer?
+                                              (or/c exact-nonnegative-integer?
                                                     false/c
                                                     evt?))]
                            [close (-> any)]
@@ -670,8 +670,8 @@ s
                                                     false/c)
                                               #f]
                            [get-write-evt (or/c
-                                           (bytes? nonnegative-exact-integer?
-                                                   nonnegative-exact-integer?
+                                           (bytes? exact-nonnegative-integer?
+                                                   exact-nonnegative-integer?
                                                    . -> .
                                                    evt?)
                                            false/c)
@@ -683,13 +683,13 @@ s
                            [get-location (or/c 
                                           (() 
                                            . ->* . 
-                                           ((or/c positive-exact-integer? false/c)
-                                            (or/c nonnegative-exact-integer? false/c)
-                                            (or/c positive-exact-integer? false/c)))
+                                           ((or/c exact-positive-integer? false/c)
+                                            (or/c exact-nonnegative-integer? false/c)
+                                            (or/c exact-positive-integer? false/c)))
                                           false/c)
                                          #f]
                            [count-lines! (-> any) void]
-                           [init-position positive-exact-integer? 1]
+                           [init-position exact-positive-integer? 1]
                            [buffer-mode (or/c (case-> 
                                                ((one-of/c 'block 'line 'none) . -> . any)
                                                (-> (one-of/c 'block 'line 'none #f)))
diff --git a/collects/scribblings/reference/dicts.scrbl b/collects/scribblings/reference/dicts.scrbl
index 8f363c9132..2994010ad8 100644
--- a/collects/scribblings/reference/dicts.scrbl
+++ b/collects/scribblings/reference/dicts.scrbl
@@ -233,7 +233,7 @@ side-effects of @scheme[proc]) in an unspecified order. The procedure
 
 
 @defproc[(dict-count [dict dict?])
-         nonnegative-exact-integer?]{
+         exact-nonnegative-integer?]{
 
 Returns the number of keys mapped by @scheme[dict], usually in
 constant time.
diff --git a/collects/scribblings/reference/exns.scrbl b/collects/scribblings/reference/exns.scrbl
index 6f6f575a86..7ddf0f2265 100644
--- a/collects/scribblings/reference/exns.scrbl
+++ b/collects/scribblings/reference/exns.scrbl
@@ -87,7 +87,7 @@ for end users.}
 
 
 @defproc*[([(raise-type-error [name symbol?][expected string?][v any/c]) any]
-           [(raise-type-error [name symbol?][expected string?][bad-pos nonnegative-exact-integer?][v any/c]) any])]{
+           [(raise-type-error [name symbol?][expected string?][bad-pos exact-nonnegative-integer?][v any/c]) any])]{
 
 Creates an @scheme[exn:fail:contract] value and @scheme[raise]s it as
 an exception.  The @scheme[name] argument is used as the source
@@ -331,7 +331,7 @@ A parameter whose value is used as the maximum number of characters
 used to print a Scheme value that is embedded in a primitive error
 message.}
 
-@defparam[error-print-context-length cnt nonnegative-exact-integer?]{
+@defparam[error-print-context-length cnt exact-nonnegative-integer?]{
 
 A parameter whose value is used by the default error display handler
 as the maximum number of lines of context (or ``stack trace'') to
@@ -339,7 +339,7 @@ print; a single ``...'' line is printed if more lines are available
 after the first @scheme[cnt] lines. A @scheme[0] value for
 @scheme[cnt] disables context printing entirely.}
 
-@defparam[error-value->string-handler proc (any/c nonnegative-exact-integer?
+@defparam[error-value->string-handler proc (any/c exact-nonnegative-integer?
                                                   . -> .
                                                   string?)]{
 
@@ -526,10 +526,10 @@ Returns the @scheme[srcloc]-getting procedure associated with @scheme[v].}
 
 
 @defstruct[srcloc ([source any/c]
-                   [line (or/c positive-exact-integer? false/c)]
-                   [column (or/c nonnegative-exact-integer? false/c)]
-                   [position (or/c positive-exact-integer? false/c)]
-                   [span (or/c nonnegative-exact-integer? false/c)])
+                   [line (or/c exact-positive-integer? false/c)]
+                   [column (or/c exact-nonnegative-integer? false/c)]
+                   [position (or/c exact-positive-integer? false/c)]
+                   [span (or/c exact-nonnegative-integer? false/c)])
                   #:inspector #f]{
 
 The fields of an @scheme[srcloc] instance are as follows:
diff --git a/collects/scribblings/reference/filesystem.scrbl b/collects/scribblings/reference/filesystem.scrbl
index b927f200f5..476ef5c222 100644
--- a/collects/scribblings/reference/filesystem.scrbl
+++ b/collects/scribblings/reference/filesystem.scrbl
@@ -283,7 +283,7 @@ given file or directory path. On error (e.g., if no such file exists),
 the @exnraise[exn:fail:filesystem]. Under @|AllUnix|, permissions are
 checked for the current effective user instead of the real user.}
 
-@defproc[(file-size [path path-string?]) nonnegative-exact-integer?]{
+@defproc[(file-size [path path-string?]) exact-nonnegative-integer?]{
 
 Returns the (logical) size of the specified file in bytes. Under Mac
 OS X, this size excludes the resource-fork size. On error (e.g., if no
diff --git a/collects/scribblings/reference/hashes.scrbl b/collects/scribblings/reference/hashes.scrbl
index 0fd61a423e..b8604c48b7 100644
--- a/collects/scribblings/reference/hashes.scrbl
+++ b/collects/scribblings/reference/hashes.scrbl
@@ -193,7 +193,7 @@ caveat above about concurrent modification.}
 
 
 @defproc[(hash-count [hash hash?])
-         nonnegative-exact-integer?]{
+         exact-nonnegative-integer?]{
 
 Returns the number of keys mapped by @scheme[hash]. If
 @scheme[hash] is not created with @scheme['weak], then the
@@ -203,7 +203,7 @@ above about concurrent modification.}
 
 
 @defproc[(hash-iterate-first [hash hash?])
-         (or/c false/c nonnegative-exact-integer?)]{
+         (or/c false/c exact-nonnegative-integer?)]{
 
 Returns @scheme[#f] if @scheme[hash] contains no elements, otherwise
 it returns an integer that is a index to the first element in the hash
@@ -214,8 +214,8 @@ refer to the first item only as long as no items are added to or
 removed from @scheme[hash].}
 
 @defproc[(hash-iterate-next [hash hash?]
-                            [pos nonnegative-exact-integer?])
-         (or/c false/c nonnegative-exact-integer?)]{
+                            [pos exact-nonnegative-integer?])
+         (or/c false/c exact-nonnegative-integer?)]{
 
 Returns either an integer that is an index to the element in
 @scheme[hash] after the element indexed by @scheme[pos] (which is not
@@ -227,7 +227,7 @@ only as long as no items are added to or removed from @scheme[hash].}
 
 
 @defproc[(hash-iterate-key [hash hash?]
-                           [pos nonnegative-exact-integer?])
+                           [pos exact-nonnegative-integer?])
          any]{
 
 Returns the key for the element in @scheme[hash] at index
@@ -236,7 +236,7 @@ Returns the key for the element in @scheme[hash] at index
 
 
 @defproc[(hash-iterate-value [hash hash?]
-                             [pos nonnegative-exact-integer?])
+                             [pos exact-nonnegative-integer?])
          any]{
 
 Returns the value for the element in @scheme[hash] at index
diff --git a/collects/scribblings/reference/memory.scrbl b/collects/scribblings/reference/memory.scrbl
index 926ee31efc..a5734e3e2e 100644
--- a/collects/scribblings/reference/memory.scrbl
+++ b/collects/scribblings/reference/memory.scrbl
@@ -167,7 +167,7 @@ The @scheme[collect-garbage] procedure provides some control over the
 timing of collections, but garbage will obviously be collected even if
 this procedure is never called.}
 
-@defproc[(current-memory-use [cust custodian? #f]) nonnegative-exact-integer?]{
+@defproc[(current-memory-use [cust custodian? #f]) exact-nonnegative-integer?]{
 
 Returns an estimate of the number of bytes of memory occupied by
 reachable data from @scheme[cust]. (The estimate is calculated
diff --git a/collects/scribblings/reference/mpairs.scrbl b/collects/scribblings/reference/mpairs.scrbl
index 0676fa0f71..e4fdc62e2c 100644
--- a/collects/scribblings/reference/mpairs.scrbl
+++ b/collects/scribblings/reference/mpairs.scrbl
@@ -73,18 +73,18 @@ Returns a newly allocated list with the same elements as
 
 
 @defproc[(mlength [mlst mlist?])
-         nonnegative-exact-integer?]{
+         exact-nonnegative-integer?]{
 
 Returns the number of elements in @scheme[mlst].}
 
 
-@defproc[(mlist-ref [mlst mlist?][pos nonnegative-exact-integer?])
+@defproc[(mlist-ref [mlst mlist?][pos exact-nonnegative-integer?])
          any/c]{
 
 Like @scheme[list-ref], but for @tech{mutable lists}.}
 
 
-@defproc[(mlist-tail [mlst mlist?][pos nonnegative-exact-integer?])
+@defproc[(mlist-tail [mlst mlist?][pos exact-nonnegative-integer?])
          any/c]{
 
 Like @scheme[list-tail], but for @tech{mutable lists}.}
diff --git a/collects/scribblings/reference/networking.scrbl b/collects/scribblings/reference/networking.scrbl
index 05377e9953..babc6af9f6 100644
--- a/collects/scribblings/reference/networking.scrbl
+++ b/collects/scribblings/reference/networking.scrbl
@@ -13,9 +13,9 @@
 For information about TCP in general, see @italic{TCP/IP Illustrated,
  Volume 1} by W. Richard Stevens.
 
-@defproc[(tcp-listen [port-no (and/c nonnegative-exact-integer?
+@defproc[(tcp-listen [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
-                     [max-allow-wait nonnegative-exact-integer? 4]
+                     [max-allow-wait exact-nonnegative-integer? 4]
                      [reuse? any/c #f]
                      [hostname (or/c string? false/c) #f]) 
          tcp-listener?]
@@ -62,10 +62,10 @@ If the server cannot be started by @scheme[tcp-listen], the
 
 
 @defproc[(tcp-connect [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
                       [local-hostname (or/c string? false/c) #f]
-                      [local-port-no (or/c (and/c nonnegative-exact-integer?
+                      [local-port-no (or/c (and/c exact-nonnegative-integer?
                                                   (integer-in 1 65535))
                                            false/c)
                                      #f])
@@ -119,10 +119,10 @@ If a connection cannot be established by @scheme[tcp-connect], the
 @exnraise[exn:fail:network].}
 
 @defproc[(tcp-connect/enable-break [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                      (integer-in 1 65535))]
                       [local-hostname (or/c string? false/c) #f]
-                      [local-port-no (or/c (and/c nonnegative-exact-integer?
+                      [local-port-no (or/c (and/c exact-nonnegative-integer?
                                                   (integer-in 1 65535))
                                            false/c)])
           (values input-port? output-port?)]{
@@ -283,7 +283,7 @@ non-@scheme[#f], then the socket's protocol family is IPv4.}
 
 @defproc[(udp-bind! [udp-socket udp?]
                     [hostname-string (or/c string? false/c)]
-                    [port-no (and/c nonnegative-exact-integer?
+                    [port-no (and/c exact-nonnegative-integer?
                                     (integer-in 1 65535))])
          void?]{
 
@@ -319,7 +319,7 @@ If @scheme[udp-socket] is already bound or closed, the
 
 @defproc[(udp-connect! [udp-socket udp?]
                        [hostname-string (or/c string? false/c)]
-                       [port-no (or/c (and/c nonnegative-exact-integer?
+                       [port-no (or/c (and/c exact-nonnegative-integer?
                                              (integer-in 1 65535))
                                       false/c)])
          void?]{
@@ -344,11 +344,11 @@ If @scheme[udp-socket] is closed, the @exnraise[exn:fail:network].}
 
 @defproc[(udp-send-to [udp-socket udp?]
                       [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                       (integer-in 1 65535))]
                       [bstr bytes?]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          void]{
 
 Sends @scheme[(subbytes bytes start-pos end-pos)] as a datagram from
@@ -368,8 +368,8 @@ If @scheme[udp-socket] is closed or connected, the
 
 @defproc[(udp-send [udp-socket udp?]
                    [bstr bytes?]
-                   [start-pos nonnegative-exact-integer? 0]
-                   [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                   [start-pos exact-nonnegative-integer? 0]
+                   [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          void]{
 
 Like @scheme[udp-send-to], except that @scheme[udp-socket] must be
@@ -379,11 +379,11 @@ connected, and the datagram goes to the connection target.  If
 
 @defproc[(udp-send-to* [udp-socket udp?]
                        [hostname string?]
-                       [port-no (and/c nonnegative-exact-integer?
+                       [port-no (and/c exact-nonnegative-integer?
                                        (integer-in 1 65535))]
                        [bstr bytes?]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          boolean?]{
 
 Like @scheme[udp-send-to], but never blocks; if the socket's outgoing
@@ -392,8 +392,8 @@ otherwise the datagram is queued and the result is @scheme[#t].}
 
 @defproc[(udp-send* [udp-socket udp?]
                     [bstr bytes?]
-                    [start-pos nonnegative-exact-integer? 0]
-                    [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                    [start-pos exact-nonnegative-integer? 0]
+                    [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          boolean?]{
 
 Like @scheme[udp-send], except that (like @scheme[udp-send-to]) it
@@ -401,11 +401,11 @@ never blocks and returns @scheme[#f] or @scheme[#t].}
 
 @defproc[(udp-send-to/enable-break [udp-socket udp?]
                       [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                       (integer-in 1 65535))]
                       [bstr bytes?]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          void]{
 
 Like @scheme[udp-send-to], but breaking is enabled (see
@@ -417,8 +417,8 @@ is raised, but not both.}
 
 @defproc[(udp-send/enable-break [udp-socket udp?]
                    [bstr bytes?]
-                   [start-pos nonnegative-exact-integer? 0]
-                   [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                   [start-pos exact-nonnegative-integer? 0]
+                   [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          void]{
 
 Like @scheme[udp-send], except that breaks are enabled like
@@ -427,9 +427,9 @@ Like @scheme[udp-send], except that breaks are enabled like
 
 @defproc[(udp-receive! [udp-socket udp?]
                        [bstr (and/c bytes? (not immutable?))]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (values nonnegative-exact-integer?
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (values exact-nonnegative-integer?
                  string?
                  (integer-in 1 65535))]{
 
@@ -454,9 +454,9 @@ the length of @scheme[bstr], the @exnraise[exn:fail:contract].}
 
 @defproc[(udp-receive!* [udp-socket udp?]
                        [bstr (and/c bytes? (not immutable?))]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (values (or/c nonnegative-exact-integer? false/c)
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (values (or/c exact-nonnegative-integer? false/c)
                  (or/c string? false/c)
                  (or/c (integer-in 1 65535) false/c))]{
 
@@ -465,9 +465,9 @@ datagram is available, the three result values are all @scheme[#f].}
 
 @defproc[(udp-receive!/enable-break [udp-socket udp?]
                        [bstr (and/c bytes? (not immutable?))]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (values nonnegative-exact-integer?
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (values exact-nonnegative-integer?
                  string?
                  (integer-in 1 65535))]{
 
@@ -517,11 +517,11 @@ would block.}
 
 @defproc[(udp-send-to-evt [udp-socket udp?]
                       [hostname string?]
-                      [port-no (and/c nonnegative-exact-integer?
+                      [port-no (and/c exact-nonnegative-integer?
                                       (integer-in 1 65535))]
                       [bstr bytes?]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          evt?]{
 
 Returns a @tech{synchronizable event}. The event is in a blocking
@@ -534,8 +534,8 @@ bstr start-pos end-pos)], and the synchronization result is
 
 @defproc[(udp-send-evt [udp-socket udp?]
                       [bstr bytes?]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          evt?]{
 
 Returns a @tech{synchronizable event}. The event is in a blocking
@@ -549,8 +549,8 @@ attempt.}
 
 @defproc[(udp-receive!-evt [udp-socket udp?]
                        [bstr (and/c bytes? (not immutable?))]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (bytes-length bstr)])
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (bytes-length bstr)])
          evt?]{
 
 Returns a @tech{synchronizable event}. The event is in a blocking
diff --git a/collects/scribblings/reference/numbers.scrbl b/collects/scribblings/reference/numbers.scrbl
index 67844e97f5..e75e30d77e 100644
--- a/collects/scribblings/reference/numbers.scrbl
+++ b/collects/scribblings/reference/numbers.scrbl
@@ -593,7 +593,7 @@ produces @scheme[+nan.0] in the case that neither @scheme[y] nor
 @defproc*[([(random [k (integer-in 1 4294967087)]
                     [generator pseudo-random-generator?
                                (current-pseudo-random-generator)])
-            nonnegative-exact-integer?]
+            exact-nonnegative-integer?]
            [(random [generator pseudo-random-generator?
                                (current-pseudo-random-generator)]) 
             (and/c real? inexact? (>/c 0) (</c 1))])]{  
@@ -700,7 +700,7 @@ which can be overriden by @litchar{#b}, @litchar{#o}, @litchar{#d}, or
           (string->number "111" 7)  (string->number "#b111" 7)]
 }
 
-@defproc[(real->decimal-string [n real?] [decimal-digits nonnegative-exact-integer? 2])
+@defproc[(real->decimal-string [n real?] [decimal-digits exact-nonnegative-integer? 2])
          string?]{
 
 Prints @scheme[n] into a string and returns the string. The printed
diff --git a/collects/scribblings/reference/pairs.scrbl b/collects/scribblings/reference/pairs.scrbl
index bfa8143e4a..900f7c306d 100644
--- a/collects/scribblings/reference/pairs.scrbl
+++ b/collects/scribblings/reference/pairs.scrbl
@@ -117,12 +117,12 @@ is the value produced by @scheme[(proc _i)].
 @section{List Operations}
 
 @defproc[(length [lst list?])
-         nonnegative-exact-integer?]{
+         exact-nonnegative-integer?]{
 
 Returns the number of elements in @scheme[lst].}
 
 
-@defproc[(list-ref [lst any/c] [pos nonnegative-exact-integer?])
+@defproc[(list-ref [lst any/c] [pos exact-nonnegative-integer?])
          any/c]{
 
 Returns the element of @scheme[lst] at position @scheme[pos], where
@@ -134,7 +134,7 @@ The @scheme[lst] argument need not actually be a list; @scheme[lst]
 must merely start with a chain of at least @scheme[pos] pairs.}
 
 
-@defproc[(list-tail [lst any/c] [pos nonnegative-exact-integer?])
+@defproc[(list-tail [lst any/c] [pos exact-nonnegative-integer?])
          any/c]{
 
 Returns the list after the first @scheme[pos] elements of
@@ -515,7 +515,7 @@ Like @scheme[assoc], but finds an element using the predicate
 @defproc[(last-pair [p pair?]) pair?]{
 Returns the last pair of a (possibly improper) list.}
 
-@defproc[(take [lst any/c] [pos nonnegative-exact-integer?]) list?]{
+@defproc[(take [lst any/c] [pos exact-nonnegative-integer?]) list?]{
 Returns a fresh list whose elements are the first @scheme[pos] elements of
 @scheme[lst].  If @scheme[lst] has fewer than
 @scheme[pos] elements, the @exnraise[exn:fail:contract].
@@ -528,10 +528,10 @@ must merely start with a chain of at least @scheme[pos] pairs.
  (take 'non-list 0)
 ]}
 
-@defproc[(drop [lst any/c] [pos nonnegative-exact-integer?]) any/c]{
+@defproc[(drop [lst any/c] [pos exact-nonnegative-integer?]) any/c]{
 Just like @scheme[list-tail].}
 
-@defproc[(split-at [lst any/c] [pos nonnegative-exact-integer?])
+@defproc[(split-at [lst any/c] [pos exact-nonnegative-integer?])
          (values list? any/c)]{
 Returns the same result as
 
@@ -539,7 +539,7 @@ Returns the same result as
 
 except that it can be faster.}
 
-@defproc[(take-right [lst any/c] [pos nonnegative-exact-integer?]) any/c]{
+@defproc[(take-right [lst any/c] [pos exact-nonnegative-integer?]) any/c]{
 Returns the @scheme[list]'s @scheme[pos]-length tail. If @scheme[lst]
 has fewer than @scheme[pos] elements, then the
 @exnraise[exn:fail:contract].
@@ -552,7 +552,7 @@ must merely end with a chain of at least @scheme[pos] pairs.
  (take-right 'non-list 0)
 ]}
 
-@defproc[(drop-right [lst any/c] [pos nonnegative-exact-integer?]) list?]{
+@defproc[(drop-right [lst any/c] [pos exact-nonnegative-integer?]) list?]{
 Returns a fresh list whose elements are the prefix of @scheme[lst],
 dropping its @scheme[pos]-length tail. If @scheme[lst] has fewer than
 @scheme[pos] elements, then the @exnraise[exn:fail:contract].
@@ -565,7 +565,7 @@ must merely end with a chain of at least @scheme[pos] pairs.
  (drop-right 'non-list 0)
 ]}
 
-@defproc[(split-at-right [lst any/c] [pos nonnegative-exact-integer?])
+@defproc[(split-at-right [lst any/c] [pos exact-nonnegative-integer?])
          (values list? any/c)]{
 Returns the same result as
 
diff --git a/collects/scribblings/reference/pipes.scrbl b/collects/scribblings/reference/pipes.scrbl
index 6c9ae25802..c51b8366d9 100644
--- a/collects/scribblings/reference/pipes.scrbl
+++ b/collects/scribblings/reference/pipes.scrbl
@@ -7,7 +7,7 @@ A Scheme @deftech{pipe} is internal to Scheme, and not related to
 OS-level pipes (which are @tech{file-stream ports}) for communicating
 between different processes.
 
-@defproc[(make-pipe [limit positive-exact-integer? #f]
+@defproc[(make-pipe [limit exact-positive-integer? #f]
                     [input-name any/c 'pipe]
                     [output-name any/c 'pipe])
          (values input-port? output-port?)]{
diff --git a/collects/scribblings/reference/port-buffers.scrbl b/collects/scribblings/reference/port-buffers.scrbl
index 7671f6ad7b..9b5e4b180e 100644
--- a/collects/scribblings/reference/port-buffers.scrbl
+++ b/collects/scribblings/reference/port-buffers.scrbl
@@ -76,8 +76,8 @@ If @scheme[mode] is not provided, the current mode is returned, or
 @scheme[file-stream-port] is an input port and @scheme[mode] is
 @scheme['line], the @exnraise[exn:fail:contract].}
 
-@defproc*[([(file-position [port port?]) nonnegative-exact-integer?]
-           [(file-position [port port?] [pos (or/c nonnegative-exact-integer? eof-object?)]) void?])]{
+@defproc*[([(file-position [port port?]) exact-nonnegative-integer?]
+           [(file-position [port port?] [pos (or/c exact-nonnegative-integer? eof-object?)]) void?])]{
 
 Returns or sets the current read/write position of @scheme[port]. 
 
diff --git a/collects/scribblings/reference/port-lib.scrbl b/collects/scribblings/reference/port-lib.scrbl
index 9f07689efd..a89d5dd192 100644
--- a/collects/scribblings/reference/port-lib.scrbl
+++ b/collects/scribblings/reference/port-lib.scrbl
@@ -48,13 +48,13 @@ input ports as it becomes available.}
           [get-location (or/c 
                          (->
                           (values
-                           (or/c positive-exact-integer? false/c)
-                           (or/c nonnegative-exact-integer? false/c)
-                           (or/c positive-exact-integer? false/c)))
+                           (or/c exact-positive-integer? false/c)
+                           (or/c exact-nonnegative-integer? false/c)
+                           (or/c exact-positive-integer? false/c)))
                          false/c)
                         #f]
           [count-lines! (-> any) void]
-          [init-position positive-exact-integer? 1]
+          [init-position exact-positive-integer? 1]
           [buffer-mode (or/c (case-> ((one-of/c 'block 'none) . -> . any)
                                      (-> (one-of/c 'block 'none #f)))
                              false/c)
diff --git a/collects/scribblings/reference/port-line-counting.scrbl b/collects/scribblings/reference/port-line-counting.scrbl
index b4de6e062e..85e713fcca 100644
--- a/collects/scribblings/reference/port-line-counting.scrbl
+++ b/collects/scribblings/reference/port-line-counting.scrbl
@@ -50,9 +50,9 @@ counting is automatically enabled for the port. Line counting cannot
 be disabled for a port after it is enabled.}
 
 @defproc[(port-next-location [port port?]) 
-         (values (or/c positive-exact-integer? false/c)
-                 (or/c nonnegative-exact-integer? false/c)
-                 (or/c positive-exact-integer? false/c))]{
+         (values (or/c exact-positive-integer? false/c)
+                 (or/c exact-nonnegative-integer? false/c)
+                 (or/c exact-positive-integer? false/c))]{
 
 Returns three values: an integer or @scheme[#f] for the line number of
 the next read/written item, an integer or @scheme[#f] for the next
diff --git a/collects/scribblings/reference/procedures.scrbl b/collects/scribblings/reference/procedures.scrbl
index 168ca303b5..9fdefe436b 100644
--- a/collects/scribblings/reference/procedures.scrbl
+++ b/collects/scribblings/reference/procedures.scrbl
@@ -226,7 +226,7 @@ must require no more keywords than the ones listed din
 (show #:init 0 1 2 3 #:extra 4 #:more 7)
 ]}
 
-@defstruct[arity-at-least ([value nonnegative-exact-integer?])]{
+@defstruct[arity-at-least ([value exact-nonnegative-integer?])]{
 
 This structure type is used for the result of @scheme[procedure-arity].
 See also @scheme[procedure-arity?].}
diff --git a/collects/scribblings/reference/regexps.scrbl b/collects/scribblings/reference/regexps.scrbl
index d9553444d1..a2f2148ef4 100644
--- a/collects/scribblings/reference/regexps.scrbl
+++ b/collects/scribblings/reference/regexps.scrbl
@@ -203,8 +203,8 @@ case-sensitively.
 
 @defproc[(regexp-match [pattern (or/c string? bytes? regexp? byte-regexp?)]
                        [input (or/c string? bytes? input-port?)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                        [output-port (or/c output-port? false/c) #f])
          (or/c (listof (or/c (cons (or/c string? bytes?)
                                    (or/c string? bytes?))
@@ -303,8 +303,8 @@ bytes. To avoid such interleaving, use @scheme[regexp-match-peek]
 
 @defproc[(regexp-match* [pattern (or/c string? bytes? regexp? byte-regexp?)]
                         [input (or/c string? bytes? input-port?)]
-                        [start-pos nonnegative-exact-integer? 0]
-                        [end-pos (or/c nonnegative-exact-integer? false/c) #f])
+                        [start-pos exact-nonnegative-integer? 0]
+                        [end-pos (or/c exact-nonnegative-integer? false/c) #f])
          (listof (or/c string? bytes?))]{
 
 Like @scheme[regexp-match], but the result is a list of strings or
@@ -334,8 +334,8 @@ port).
 @defproc[(regexp-try-match
                        [pattern (or/c string? bytes? regexp? byte-regexp?)]
                        [input input-port?]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                        [output-port (or/c output-port? false/c) #f])
          (or/c (listof (or/c (cons (or/c string? bytes?)
                                    (or/c string? bytes?))
@@ -355,11 +355,11 @@ fails.}
 
 @defproc[(regexp-match-positions [pattern (or/c string? bytes? regexp? byte-regexp?)]
                         [input (or/c string? bytes? input-port?)]
-                        [start-pos nonnegative-exact-integer? 0]
-                        [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                        [start-pos exact-nonnegative-integer? 0]
+                        [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                         [output-port (or/c output-port? false/c) #f])
-          (or/c (listof (or/c (cons nonnegative-exact-integer?
-                                    nonnegative-exact-integer?)
+          (or/c (listof (or/c (cons exact-nonnegative-integer?
+                                    exact-nonnegative-integer?)
                               false/c))
                 false/c)]{
 
@@ -386,10 +386,10 @@ positions indicate the number of bytes that were read, including
 
 @defproc[(regexp-match-positions* [pattern (or/c string? bytes? regexp? byte-regexp?)]
                         [input (or/c string? bytes? input-port?)]
-                        [start-pos nonnegative-exact-integer? 0]
-                        [end-pos (or/c nonnegative-exact-integer? false/c) #f])
-         (listof (cons nonnegative-exact-integer?
-                       nonnegative-exact-integer?))]{
+                        [start-pos exact-nonnegative-integer? 0]
+                        [end-pos (or/c exact-nonnegative-integer? false/c) #f])
+         (listof (cons exact-nonnegative-integer?
+                       exact-nonnegative-integer?))]{
 
 Like @scheme[regexp-match-positions], but returns multiple matches
 like @scheme[regexp-match*].
@@ -401,8 +401,8 @@ like @scheme[regexp-match*].
 
 @defproc[(regexp-match? [pattern (or/c string? bytes? regexp? byte-regexp?)]
                         [input (or/c string? bytes? input-port?)]
-                        [start-pos nonnegative-exact-integer? 0]
-                        [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                        [start-pos exact-nonnegative-integer? 0]
+                        [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                         [output-port (or/c output-port? false/c) #f])
            boolean?]{
 
@@ -430,8 +430,8 @@ entire content of @scheme[input] matches @scheme[pattern].
 
 @defproc[(regexp-match-peek [pattern (or/c string? bytes? regexp? byte-regexp?)]
                             [input input-port?]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                             [progress (or/c evt false/c) #f])
           (or/c (listof (or/c (cons bytes? bytes?)
                               false/c))
@@ -460,11 +460,11 @@ information if another process meanwhile reads from
 
 @defproc[(regexp-match-peek-positions [pattern (or/c string? bytes? regexp? byte-regexp?)]
                             [input input-port?]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                             [progress (or/c evt false/c) #f])
-          (or/c (listof (or/c (cons nonnegative-exact-integer?
-                                    nonnegative-exact-integer?)
+          (or/c (listof (or/c (cons exact-nonnegative-integer?
+                                    exact-nonnegative-integer?)
                               false/c))
                 false/c)]{
 
@@ -475,8 +475,8 @@ bytes from @scheme[input-port] instead of reading them, and with a
 
 @defproc[(regexp-match-peek-immediate [pattern (or/c string? bytes? regexp? byte-regexp?)]
                             [input input-port?]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                             [progress (or/c evt false/c) #f])
           (or/c (listof (or/c (cons bytes? bytes?)
                               false/c))
@@ -490,11 +490,11 @@ match fails if not-yet-available characters might be used to match
 
 @defproc[(regexp-match-peek-positions-immediate [pattern (or/c string? bytes? regexp? byte-regexp?)]
                             [input input-port?]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos (or/c nonnegative-exact-integer? false/c) #f]
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos (or/c exact-nonnegative-integer? false/c) #f]
                             [progress (or/c evt false/c) #f])
-          (or/c (listof (or/c (cons nonnegative-exact-integer?
-                                    nonnegative-exact-integer?)
+          (or/c (listof (or/c (cons exact-nonnegative-integer?
+                                    exact-nonnegative-integer?)
                               false/c))
                 false/c)]{
 
@@ -506,10 +506,10 @@ used to match @scheme[pattern].}
 
 @defproc[(regexp-match-peek-positions* [pattern (or/c string? bytes? regexp? byte-regexp?)]
                             [input input-port?]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos (or/c nonnegative-exact-integer? false/c) #f])
-         (listof (cons nonnegative-exact-integer?
-                       nonnegative-exact-integer?))]{
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos (or/c exact-nonnegative-integer? false/c) #f])
+         (listof (cons exact-nonnegative-integer?
+                       exact-nonnegative-integer?))]{
 
 Like @scheme[regexp-match-peek-positions], but returns multiple matches like
 @scheme[regexp-match*].}
@@ -519,8 +519,8 @@ Like @scheme[regexp-match-peek-positions], but returns multiple matches like
 
 @defproc[(regexp-split [pattern (or/c string? bytes? regexp? byte-regexp?)]
                        [input (or/c string? bytes? input-port?)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos (or/c nonnegative-exact-integer? false/c) #f])
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos (or/c exact-nonnegative-integer? false/c) #f])
          (listof (or/c string? bytes?))]{
 
 The complement of @scheme[regexp-match*]: the result is a list of
diff --git a/collects/scribblings/reference/semaphores.scrbl b/collects/scribblings/reference/semaphores.scrbl
index 24ef6bc775..17e62d3d46 100644
--- a/collects/scribblings/reference/semaphores.scrbl
+++ b/collects/scribblings/reference/semaphores.scrbl
@@ -19,7 +19,7 @@ thread is eventually unblocked.
 In addition to its use with semaphore-specific procedures, semaphores
 can be used as events; see @secref["sync"].
 
-@defproc[(make-semaphore [init nonnegative-exact-integer? 0]) semaphore?]{
+@defproc[(make-semaphore [init exact-nonnegative-integer? 0]) semaphore?]{
 
 Creates and returns a new semaphore with the counter initially set to
 @scheme[init]. If @scheme[init-k] is larger than a semaphore's maximum
diff --git a/collects/scribblings/reference/string-input.scrbl b/collects/scribblings/reference/string-input.scrbl
index 21bf93413a..0fc648e27a 100644
--- a/collects/scribblings/reference/string-input.scrbl
+++ b/collects/scribblings/reference/string-input.scrbl
@@ -70,7 +70,7 @@ is opened in text mode, @scheme['linefeed] is usually the appropriate
          (or/c bytes? eof-object?)]{
 Like @scheme[read-line], but reads bytes and produces a byte string.}
 
-@defproc[(read-string [amt nonnegative-exact-integer?]
+@defproc[(read-string [amt exact-nonnegative-integer?]
                       [in input-port? (current-input-port)])
          (or/c string? eof-object)]{
 
@@ -91,16 +91,16 @@ If an error occurs during reading, some characters may be lost; that
 is, if @scheme[read-string] successfully reads some characters before
 encountering an error, the characters are dropped.}
 
-@defproc[(read-bytes [amt nonnegative-exact-integer?]
+@defproc[(read-bytes [amt exact-nonnegative-integer?]
                      [in input-port? (current-input-port)])
          (or/c bytes? eof-object)]{
 Like @scheme[read-string], but reads bytes and produces a byte string.}
 
 @defproc[(read-string! [str (and/c string? (not/c immutable?))]
                        [in input-port? (current-input-port)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (string-length str)])
-         (or/c positive-exact-integer? eof-object?)]{
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (string-length str)])
+         (or/c exact-positive-integer? eof-object?)]{
 
 Reads characters from @scheme[in] like @scheme[read-string], but puts
 them into @scheme[str] starting from index @scheme[start-pos]
@@ -120,17 +120,17 @@ not modified at indices @math{@scheme[start-pos]+m} though
 
 @defproc[(read-bytes! [bstr bytes?]
                       [in input-port? (current-input-port)]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c positive-exact-integer? eof-object?)]{
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-positive-integer? eof-object?)]{
 Like @scheme[read-string!], but reads bytes, puts them into a byte
 string, and returns the number of bytes read.}
 
 @defproc[(read-bytes-avail! [bstr bytes?]
                             [in input-port? (current-input-port)]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c positive-exact-integer? eof-object? procedure?)]{
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-positive-integer? eof-object? procedure?)]{
 
 Like @scheme[read-bytes!], but it returns without blocking after
 reading immediately-available bytes, and it may return a procedure for
@@ -156,9 +156,9 @@ as are available before a special value in the port's stream.}
 
 @defproc[(read-bytes-avail!* [bstr bytes?]
                              [in input-port? (current-input-port)]
-                             [start-pos nonnegative-exact-integer? 0]
-                             [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c nonnegative-exact-integer? eof-object? procedure?)]{
+                             [start-pos exact-nonnegative-integer? 0]
+                             [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-nonnegative-integer? eof-object? procedure?)]{
 
 Like @scheme[read-bytes-avail!], but returns @scheme[0] immediately if
 no bytes (or specials) are available for reading and the end-of-file
@@ -166,9 +166,9 @@ is not reached.}
 
 @defproc[(read-bytes-avail!/enable-break [bstr bytes?]
                                          [in input-port? (current-input-port)]
-                                         [start-pos nonnegative-exact-integer? 0]
-                                         [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c positive-exact-integer? eof-object? procedure?)]{
+                                         [start-pos exact-nonnegative-integer? 0]
+                                         [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-positive-integer? eof-object? procedure?)]{
 
 Like @scheme[read-bytes-avail!], but breaks are enabled during the
 read (see also @secref["breakhandler"]). If breaking is disabled
@@ -177,8 +177,8 @@ when @scheme[read-bytes-avail!/enable-break] is called, and if the
 no bytes will have been read from @scheme[in].}
 
 
-@defproc[(peek-string [amt nonnegative-exact-integer?]
-                      [skip-bytes-amt nonnegative-exact-integer?]
+@defproc[(peek-string [amt exact-nonnegative-integer?]
+                      [skip-bytes-amt exact-nonnegative-integer?]
                       [in input-port? (current-input-port)])
          (or/c string? eof-object)]{
 
@@ -204,37 +204,37 @@ If a port produces @scheme[eof] mid-stream, peek skips beyond the
 @scheme[eof] always produce @scheme[eof] until the @scheme[eof] is
 read.}
 
-@defproc[(peek-bytes [amt nonnegative-exact-integer?]
-                     [skip-bytes-amt nonnegative-exact-integer?]
+@defproc[(peek-bytes [amt exact-nonnegative-integer?]
+                     [skip-bytes-amt exact-nonnegative-integer?]
                      [in input-port? (current-input-port)])
          (or/c bytes? eof-object)]{
 Like @scheme[peek-string], but peeks bytes and produces a byte string.}
 
 @defproc[(peek-string! [str (and/c string? (not/c immutable?))]
-                       [skip-bytes-amt nonnegative-exact-integer?]
+                       [skip-bytes-amt exact-nonnegative-integer?]
                        [in input-port? (current-input-port)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (string-length str)])
-         (or/c positive-exact-integer? eof-object?)]{
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (string-length str)])
+         (or/c exact-positive-integer? eof-object?)]{
 Like @scheme[read-string!], but for peeking, and with a
 @scheme[skip-bytes-amt] argument like @scheme[peek-string].}
 
 @defproc[(peek-bytes! [bstr (and/c bytes? (not/c immutable?))]
-                      [skip-bytes-amt nonnegative-exact-integer?]
+                      [skip-bytes-amt exact-nonnegative-integer?]
                       [in input-port? (current-input-port)]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c positive-exact-integer? eof-object?)]{
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-positive-integer? eof-object?)]{
 Like @scheme[peek-string!], but peeks bytes, puts them into a byte
 string, and returns the number of bytes read.}
 
 @defproc[(peek-bytes-avail! [bstr (and/c bytes? (not/c immutable?))]
-                            [skip-bytes-amt nonnegative-exact-integer?]
+                            [skip-bytes-amt exact-nonnegative-integer?]
                             [progress (or/c evt? false/c) #f]
                             [in input-port? (current-input-port)]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c nonnegative-exact-integer? eof-object? procedure?)]{
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-nonnegative-integer? eof-object? procedure?)]{
 
 Like @scheme[read-bytes-avail!], but for peeking, and with two extra
 arguments. The @scheme[skip-bytes-amt] argument is as in
@@ -253,12 +253,12 @@ The result of @scheme[peek-bytes-avail!] is @scheme[0] only in the
 case that @scheme[progress] becomes ready before bytes are peeked.}
 
 @defproc[(peek-bytes-avail!* [bstr (and/c bytes? (not/c immutable?))]
-                             [skip-bytes-amt nonnegative-exact-integer?]
+                             [skip-bytes-amt exact-nonnegative-integer?]
                              [progress (or/c evt? false/c) #f]
                              [in input-port? (current-input-port)]
-                             [start-pos nonnegative-exact-integer? 0]
-                             [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c nonnegative-exact-integer? eof-object? procedure?)]{
+                             [start-pos exact-nonnegative-integer? 0]
+                             [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-nonnegative-integer? eof-object? procedure?)]{
 
 Like @scheme[read-bytes-avail!*], but for peeking, and with
 @scheme[skip-bytes-amt] and @scheme[progress] arguments like
@@ -267,12 +267,12 @@ return before even @scheme[skip-amt] bytes are available from the
 port.}
 
 @defproc[(peek-bytes-avail!/enable-break [bstr (and/c bytes? (not/c immutable?))]
-                                         [skip-bytes-amt nonnegative-exact-integer?]
+                                         [skip-bytes-amt exact-nonnegative-integer?]
                                          [progress (or/c evt? false/c) #f]
                                          [in input-port? (current-input-port)]
-                                         [start-pos nonnegative-exact-integer? 0]
-                                         [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c nonnegative-exact-integer? eof-object? procedure?)]{
+                                         [start-pos exact-nonnegative-integer? 0]
+                                         [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-nonnegative-integer? eof-object? procedure?)]{
 Like @scheme[read-bytes-avail!/enable-break], but for peeking, and
 with @scheme[skip-bytes-amt] and @scheme[progress] arguments like
 @scheme[peek-bytes-avail!].}
@@ -293,7 +293,7 @@ Like @scheme[read-char-or-special], but reads and returns a byte
 instead of a character.}
 
 @defproc[(peek-char [in input-port? (current-input-port)]
-                    [skip-bytes-amt nonnegative-exact-integer? 0])
+                    [skip-bytes-amt exact-nonnegative-integer? 0])
          (or/c character? eof-object?)]{
 
 Like @scheme[read-char], but peeks instead of reading, and skipping
@@ -301,21 +301,21 @@ Like @scheme[read-char], but peeks instead of reading, and skipping
 port.}
 
 @defproc[(peek-byte [in input-port? (current-input-port)]
-                    [skip-bytes-amt nonnegative-exact-integer? 0])
+                    [skip-bytes-amt exact-nonnegative-integer? 0])
          (or/c byte? eof-object?)]{
 
 Like @scheme[peek-char], but reads and returns a byte instead of a
 character.}
 
 @defproc[(peek-char-or-special [in input-port? (current-input-port)]
-                               [skip-bytes-amt nonnegative-exact-integer? 0])
+                               [skip-bytes-amt exact-nonnegative-integer? 0])
          (or/c character? eof-object? any/c)]{
 
 Like @scheme[peek-char], but if the input port returns a non-byte
 value after @scheme[skip-bytes-amt] byte positions, it is returned.}
 
 @defproc[(peek-byte-or-special [in input-port? (current-input-port)]
-                               [skip-bytes-amt nonnegative-exact-integer? 0]
+                               [skip-bytes-amt exact-nonnegative-integer? 0]
                                [progress (or/c evt? false/c) #f])
          (or/c character? eof-object? any/c)]{
 
@@ -339,7 +339,7 @@ for @scheme[in]. All built-in kinds of ports support progress events,
 but ports created with @scheme[make-input-port] (see
 @secref["customport"]) may not.}
  
-@defproc[(port-commit-peeked [amt nonnegative-exact-integer?]
+@defproc[(port-commit-peeked [amt exact-nonnegative-integer?]
                              [progress evt?]
                              [evt evt?]
                              [in input-port? (current-input-port)])
diff --git a/collects/scribblings/reference/string-output.scrbl b/collects/scribblings/reference/string-output.scrbl
index bd371d52d4..cd0b75af83 100644
--- a/collects/scribblings/reference/string-output.scrbl
+++ b/collects/scribblings/reference/string-output.scrbl
@@ -22,8 +22,8 @@ The same as @scheme[(write-char #\newline out)].}
 
 @defproc[(write-string [str string?]
                        [out output-port? (current-output-port)]
-                       [start-pos nonnegative-exact-integer? 0]
-                       [end-pos nonnegative-exact-integer? (string-length str)])
+                       [start-pos exact-nonnegative-integer? 0]
+                       [end-pos exact-nonnegative-integer? (string-length str)])
          void?]{
 
 Writes characters to @scheme[out] from @scheme[str] starting from
@@ -37,17 +37,17 @@ is always @scheme[(- end-pos start-pos)].}
 
 @defproc[(write-bytes [bstr bytes?]
                       [out output-port? (current-output-port)]
-                      [start-pos nonnegative-exact-integer? 0]
-                      [end-pos nonnegative-exact-integer? (bytes-length bstr)])
+                      [start-pos exact-nonnegative-integer? 0]
+                      [end-pos exact-nonnegative-integer? (bytes-length bstr)])
          void?]{
 
 Like @scheme[write-string], but writes bytes instead of characters.}
 
 @defproc[(write-bytes-avail [bstr bytes?]
                             [out output-port? (current-output-port)]
-                            [start-pos nonnegative-exact-integer? 0]
-                            [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         nonnegative-exact-integer?]{
+                            [start-pos exact-nonnegative-integer? 0]
+                            [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         exact-nonnegative-integer?]{
 
 Like @scheme[write-bytes], but returns without blocking after writing
 as many bytes as it can immediately flush. It blocks only if no bytes
@@ -67,9 +67,9 @@ is raised.}
 
 @defproc[(write-bytes-avail* [bstr bytes?]
                              [out output-port? (current-output-port)]
-                             [start-pos nonnegative-exact-integer? 0]
-                             [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         (or/c nonnegative-exact-integer? false/c)]{
+                             [start-pos exact-nonnegative-integer? 0]
+                             [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         (or/c exact-nonnegative-integer? false/c)]{
 
 Like @scheme[write-bytes-avail], but never blocks, returns @scheme[#f]
 if the port contains buffered data that cannot be written immediately,
@@ -78,9 +78,9 @@ flushed but no additional bytes can be written immediately.}
 
 @defproc[(write-bytes-avail/enable-break [bstr bytes?]
                                          [out output-port? (current-output-port)]
-                                         [start-pos nonnegative-exact-integer? 0]
-                                         [end-pos nonnegative-exact-integer? (bytes-length bstr)])
-         nonnegative-exact-integer?]{
+                                         [start-pos exact-nonnegative-integer? 0]
+                                         [end-pos exact-nonnegative-integer? (bytes-length bstr)])
+         exact-nonnegative-integer?]{
 
 Like @scheme[write-bytes-avail], except that breaks are enabled during
 the write. The procedure provides a guarantee about the interaction of
@@ -106,8 +106,8 @@ is written.}
 
 @defproc[(write-bytes-avail-evt [bstr bytes?]
                                 [out output-port? (current-output-port)]
-                                [start-pos nonnegative-exact-integer? 0]
-                                [end-pos nonnegative-exact-integer? (bytes-length bstr)]) 
+                                [start-pos exact-nonnegative-integer? 0]
+                                [end-pos exact-nonnegative-integer? (bytes-length bstr)]) 
          evt?]{
 
 Similar to @scheme[write-bytes-avail], but instead of writing bytes
diff --git a/collects/scribblings/reference/string-ports.scrbl b/collects/scribblings/reference/string-ports.scrbl
index a4fb938b8e..2ce5116f38 100644
--- a/collects/scribblings/reference/string-ports.scrbl
+++ b/collects/scribblings/reference/string-ports.scrbl
@@ -31,8 +31,8 @@ same as @scheme[open-output-bytes].}
 
 @defproc[(get-output-bytes [out output-port?]
                            [reset? any/c #f]
-                           [start-pos nonnegative-exact-integer? 0]
-                           [end-pos nonnegative-exact-integer? #f])
+                           [start-pos exact-nonnegative-integer? 0]
+                           [end-pos exact-nonnegative-integer? #f])
          bytes?]{
 
 Returns the bytes accumulated in @scheme[out] so far in a
diff --git a/collects/scribblings/reference/struct-inspectors.scrbl b/collects/scribblings/reference/struct-inspectors.scrbl
index fc14b9ab1b..f4a98cee1b 100644
--- a/collects/scribblings/reference/struct-inspectors.scrbl
+++ b/collects/scribblings/reference/struct-inspectors.scrbl
@@ -72,11 +72,11 @@ Returns two values:
 
 @defproc[(struct-type-info [struct-type struct-type?])
          (values symbol?
-                 nonnegative-exact-integer?
-                 nonnegative-exact-integer?
+                 exact-nonnegative-integer?
+                 exact-nonnegative-integer?
                  struct-accessor-procedure?
                  struct-mutator-procedure?
-                 (listof nonnegative-exact-integer?)
+                 (listof exact-nonnegative-integer?)
                  (or/c struct-type? false/c)
                  boolean?)]{
 
diff --git a/collects/scribblings/reference/stx-ops.scrbl b/collects/scribblings/reference/stx-ops.scrbl
index 3b5b1c5c64..999df9cf24 100644
--- a/collects/scribblings/reference/stx-ops.scrbl
+++ b/collects/scribblings/reference/stx-ops.scrbl
@@ -19,7 +19,7 @@ object that is marshaled as part of compiled code; see also
 
 
 @defproc[(syntax-line [stx syntax?]) 
-         (or/c positive-exact-integer?
+         (or/c exact-positive-integer?
                false/c)]{
 
 Returns the line number (positive exact integer) for the start of the
@@ -43,7 +43,7 @@ about marshaling compiled @tech{syntax object}s.}
 
 
 @defproc[(syntax-position [stx syntax?])
-         (or/c positive-exact-integer?
+         (or/c exact-positive-integer?
                false/c)]{
 
 Returns the character position (positive exact integer) for the start
diff --git a/collects/scribblings/reference/subprocess.scrbl b/collects/scribblings/reference/subprocess.scrbl
index f2f85066a2..15d4f5d16e 100644
--- a/collects/scribblings/reference/subprocess.scrbl
+++ b/collects/scribblings/reference/subprocess.scrbl
@@ -90,7 +90,7 @@ Blocks until the process represented by @scheme[subproc] terminates.}
 
 @defproc[(subprocess-status [subproc subprocess?]) 
          (or/c (one-of/c 'running)
-               nonnegative-exact-integer?)]{
+               exact-nonnegative-integer?)]{
 
 Returns @indexed-scheme['running] if the process represented by
 @scheme[subproc] is still running, or its exit code otherwise. The
@@ -111,7 +111,7 @@ might handle the signal without terminating). Under Windows, no action
 is taken when @scheme[force?] is @scheme[#f].}
 
 
-@defproc[(subprocess-pid [subproce subprocess?]) nonnegative-exact-integer?]{
+@defproc[(subprocess-pid [subproce subprocess?]) exact-nonnegative-integer?]{
 
 Returns the operating system's numerical ID (if any) for the process
 represented by @scheme[subproc], valid only as long as the process is
@@ -265,7 +265,7 @@ Like @scheme[system*], but returns the exit code like
 @defproc[(process [command string?])
          (list input-port?
                output-port?
-               nonnegative-exact-integer?
+               exact-nonnegative-integer?
                input-port?
                ((one-of/c 'status 'wait 'interrupt 'kill) . -> . any))]{
 
diff --git a/collects/scribblings/reference/vectors.scrbl b/collects/scribblings/reference/vectors.scrbl
index 2eaf1fa227..34fe5a94f2 100644
--- a/collects/scribblings/reference/vectors.scrbl
+++ b/collects/scribblings/reference/vectors.scrbl
@@ -27,7 +27,7 @@ of the sequence. See also @scheme[in-vector].
 Returns @scheme[#t] if @scheme[v] is a vector, @scheme[#f] otherwise.}
 
 
-@defproc[(make-vector [size nonnegative-exact-integer?]
+@defproc[(make-vector [size exact-nonnegative-integer?]
                       [v any/c 0]) vector?]{
 
 Returns a mutable vector with @scheme[size] slots, where all slots are
@@ -50,19 +50,19 @@ order.}
 
 
 
-@defproc[(vector-length [vec vector?]) nonnegative-exact-integer?]{
+@defproc[(vector-length [vec vector?]) exact-nonnegative-integer?]{
 
 Returns the length of @scheme[vec] (i.e., the number of slots in the
 vector).}
 
-@defproc[(vector-ref [vec vector?][pos nonnegative-exact-integer?]) any/c]{
+@defproc[(vector-ref [vec vector?][pos exact-nonnegative-integer?]) any/c]{
 
 Returns the element in slot @scheme[pos] of @scheme[vec]. The first
 slot is position @scheme[0], and the last slot is one less than
 @scheme[(vector-length vec)].}
 
 @defproc[(vector-set! [vec (and/c vector? (not/c immutable?))]
-                      [pos nonnegative-exact-integer?]
+                      [pos exact-nonnegative-integer?]
                       [v any/c])
          void?]{
 
@@ -121,8 +121,8 @@ Changes all slots of @scheme[vec] to contain @scheme[v].}
 
 
 @defproc[(vector->values [vec vector?]
-                         [start-pos nonnegative-exact-integer? 0]
-                         [end-pos nonnegative-exact-integer? (vector-length vec)])
+                         [start-pos exact-nonnegative-integer? 0]
+                         [end-pos exact-nonnegative-integer? (vector-length vec)])
          any]{
 
 Returns @math{@scheme[end-pos] - @scheme[start-pos]} values, which are
diff --git a/collects/scribblings/scribble/basic.scrbl b/collects/scribblings/scribble/basic.scrbl
index cc26e22ffc..1ccdf871d5 100644
--- a/collects/scribblings/scribble/basic.scrbl
+++ b/collects/scribblings/scribble/basic.scrbl
@@ -150,7 +150,7 @@ an element with style @scheme[#f].}
 @def-style-proc[subscript]
 @def-style-proc[superscript]
 
-@defproc[(hspace [n nonnegative-exact-integer?]) element?]{
+@defproc[(hspace [n exact-nonnegative-integer?]) element?]{
 
 Produces an element containing @scheme[n] spaces and style
 @scheme['hspace].}
diff --git a/collects/scribblings/scribble/struct.scrbl b/collects/scribblings/scribble/struct.scrbl
index 7096bfda2e..48d4136d0d 100644
--- a/collects/scribblings/scribble/struct.scrbl
+++ b/collects/scribblings/scribble/struct.scrbl
@@ -689,14 +689,14 @@ Like @scheme[content->string], but for a single @tech{element}.
 
 }
 
-@defproc[(element-width (element any/c)) nonnegative-exact-integer?]{
+@defproc[(element-width (element any/c)) exact-nonnegative-integer?]{
 
 Returns the width in characters of the given @tech{element}.
 
 }
 
 
-@defproc[(block-width (e block?)) nonnegative-exact-integer?]{
+@defproc[(block-width (e block?)) exact-nonnegative-integer?]{
 
 Returns the width in characters of the given @tech{block}.}
 
diff --git a/collects/scribblings/slideshow/picts.scrbl b/collects/scribblings/slideshow/picts.scrbl
index 246830b444..40a044e07d 100644
--- a/collects/scribblings/slideshow/picts.scrbl
+++ b/collects/scribblings/slideshow/picts.scrbl
@@ -924,7 +924,7 @@ factor. If the factor is greater tham 1, the color is lightened by
 dividing the gap between the RGB components and 255 by the factor.}
 
 @defproc[(color-series [dc (is-a?/c dc<%>)]
-                       [max-step nonnegative-exact-integer?]
+                       [max-step exact-nonnegative-integer?]
                        [step-delta (and/c exact? positive?)]
                        [start (or/c string? (is-a?/c color%))]
                        [end (or/c string? (is-a?/c color%))]
@@ -978,8 +978,8 @@ repeated calls to @scheme[draw-pict].}
 
 
 @defproc[(show-pict [pict pict?]
-                    [w (or/c false/c nonnegative-exact-integer?) #f] 
-                    [h (or/c false/c nonnegative-exact-integer?) #f])
+                    [w (or/c false/c exact-nonnegative-integer?) #f] 
+                    [h (or/c false/c exact-nonnegative-integer?) #f])
          void?]{
 
 Opens a frame that displays @scheme[pict].  The frame adds one method,
diff --git a/collects/scribblings/slideshow/slides.scrbl b/collects/scribblings/slideshow/slides.scrbl
index e1a3b7b345..04e6927954 100644
--- a/collects/scribblings/slideshow/slides.scrbl
+++ b/collects/scribblings/slideshow/slides.scrbl
@@ -386,7 +386,7 @@ triggered via the @DFlag{condense} command-line flag.}
 
 @section{Configuration}
 
-@defparam[current-font-size n nonnegative-exact-integer?]{
+@defparam[current-font-size n exact-nonnegative-integer?]{
 
 Parameter that determines he font size used by @scheme[t],
 @scheme[para], etc. The default size is @scheme[32].}
@@ -400,13 +400,13 @@ initial values include @scheme['swiss], @scheme["Verdana"], and
 @scheme["Gill Sans"].}
 
 
-@defparam[current-line-sep n nonnegative-exact-integer?]{
+@defparam[current-line-sep n exact-nonnegative-integer?]{
 
 Parameter that controls the amount of space used between lines by
 @scheme[para], @scheme[item], and @scheme[subitem].}
 
 
-@defparam[current-para-width n nonnegative-exact-integer?]{
+@defparam[current-para-width n exact-nonnegative-integer?]{
 
 Parameter that controls the width of a pict created by
 @scheme[para], @scheme[item], and @scheme[subitem].}
@@ -419,7 +419,7 @@ title. The default is @scheme["black"].}
 
 
 @defparam[current-slide-assembler proc ((or/c string? false/c)
-                                        nonnegative-exact-integer?
+                                        exact-nonnegative-integer?
                                         pict?
                                         . -> .
                                         pict?)]{