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scribblings/stdlib.scrbl

@@ -9,3 +9,5 @@ Cur has a small standard library, primary for demonstration purposes.
 
 @include-section{stdlib/tactics.scrbl}
 @include-section{stdlib/sugar.scrbl}
+@include-section{stdlib/bool.scrbl}
+@include-section{stdlib/nat.scrbl}

scribblings/stdlib/nat.scrbl

@@ -0,0 +1,69 @@
+#lang scribble/manual
+
+@(require
+  "../defs.rkt"
+  scribble/eval)
+
+@(define curnel-eval (curnel-sandbox "(require cur/stdlib/bool cur/stdlib/nat cur/stdlib/sugar)"))
+
+@title{Nat}
+@defmodule[cur/stdlib/nat]
+This library defines the datatype @racket[Nat] and several functions on them.
+
+@deftogether[(@defthing[Nat Type]
+              @defthing[z Nat]
+	      @defthing[s (-> Nat Nat)])]{
+The natural number datatype.
+}
+
+@defproc[(add1 [n Nat]) Nat]{
+A more lispy name for @racket[s].
+
+@examples[#:eval curnel-eval
+          (s z)
+	  (add1 z)]
+}
+
+@defproc[(sub1 [n Nat]) Nat]{
+Return the predecessor of @racket[n], or @racket[z] is @racket[n] is @racket[z].
+
+@examples[#:eval curnel-eval
+          (sub1 (s z))]
+
+}
+
+@defproc[(plus [n Nat] [m Nat]) Nat]{
+Add @racket[n] and @racket[m].
+
+@examples[#:eval curnel-eval
+          (plus (s z) (s z))
+	  (plus z (s z))
+	  (plus (s (s z)) (s z))]
+}
+
+@defproc[(nat-equal? [n Nat] [m Nat]) Bool]{
+Return @racket[true] if and only if @racket[n] is equal to @racket[m].
+
+@examples[#:eval curnel-eval
+          (nat-equal? (s z) (s z))
+	  (nat-equal? z (s z))]
+}
+
+@defproc[(even? [n Nat]) Bool]{
+Return @racket[true] if and only if @racket[n] is even.
+
+@examples[#:eval curnel-eval
+          (even? (s z))
+	  (even? z)
+	  (even? (s (s z)))]
+
+}
+
+@defproc[(odd? [n Nat]) Bool]{
+Return @racket[true] if and only if @racket[n] is not even.
+
+@examples[#:eval curnel-eval
+          (odd? (s z))
+	  (odd? z)
+	  (odd? (s (s z)))]
+}

stdlib/nat.rkt

@@ -2,7 +2,7 @@
 (require "sugar.rkt" "bool.rkt")
 ;; TODO: override (all-defined-out) to enable exporting all these
 ;; properly.
-(provide Nat z s add1 sub1 plus )
+(provide Nat z s add1 sub1 plus nat-equal? even? odd?)
 (module+ test
   (require rackunit))