Fixing exports and actually adding docs
This commit is contained in:
Jay McCarthy
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666
pkgs/data-pkgs/data-doc/data/scribblings/enumerate.scrbl
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666
pkgs/data-pkgs/data-doc/data/scribblings/enumerate.scrbl
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#lang scribble/manual
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@(require scribble/eval
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(for-label data/enumerate
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racket/contract
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racket/base))
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@title{Enumerations}
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@(define the-eval (make-base-eval))
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@(the-eval '(require data/enumerate racket/string))
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@defmodule[data/enumerate]
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@author[@author+email["Max S. New" "maxsnew@gmail.com"]]
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This library defines @deftech{enumerations}. Enumerations are
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bijections between the natural numbers (or a prefix thereof) and a
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data-type. Most of the bijections defined in this library guarantee
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that the enumeration is efficient, meaning that the decoding a number
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is linear in the bits of the number.
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@; XXX explain fairness
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@; XXX add citations
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@defproc[(nat? [x any/c]) boolean?]{
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Identifies a value as a natural number.}
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@defproc[(extended-nat? [x any/c]) boolean?]{
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Identifies a value as a natural number or positive infinity.}
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@defproc[(enum [size extended-nat?]
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[from (-> nat? any/c)]
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[to (-> any/c nat?)])
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enum?]{
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Constructs an @tech{enumeration} of size @racket[size] where
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@racket[from] is the decoding function and @racket[to] is the encoding
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function. }
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@defproc[(enum? [x any/c]) boolean?]{
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Identifies a value as an @tech{enumeration}.}
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@defproc[(size [e enum?]) extended-nat?]{
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Returns the size of an @tech{enumeration}.}
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@defproc[(decode [e enum?] [n nat?]) any/c]{
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Uses @racket[e] to decode @racket[n].}
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@defproc[(encode [e enum?] [x any/c]) nat?]{
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Uses @racket[e] to encode @racket[x].}
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@defthing[nat/e enum?]{
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An @tech{enumeration} of the natural numbers.
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@examples[#:eval the-eval
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(decode nat/e 5)
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(encode nat/e 5)
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]}
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@defproc[(map/e [f (-> a ... b)]
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[inv-f (-> b (values a ...))]
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[e enum?] ...+) enum?]{
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Uses @racket[f] and @racket[inv-f] around the encoding and decoding
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functions of @racket[e].
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@examples[#:eval the-eval
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(define map-1/e
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(map/e number->string string->number nat/e))
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(decode map-1/e 5)
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(encode map-1/e "5")
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(define map-2/e
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(map/e (λ (x y)
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(string-join
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(list (number->string x)
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(number->string y))))
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(λ (x)
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(apply values (map string->number (string-split x))))
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nat/e nat/e))
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(decode map-2/e 5)
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(encode map-2/e "1 2")
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]}
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@defproc[(filter/e [e enum?] [p (-> any/c boolean?)]) enum?]{
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Returns an @tech{enumeration} identical to @racket[e] except that only
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elements where @racket[p] returns true are included. The encoding
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function and the size are wrong in the result and this is inefficient,
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so only use it for very small enumerations.
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@examples[#:eval the-eval
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(define filter-1/e
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(filter/e nat/e even?))
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(decode filter-1/e 5)
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(encode filter-1/e 8)
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]}
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@defproc[(except/e [e enum?] [x any/c] ...) enum?]{
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Returns an @tech{enumeration} identical to @racket[e] except that all
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@racket[x] are not included in the decoding and cannot be encoded.
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@examples[#:eval the-eval
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(define except-1/e
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(except/e nat/e 3))
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(decode except-1/e 5)
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(encode except-1/e 8)
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]}
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@defproc[(to-stream [e enum?]) stream?]{
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Returns a stream of the values in @racket[e].
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@examples[#:eval the-eval
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(to-stream map-2/e)
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]}
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@defproc[(approximate [e enum?] [n nat?]) list?]{
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Returns a list of the first @racket[n] values in @racket[e].
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@examples[#:eval the-eval
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(approximate map-2/e 5)
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]}
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@defproc[(to-list [e enum?]) list?]{
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Returns a list of the @racket[n] values in @racket[e]. This will
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diverge if @racket[e] is infinite.
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@examples[#:eval the-eval
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(to-list (take/e map-2/e 5))
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]}
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@defproc[(take/e [e enum?] [n nat?]) enum?]{
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Identical to @racket[e] but only includes the first @racket[n] values.
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@examples[#:eval the-eval
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(decode (take/e map-2/e 5) 3)
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(encode (take/e map-2/e 5) "1 1")
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]}
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@defproc[(slice/e [e enum?] [lo nat?] [hi nat?]) enum?]{
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Identical to @racket[e] but only includes the values between
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@racket[lo] and @racket[hi].
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@examples[#:eval the-eval
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(to-list (slice/e map-2/e 5 10))
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]}
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@defproc[(below/e [max nat?]) enum?]{
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An @tech{enumeration} of the first @racket[max] naturals.
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@examples[#:eval the-eval
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(to-list (below/e 10))
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]}
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@defthing[empty/e enum?]{
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An empty @tech{enumeration}.
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@examples[#:eval the-eval
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(to-list empty/e)
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]}
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@defproc[(const/e [x any/c]) enum?]{
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An @tech{enumeration} of exactly @racket[x].
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@examples[#:eval the-eval
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(to-list (const/e 42))
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]}
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@defproc[(from-list/e [xs list?]) enum?]{
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An @tech{enumeration} of each @racket[eq?] value in
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@racket[xs]. @racket[xs] should not contain duplicates, but
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@racket[from-list/e] doesn't check.
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@examples[#:eval the-eval
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(to-list (from-list/e '("Brian" "Jenny" "Ki" "Ted")))
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]}
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@defproc[(fin/e [x any/c] ...) enum?]{
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An @tech{enumeration} of each @racket[x]. If a value is duplicated in
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the input, it is only in the enumeration once.
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@examples[#:eval the-eval
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(to-list (fin/e "Brian" "Jenny" "Ki" "Ted"))
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]}
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@defthing[int/e enum?]{
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An @tech{enumeration} of the integers.
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@examples[#:eval the-eval
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(approximate int/e 10)
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]}
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@defproc[(disj-sum/e [e-p (cons/c enum? (-> any/c boolean?))] ...) enum?]{
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An @tech{enumeration} of the disjoint sum of the enumerations given in
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@racket[e-p]. Each @racket[e-p] is a pair of an enumeration and a
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predicate identifying elements of it. Only one or zero predicates
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should return true on any value.
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@examples[#:eval the-eval
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(approximate (disj-sum/e (cons nat/e nat?) (cons map-1/e string?)) 10)
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]}
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@defproc[(disj-append/e [e-p (cons/c enum? (-> any/c boolean?))] ...+) enum?]{
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An @tech{enumeration} of the disjoint sum of the enumerations given in
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@racket[e-p] that fully enumerates each enumeration before enumerating
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the next. @racket[e-p] are formatted as in @racket[disj-sum/e]. All
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but the last enumeration should be finite.
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@examples[#:eval the-eval
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(approximate (disj-append/e (cons (take/e nat/e 4) nat?)
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(cons map-1/e string?))
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10)
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]}
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@defproc[(fin-cons/e [x enum?] [y enum?]) enum?]{
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An @tech{enumeration} of pairs of the values from @racket[x] and
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@racket[y]. Both enumerations should be finite.
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@examples[#:eval the-eval
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(approximate (fin-cons/e (take/e nat/e 4) (take/e nat/e 5)) 5)
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]}
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@defproc[(cons/e [x enum?] [y enum?]) enum?]{
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An @tech{enumeration} of pairs of the values from @racket[x] and
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@racket[y].
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@examples[#:eval the-eval
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(approximate (cons/e (take/e nat/e 4) (take/e nat/e 5)) 5)
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(approximate (cons/e nat/e (take/e nat/e 5)) 5)
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(approximate (cons/e (take/e nat/e 4) nat/e) 5)
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(approximate (cons/e nat/e nat/e) 5)
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]}
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@defproc[(elegant-cons/e [x enum?] [y enum?]) enum?]{
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An @tech{enumeration} of pairs of the values from @racket[x] and
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@racket[y]. The enumeration is in a different order than
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@racket[cons/e]. Both enumerations should be infinite.
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@examples[#:eval the-eval
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(approximate (elegant-cons/e nat/e nat/e) 5)
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]}
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@defproc[(traverse/e [f (-> any/c enum?)] [xs (listof any/c)]) enum?]{
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Constructs an @tech{enumeration} that simulatenously enumerates each
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of the enumerations returned by @racket[f] applied to each element of
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@racket[xs].
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@examples[#:eval the-eval
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(define traverse-1/e
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(traverse/e (λ (x) (map/e (λ (n) (cons x n))
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(λ (y) (cdr y))
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nat/e))
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'("Brian" "Jenny" "Ted" "Ki")))
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(approximate traverse-1/e 5)
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(encode traverse-1/e
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'(("Brian" . 11) ("Jenny" . 15) ("Ted" . 16) ("Ki" . 7)))
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]}
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@defproc[(hash-traverse/e [f (-> any/c enum?)] [xs (listof any/c)]) enum?]{
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Constructs an @tech{enumeration} that simulatenously enumerates each
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of the enumerations returned by @racket[f] applied to each value of
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@racket[xs].
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@examples[#:eval the-eval
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(define hash-traverse-1/e
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(hash-traverse/e (λ (n) (below/e n))
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(hash "Brian" 5 "Jenny" 15 "Ted" 25 "Ki" 30)))
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(approximate hash-traverse-1/e 5)
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(encode hash-traverse-1/e
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'#hash(("Brian" . 4) ("Jenny" . 1) ("Ted" . 16) ("Ki" . 7)))
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]}
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@defproc[(dep/e [a enum?] [b (-> any/c enum?)]) enum?]{
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Constructs an @tech{enumeration} of pairs of values @racket[a] and
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@racket[(b a)].
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@examples[#:eval the-eval
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(define dep-1/e
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(dep/e nat/e (λ (a) (below/e a))))
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(approximate dep-1/e 5)
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(encode dep-1/e (cons 17 10))
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]}
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@defproc[(dep2/e [n extended-nat?] [a enum?] [b (-> any/c enum?)]) enum?]{
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Like @racket[dep2/e] but requires the size of the resulting
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enumeration be given as @racket[n]. This is more efficient than
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@racket[dep/e], particularly when @racket[n] is finite.
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@examples[#:eval the-eval
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(define (! n)
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(if (zero? n) 1 (* n (! (sub1 n)))))
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(define dep2-1/e
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(dep2/e (+ (! 1) (! 2) (! 3) (! 4) (! 5))
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(below/e 5)
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(λ (a) (below/e a))))
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(approximate dep2-1/e 5)
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(encode dep2-1/e (cons 4 3))
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]}
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@defproc[(fold-enum [f (-> (listof a) b enum?)] [bs (listof b)]) enum?]{
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This is like @racket[foldr], but @racket[f] returns
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@tech{enumerations} of @racket[_a]s and assumes that the accumulator
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is initialized to @racket['()].
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@examples[#:eval the-eval
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(define fold-enum-1/e
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(fold-enum (λ (as b)
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(below/e (+ (foldr + 0 as) b)))
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(list 1 2 3)))
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(approximate fold-enum-1/e 5)
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(encode fold-enum-1/e (list 0 1 1))
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]}
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@defproc[(range/e [lo nat?] [hi nat?]) enum?]{
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An @tech{enumeration} of the naturals between @racket[lo] and @racket[hi].
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@examples[#:eval the-eval
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(approximate (range/e 42 64) 5)
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]}
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@defproc[(thunk/e [size extended-nat?] [ep (-> enum?)]) enum?]{
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A delayed @tech{enumeration} identical to @racket[ep]. This is
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typically used with @racket[fix/e].
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@examples[#:eval the-eval
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(approximate (thunk/e +inf.0 (λ () nat/e)) 5)
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]}
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@defproc*[([(fix/e [f (-> enum? enum?)]) enum?]
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[(fix/e [size extended-nat?] [f (-> enum? enum?)]) enum?])]{
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An @tech{enumeration} calculated as the fixed-point of @racket[f]. If
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@racket[size] is not given, it is assumed to be @racket[+inf.0].
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@examples[#:eval the-eval
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(approximate
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(fix/e
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+inf.0
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(λ (self) (disj-sum/e (cons (fin/e '()) null?)
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(cons (cons/e nat/e self) pair?))))
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5)
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]}
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@defproc*[([(many/e [e enum?]) enum?]
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[(many/e [e enum?] [n nat?]) enum?])]{
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An @tech{enumeration} of lists of length @racket[n] of values
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enumerated by @racket[e]. If @racket[n] is not given, lists of any
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size are enumerated.
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@examples[#:eval the-eval
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(approximate (many/e nat/e) 5)
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(approximate (many/e nat/e 5) 5)
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]}
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@defproc[(many1/e [e enum?]) enum?]{
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An @tech{enumeration} of non-empty lists of values enumerated by
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@racket[e].
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@examples[#:eval the-eval
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(approximate (many1/e nat/e) 5)
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]}
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@defproc[(cantor-vec/e [e enum?] ...) enum?]{
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An @tech{enumeration} of vectors of values enumerated by the
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@racket[e].
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@examples[#:eval the-eval
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(approximate (cantor-vec/e (fin/e "Brian" "Jenny" "Ki" "Ted")
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nat/e
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(fin/e "Terra" "Locke" "Edgar" "Mash"))
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5)
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]}
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@defproc[(vec/e [e enum?] ...) enum?]{
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An @tech{enumeration} of vectors of values enumerated by the
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@racket[e].
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@examples[#:eval the-eval
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(approximate (vec/e (fin/e "Brian" "Jenny" "Ki" "Ted")
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nat/e
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(fin/e "Terra" "Locke" "Edgar" "Mash"))
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5)
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]}
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@defproc[(box-vec/e [e enum?] ...) enum?]{
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An @tech{enumeration} of vectors of values enumerated by the
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@racket[e].
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@examples[#:eval the-eval
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(approximate (box-vec/e (fin/e "Brian" "Jenny" "Ki" "Ted")
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nat/e
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(fin/e "Terra" "Locke" "Edgar" "Mash"))
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5)
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]}
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@defproc[(inf-fin-fair-list/e [e enum?] ...) enum?]{
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An @tech{enumeration} of lists of values enumerated by the
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@racket[e].
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@examples[#:eval the-eval
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(approximate (inf-fin-fair-list/e
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(fin/e "Brian" "Jenny" "Ki" "Ted")
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nat/e
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(fin/e "Terra" "Locke" "Edgar" "Mash"))
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5)
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]}
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@defproc[(mixed-box-tuples/e [es (listof enum?)]) enum?]{
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An @tech{enumeration} of lists of values enumerated by the
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enumerations in @racket[es].
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@examples[#:eval the-eval
|
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(approximate (mixed-box-tuples/e
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(list (fin/e "Brian" "Jenny" "Ki" "Ted")
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nat/e
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(fin/e "Terra" "Locke" "Edgar" "Mash")))
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5)
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]}
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@defproc[(inf-fin-cons/e [x enum?] [y enum?]) enum?]{
|
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An @tech{enumeration} of pairs of the values from @racket[x] and
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@racket[y]. One of the enumerations must be finite.
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@examples[#:eval the-eval
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(approximate (inf-fin-cons/e (take/e nat/e 4) (take/e nat/e 5)) 5)
|
||||
(approximate (inf-fin-cons/e nat/e (take/e nat/e 5)) 5)
|
||||
(approximate (inf-fin-cons/e (take/e nat/e 4) nat/e) 5)
|
||||
]}
|
||||
|
||||
@defproc[(list/e [e enum?] ...) enum?]{
|
||||
|
||||
An @tech{enumeration} of lists of values enumerated by the
|
||||
@racket[e].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (list/e
|
||||
(fin/e "Brian" "Jenny" "Ki" "Ted")
|
||||
nat/e
|
||||
(fin/e "Terra" "Locke" "Edgar" "Mash"))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(nested-cons-list/e [e enum?] ...) enum?]{
|
||||
|
||||
An @tech{enumeration} of lists of values enumerated by the
|
||||
@racket[e].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (nested-cons-list/e
|
||||
(fin/e "Brian" "Jenny" "Ki" "Ted")
|
||||
nat/e
|
||||
(fin/e "Terra" "Locke" "Edgar" "Mash"))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(cantor-list/e [e enum?] ...) enum?]{
|
||||
|
||||
An @tech{enumeration} of lists of values enumerated by the
|
||||
@racket[e].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (cantor-list/e
|
||||
(fin/e "Brian" "Jenny" "Ki" "Ted")
|
||||
nat/e
|
||||
(fin/e "Terra" "Locke" "Edgar" "Mash"))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(box-list/e [e enum?] ...) enum?]{
|
||||
|
||||
An @tech{enumeration} of lists of values enumerated by the
|
||||
@racket[e].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (box-list/e
|
||||
(fin/e "Brian" "Jenny" "Ki" "Ted")
|
||||
nat/e
|
||||
(fin/e "Terra" "Locke" "Edgar" "Mash"))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(prime-length-box-list/e [es (listof enum?)]) enum?]{
|
||||
|
||||
An @tech{enumeration} of lists of values enumerated by the
|
||||
enumerations in @racket[es].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (prime-length-box-list/e
|
||||
(list (fin/e "Brian" "Jenny" "Ki" "Ted")
|
||||
nat/e
|
||||
(fin/e "Terra" "Locke" "Edgar" "Mash")))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(box-tuples/e [k nat?]) enum?]{
|
||||
|
||||
An @tech{enumeration} of tuples of naturals of length @racket[k].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (box-tuples/e 3)
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(bounded-list/e [k nat?] [n nat?]) enum?]{
|
||||
|
||||
An @tech{enumeration} of tuples of naturals up to @racket[n] of length @racket[k].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (bounded-list/e 3 2)
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(nat+/e [lo nat?]) enum?]{
|
||||
|
||||
An @tech{enumeration} of tuples of naturals of larger than @racket[lo].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (nat+/e 42)
|
||||
5)
|
||||
]}
|
||||
|
||||
@defproc[(fail/e [e exn?]) enum?]{
|
||||
|
||||
An @tech{enumeration} raises @racket[e] if @racket[decode] or
|
||||
@racket[encode] is called with on.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate (fail/e (exn:fail "Don't do that!" (current-continuation-marks)))
|
||||
5)
|
||||
]}
|
||||
|
||||
@defthing[char/e enum?]{
|
||||
|
||||
An @tech{enumeration} of characters.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate char/e 5)
|
||||
]}
|
||||
|
||||
@defthing[string/e enum?]{
|
||||
|
||||
An @tech{enumeration} of strings.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate string/e 5)
|
||||
]}
|
||||
|
||||
@defthing[from-1/e enum?]{
|
||||
|
||||
An @tech{enumeration} of naturals starting from @racket[1].
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate from-1/e 5)
|
||||
]}
|
||||
|
||||
@defthing[integer/e enum?]{
|
||||
|
||||
An @tech{enumeration} of integers.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate integer/e 5)
|
||||
]}
|
||||
|
||||
@defthing[float/e enum?]{
|
||||
|
||||
An @tech{enumeration} of flonums.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate float/e 5)
|
||||
]}
|
||||
|
||||
@defthing[real/e enum?]{
|
||||
|
||||
An @tech{enumeration} of reals.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate real/e 5)
|
||||
]}
|
||||
|
||||
@defthing[non-real/e enum?]{
|
||||
|
||||
An @tech{enumeration} of non-real numbers.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate non-real/e 5)
|
||||
]}
|
||||
|
||||
@defthing[num/e enum?]{
|
||||
|
||||
An @tech{enumeration} of numbers.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate num/e 5)
|
||||
]}
|
||||
|
||||
@defthing[bool/e enum?]{
|
||||
|
||||
An @tech{enumeration} of booleans.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(to-list bool/e)
|
||||
]}
|
||||
|
||||
@defthing[symbol/e enum?]{
|
||||
|
||||
An @tech{enumeration} of symbols.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate symbol/e 5)
|
||||
]}
|
||||
|
||||
@defthing[base/e enum?]{
|
||||
|
||||
An @tech{enumeration} of atomic Racket values.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate base/e 5)
|
||||
]}
|
||||
|
||||
@defthing[any/e enum?]{
|
||||
|
||||
An @tech{enumeration} of S-expressions.
|
||||
|
||||
@examples[#:eval the-eval
|
||||
(approximate any/e 5)
|
||||
]}
|
||||
|
||||
@close-eval[the-eval]
|
||||
|
|
@ -78,6 +78,9 @@
|
|||
[const/e
|
||||
(-> any/c
|
||||
enum?)]
|
||||
[from-list/e
|
||||
(-> list?
|
||||
enum?)]
|
||||
[fin/e
|
||||
(->* () #:rest list?
|
||||
enum?)]
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user