Add some shortcuts for the examples.
Inspired from the scribblings in Typed Racket.
This commit is contained in:
Sergiu Ivanov
parent
8ded018c05
commit
e1a97235c0
|
|
@ -4,6 +4,15 @@
|
|||
typed/racket/unsafe
|
||||
(only-in racket stream->list stream-first)))
|
||||
|
||||
@(define functions-evaluator
|
||||
(parameterize ([sandbox-output 'string]
|
||||
[sandbox-error-output 'string]
|
||||
[sandbox-memory-limit 50])
|
||||
(make-evaluator 'typed/racket #:requires '((submod "functions.rkt" typed)))))
|
||||
|
||||
@(define-syntax-rule (ex . args)
|
||||
(examples #:eval functions-evaluator . args))
|
||||
|
||||
@title[#:tag "functions"]{dds/functions: Formal Functions}
|
||||
|
||||
@defmodule[dds/functions]
|
||||
|
|
@ -13,12 +22,6 @@ This modules provides some definitions for working with functions: tabulating,
|
|||
Some definitions of particular kinds of functions are also provided (threshold
|
||||
Boolean functions, etc.).
|
||||
|
||||
@(define functions-evaluator
|
||||
(parameterize ([sandbox-output 'string]
|
||||
[sandbox-error-output 'string]
|
||||
[sandbox-memory-limit 50])
|
||||
(make-evaluator 'typed/racket #:requires '((submod "functions.rkt" typed)))))
|
||||
|
||||
@section[#:tag "pseudovariadic"]{Pseudovariadic functions}
|
||||
|
||||
Functions for @seclink["tabulating"]{tabulating functions} take as an argument
|
||||
|
|
@ -35,7 +38,7 @@ Racket treats @racket[apply] in
|
|||
special way}. This means that a user-defined function with the same type as
|
||||
@racket[apply] and directly calling it will not work in the same way.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
apply
|
||||
(define myapply apply)
|
||||
myapply
|
||||
|
|
@ -54,7 +57,7 @@ this documentation.
|
|||
|
||||
Define a pseudovariadic anonymous function.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(: f (-> Boolean * Boolean))
|
||||
(define f (pseudovariadic-lambda (x y) (and x y)))
|
||||
(f #t #f)
|
||||
|
|
@ -66,7 +69,7 @@ Define a pseudovariadic anonymous function.
|
|||
|
||||
Define a pseudovariadic function called @racket[name].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(: g (-> Boolean * Boolean))
|
||||
(pseudovariadic-define (g x y) (and x y))
|
||||
(g #t #f)
|
||||
|
|
@ -82,7 +85,7 @@ Given a function @racket[func] and a list of domains @racket[doms] for each of
|
|||
its arguments, in order, produces a list of lists giving the values of
|
||||
arguments and the value of the functions for these inputs.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate (λ (x y) (and x y)) '((#f #t) (#f #t)))
|
||||
]}
|
||||
|
||||
|
|
@ -98,7 +101,7 @@ elements of types @racket[a ...], followed by an element of type @racket[b].
|
|||
This is why this function returns a list of lists, each containing first a list
|
||||
of inputs, and then the output of @racket[func].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/strict (λ (x y) (and x y)) '((#f #t) (#f #t)))
|
||||
]}
|
||||
|
||||
|
|
@ -109,7 +112,7 @@ of inputs, and then the output of @racket[func].
|
|||
Like @racket[tabulate], but @racket[func]
|
||||
@seclink["pseudovariadic"]{pseudovariadic}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/pv (pvλ (x y) (and x y)) '((#f #t) (#f #t)))
|
||||
]}
|
||||
|
||||
|
|
@ -119,7 +122,7 @@ Like @racket[tabulate], but @racket[func]
|
|||
|
||||
Like @racket[tabulate/list], but @racket[func] takes its arguments as a list.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/list (λ ([xs : (Listof Boolean)])
|
||||
(and (car xs) (car xs)))
|
||||
'((#f #t) (#f #t)))
|
||||
|
|
@ -132,7 +135,7 @@ Like @racket[tabulate/list], but @racket[func] takes its arguments as a list.
|
|||
Like @racket[tabulate], but @racket[funcs] is a list of functions taking the
|
||||
same arguments over the same domains.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate* (list (λ (x y) (and x y))
|
||||
(λ (x y) (or x y)))
|
||||
'((#f #t) (#f #t)))
|
||||
|
|
@ -150,7 +153,7 @@ elements of types @racket[a ...], followed by a list of elements of type
|
|||
@racket[b]. This is why this function returns a list of lists, each containing
|
||||
first a list of inputs, and then the list of outputs of @racket[funcs].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/strict (list (λ (x y) (and x y))
|
||||
(λ (x y) (or x y)))
|
||||
'((#f #t) (#f #t)))
|
||||
|
|
@ -159,7 +162,7 @@ first a list of inputs, and then the list of outputs of @racket[funcs].
|
|||
The result of @racket[tabulate*] can be obtained by applying
|
||||
@racket[append-lists]:
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(require (only-in "utils.rkt" append-lists))
|
||||
(append-lists (tabulate*/strict (list (λ (x y) (and x y))
|
||||
(λ (x y) (or x y)))
|
||||
|
|
@ -173,7 +176,7 @@ The result of @racket[tabulate*] can be obtained by applying
|
|||
Like @racket[tabulate*], but the functions in @racket[funcs]
|
||||
are @seclink["pseudovariadic"]{pseudovariadic}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/pv (list (pvλ (x y) (and x y))
|
||||
(pvλ (x y) (or x y)))
|
||||
'((#f #t) (#f #t)))
|
||||
|
|
@ -186,7 +189,7 @@ are @seclink["pseudovariadic"]{pseudovariadic}.
|
|||
Like @racket[tabulate*], but the functions in @racket[funcs] take their
|
||||
arguments as a list.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/list (list (λ ([xs : (Listof Boolean)])
|
||||
(and (car xs) (cadr xs)))
|
||||
(λ ([xs : (Listof Boolean)])
|
||||
|
|
@ -200,7 +203,7 @@ arguments as a list.
|
|||
Like @racket[tabulate/pv], but assumes the domains of all variables of the
|
||||
function are Boolean. The arity of @racket[func] must be explicitly supplied.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/pv/boolean 2 (pvλ (x y) (and x y)))
|
||||
]
|
||||
|
||||
|
|
@ -210,7 +213,7 @@ a pseudovariadic function cannot be determined programmatically. Note that
|
|||
@racket[tabulate] requires a cast is required the domains argument
|
||||
@racket[doms].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate (λ (x y) (and x y))
|
||||
(cast (make-list 2 '(#f #t))
|
||||
(List (Listof Boolean) (Listof Boolean))))
|
||||
|
|
@ -232,7 +235,7 @@ this function.
|
|||
Like @racket[tabulate/pv/boolean], but takes a list of functions of the
|
||||
same arity.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/pv/boolean 2 (list (pvλ (x y) (and x y))
|
||||
(pvλ (x y) (or x y))))
|
||||
]}
|
||||
|
|
@ -244,7 +247,7 @@ Like @racket[tabulate/pv], but assumes the domains of all variables of the
|
|||
function are @tt{{0,1}}. The arity of @racket[func] must be
|
||||
explicitly supplied.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/pv/01 2 (pvλ (x y)
|
||||
(cast (modulo (+ x y) 2)
|
||||
(U Zero One))))
|
||||
|
|
@ -261,7 +264,7 @@ See @racket[tabulate/pv/boolean] for an explanation of the explicit
|
|||
|
||||
Like @racket[tabulate/pv/01], but takes a list of functions of the same arity.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/pv/01 2 `(,(pvλ (x y) (cast (min x y) (U Zero One)))
|
||||
,(pvλ (x y) (cast (max x y) (U Zero One)))))
|
||||
]}
|
||||
|
|
@ -273,7 +276,7 @@ Like @racket[tabulate/pv/01], but takes a list of functions of the same arity.
|
|||
Like @racket[tabulate/list], but assumes the domains of all variables of the
|
||||
function are Boolean.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/list/boolean 2 (λ (xs) (and (car xs) (cadr xs))))
|
||||
]}
|
||||
|
||||
|
|
@ -284,7 +287,7 @@ function are Boolean.
|
|||
Like @racket[tabulate*/list], but assumes the domains of all variables of the
|
||||
function are Boolean.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/list/boolean 2 (list (λ (xs) (and (car xs) (cadr xs)))
|
||||
(λ (xs) (or (car xs) (cadr xs)))))
|
||||
]}
|
||||
|
|
@ -296,7 +299,7 @@ function are Boolean.
|
|||
Like @racket[tabulate/list], but assumes the domains of all variables of the
|
||||
function are @tt{{0,1}}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate/list/01 2 (λ (xs)
|
||||
(cast (modulo (+ (car xs) (cadr xs)) 2) (U Zero One))))
|
||||
]}
|
||||
|
|
@ -308,7 +311,7 @@ function are @tt{{0,1}}.
|
|||
Like @racket[tabulate*/list], but assumes the domains of all variables of the
|
||||
function are @tt{{0,1}}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tabulate*/list/01
|
||||
2
|
||||
`(,(λ (xs) (cast (min (car xs) (cadr xs)) (U Zero One)))
|
||||
|
|
@ -327,7 +330,7 @@ More precisely, given a line of @racket[table] without its last element, the
|
|||
function returned by @racket[table->function/list] produces the corresponding
|
||||
last element.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define tab : (Listof (Listof Boolean))
|
||||
'((#f #f #f)
|
||||
(#f #t #f)
|
||||
|
|
@ -344,7 +347,7 @@ last element.
|
|||
Like @racket[table->function/list], but the resulting function takes a variable
|
||||
number of arguments rather than a list of values.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define my-and (table->function tab))
|
||||
(my-and #f #t)
|
||||
(my-and #t #t)
|
||||
|
|
@ -359,7 +362,7 @@ raised by the function returned by @racket[table->function]. In other words,
|
|||
the returned by @racket[table->function/pv] is
|
||||
@seclink["pseudovariadic"]{pseudovariadic}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define my-and/pv (table->function/pv tab))
|
||||
(my-and/pv #f #t)
|
||||
(eval:error (my-and/pv #f))
|
||||
|
|
@ -374,7 +377,7 @@ arity @racket[n].
|
|||
|
||||
There are @tt{2^(2^n)} Boolean functions of arity @racket[n].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(require typed/racket/stream)
|
||||
(stream->list (enumerate-boolean-tables 1))
|
||||
]}
|
||||
|
|
@ -386,7 +389,7 @@ Returns the stream of all Boolean functions of a given arity @racket[n].
|
|||
|
||||
There are @tt{2^(2^n)} Boolean functions of arity @racket[n].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(length (stream->list (enumerate-boolean-functions 2)))
|
||||
]}
|
||||
|
||||
|
|
@ -396,7 +399,7 @@ There are @tt{2^(2^n)} Boolean functions of arity @racket[n].
|
|||
Like @racket[enumerate-boolean-functions], but the returned functions are
|
||||
@seclink["pseudovariadic"]{pseudovariadic}.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define bool-f1/pv (stream-first (enumerate-boolean-functions/pv 2)))
|
||||
(bool-f1/pv #f #f)
|
||||
(eval:error (bool-f1/pv #f))
|
||||
|
|
@ -409,7 +412,7 @@ Like @racket[enumerate-boolean-functions], but the returned functions are
|
|||
Like @racket[enumerate-boolean-functions], but the returned functions take
|
||||
their arguments as a single list.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define bool-f1/list (stream-first (enumerate-boolean-functions/list 2)))
|
||||
(bool-f1/list '(#f #f))
|
||||
]}
|
||||
|
|
@ -420,7 +423,7 @@ their arguments as a single list.
|
|||
|
||||
Generates a random truth table for a Boolean function of arity @racket[n].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(random-boolean-table 2)
|
||||
]}
|
||||
|
||||
|
|
@ -428,7 +431,7 @@ Generates a random truth table for a Boolean function of arity @racket[n].
|
|||
|
||||
Generates a random Boolean function of arity @racket[n].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define random-bool-f (random-boolean-function 2))
|
||||
(random-bool-f #t #f)
|
||||
]}
|
||||
|
|
@ -438,7 +441,7 @@ Generates a random Boolean function of arity @racket[n].
|
|||
Like @racket[random-boolean-function], but the constructed function takes
|
||||
a list of arguments.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define random-bool-f/list (random-boolean-function/list 2))
|
||||
(random-bool-f/list '(#t #f))
|
||||
]}
|
||||
|
|
@ -464,7 +467,7 @@ Shortcuts for @racket[tbf-weights] and @racket[tbf-threshold].
|
|||
|
||||
Converts a Boolean vector to a vector of zeros and ones.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(boolean->01/vector #(#t #f #f))
|
||||
]}
|
||||
|
||||
|
|
@ -476,7 +479,7 @@ Applying a TBF consists in multiplying the weights by the corresponding inputs
|
|||
and comparing the sum of the products to the threshold. If the product is
|
||||
above the threshold, the function is 1, otherwise it is 0.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define simple-tbf (tbf #(2 -2) 1))
|
||||
(tabulate/pv/01 2 (pvλ (x y) (apply-tbf simple-tbf (vector x y))))
|
||||
]}
|
||||
|
|
@ -486,7 +489,7 @@ above the threshold, the function is 1, otherwise it is 0.
|
|||
Like @racket[apply-tbf], but takes Boolean values as inputs and outputs
|
||||
a Boolean value.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(define simple-tbf (tbf #(2 -2) 1))
|
||||
(tabulate/pv/boolean 2 (pvλ (x y) (apply-tbf/boolean simple-tbf (vector x y))))
|
||||
]}
|
||||
|
|
@ -496,7 +499,7 @@ a Boolean value.
|
|||
Converts a list of numbers to a TBF. The last element of the list is taken to
|
||||
be the threshold, while the other elements are taken to be the weights.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(list->tbf '(1 2 3))
|
||||
]}
|
||||
|
||||
|
|
@ -507,7 +510,7 @@ Converts multiple lists of numbers to a list of TBFs.
|
|||
The main use is for reading TBFs from Org-mode tables read by
|
||||
@racket[read-org-sexp].
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(lists->tbfs '((1 2 3) (2 3 4)))
|
||||
]}
|
||||
|
||||
|
|
@ -520,7 +523,7 @@ supposing that it contains the headers of the table.
|
|||
|
||||
The input is typically what @racket[read-org-sexp] reads.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(read-org-tbfs "((1 2 1) (1 0 1))")
|
||||
]}
|
||||
|
||||
|
|
@ -536,7 +539,7 @@ elements give the values of each the functions corresponding to the input.
|
|||
All the TBFs in @racket[tbfs] must have the same number of inputs as the first
|
||||
TBF in the list.
|
||||
|
||||
@examples[#:eval functions-evaluator
|
||||
@ex[
|
||||
(tbf-tabulate* (list (tbf #(2 2) 1) (tbf #(1 1) 1)))
|
||||
]}
|
||||
|
||||
|
|
@ -566,6 +569,9 @@ accompanied by the explicit mention "untyped".
|
|||
[sandbox-memory-limit 50])
|
||||
(make-evaluator 'racket #:requires '((submod "functions.rkt" typed untyped)))))
|
||||
|
||||
@(define-syntax-rule (ex/untyped . args)
|
||||
(examples #:eval functions-evaluator/untyped . args))
|
||||
|
||||
@defproc[(tabulate [funcs procedure?]
|
||||
[doms (listof list?)])
|
||||
(listof list?)]{
|
||||
|
|
@ -574,7 +580,7 @@ Given a function @racket[func] and a list of domains @racket[doms] for each of
|
|||
its arguments, in order, produces a list of lists giving the values of
|
||||
arguments and the value of the functions for these inputs.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate (λ (x y) (and x y)) '((#f #t) (#f #t)))
|
||||
]}
|
||||
|
||||
|
|
@ -585,7 +591,7 @@ arguments and the value of the functions for these inputs.
|
|||
Like @racket[tabulate] (untyped), but @racket[funcs] is a list of functions
|
||||
taking the same arguments over the same domains.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate* (list (λ (x y) (and x y))
|
||||
(λ (x y) (or x y)))
|
||||
'((#f #t) (#f #t)))
|
||||
|
|
@ -597,7 +603,7 @@ Like @racket[tabulate] (untyped), but assumes the domains of all variables of
|
|||
the function are Boolean. @racket[func] must have a fixed arity. It is an
|
||||
error to supply a function of variable arity.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate/boolean (lambda (x y) (and x y)))
|
||||
]}
|
||||
|
||||
|
|
@ -607,7 +613,7 @@ error to supply a function of variable arity.
|
|||
Like @racket[tabulate/boolean], but takes a list of functions of the
|
||||
same arity.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate*/boolean `(,(λ (x y) (and x y))
|
||||
,(λ (x y) (or x y))))
|
||||
]}
|
||||
|
|
@ -618,7 +624,7 @@ Like @racket[tabulate] (untyped), but assumes the domains of all variables of
|
|||
the function are @tt{{0,1}}. @racket[func] must have a fixed arity. It is an
|
||||
error to supply a function of variable arity.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate/01 (λ (x y) (modulo (+ x y) 2)))
|
||||
]
|
||||
|
||||
|
|
@ -630,6 +636,6 @@ The same remarks apply as for @racket[tabulate/boolean] (untyped).
|
|||
|
||||
Like @racket[tabulate/01], but takes a list of functions of the same arity.
|
||||
|
||||
@examples[#:eval functions-evaluator/untyped
|
||||
@ex/untyped[
|
||||
(tabulate*/01 `(,(λ (x y) (min x y)) ,(λ (x y) (max x y))))
|
||||
]}
|
||||
|
|
|
|||
Loading…
Reference in New Issue