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Type enumerate-boolean-tables.

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This commit is contained in:
Sergiu Ivanov 2022-04-18 01:00:34 +02:00
parent 4272cd87a8
commit fa63875022
2 changed files with 59 additions and 16 deletions
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59
functions.rkt
View file

@ -11,7 +11,7 @@
(module typed typed/racket
(require "utils.rkt"
syntax/parse/define
syntax/parse/define typed/racket/stream
(only-in typed/racket/unsafe unsafe-provide)
(for-syntax syntax/parse))
@ -19,7 +19,8 @@
pseudovariadic-lambda pvλ pseudovariadic-define pvdefine
tabulate* tabulate*/strict tabulate*/pv tabulate tabulate/strict tabulate/pv
tabulate*/pv/boolean tabulate/pv/boolean tabulate*/pv/01 tabulate/pv/01
table->function/list table->function table->function/pv)
table->function/list table->function table->function/pv
enumerate-boolean-tables)
(module+ test
(require typed/rackunit))
@ -235,6 +236,45 @@
(check-false (negation #t))
(check-exn exn:fail? (λ () (negation #f #t)))))
(: enumerate-boolean-tables (-> Integer (Sequenceof (Listof (Listof Boolean)))))
(define (enumerate-boolean-tables n)
(define inputs (boolean-power n))
(define outputs (boolean-power/stream (cast (expt 2 n) Integer)))
(: append-outputs (-> (Listof (Listof Boolean)) (Listof Boolean)
(Listof (Listof Boolean))))
(define (append-outputs ins outs)
(for/list ([row ins] [o outs]) (append row (list o))))
(: yield (-> (Sequenceof (Listof Boolean)) (Sequenceof (Listof (Listof Boolean)))))
(define (yield rest-outputs)
(if (stream-empty? rest-outputs)
(stream)
(stream-cons (append-outputs inputs (stream-first rest-outputs))
(yield (stream-rest rest-outputs)))))
(yield outputs))
(module+ test
(test-case "enumerate-boolean-tables"
(check-equal? (stream->list (enumerate-boolean-tables 2))
'(((#f #f #f) (#f #t #f) (#t #f #f) (#t #t #f))
((#f #f #f) (#f #t #f) (#t #f #f) (#t #t #t))
((#f #f #f) (#f #t #f) (#t #f #t) (#t #t #f))
((#f #f #f) (#f #t #f) (#t #f #t) (#t #t #t))
((#f #f #f) (#f #t #t) (#t #f #f) (#t #t #f))
((#f #f #f) (#f #t #t) (#t #f #f) (#t #t #t))
((#f #f #f) (#f #t #t) (#t #f #t) (#t #t #f))
((#f #f #f) (#f #t #t) (#t #f #t) (#t #t #t))
((#f #f #t) (#f #t #f) (#t #f #f) (#t #t #f))
((#f #f #t) (#f #t #f) (#t #f #f) (#t #t #t))
((#f #f #t) (#f #t #f) (#t #f #t) (#t #t #f))
((#f #f #t) (#f #t #f) (#t #f #t) (#t #t #t))
((#f #f #t) (#f #t #t) (#t #f #f) (#t #t #f))
((#f #f #t) (#f #t #t) (#t #f #f) (#t #t #t))
((#f #f #t) (#f #t #t) (#t #f #t) (#t #t #f))
((#f #f #t) (#f #t #t) (#t #f #t) (#t #t #t))))))
(module untyped racket
(module+ test
(require rackunit))
@ -316,7 +356,8 @@
tabulate tabulate/strict tabulate/pv
tabulate*/pv/boolean tabulate/pv/boolean
tabulate*/pv/01 tabulate/pv/01
table->function/list table->function table->function/pv)
table->function/list table->function table->function/pv
enumerate-boolean-tables)
(require (rename-in (submod 'typed untyped)
[tabulate tabulate/untyped]
@ -328,7 +369,6 @@
[struct tbf ((weights (vectorof number?)) (threshold number?))])
;; Functions
(contract-out
[enumerate-boolean-tables (-> number? (stream/c (listof (*list/c boolean? boolean?))))]
[enumerate-boolean-functions (-> number? (stream/c procedure?))]
[enumerate-boolean-functions/list (-> number? (stream/c procedure?))]
[random-boolean-table (-> number? (listof (*list/c boolean? boolean?)))]
@ -360,17 +400,6 @@
;;; Constructing functions
;;; ======================
;;; Returns the stream of the truth tables of all Boolean functions of
;;; a given arity.
;;;
;;; There are 2^(2^n) Boolean functions of arity n.
(define (enumerate-boolean-tables n)
(let ([inputs (boolean-power/stream n)]
[outputs (boolean-power/stream (expt 2 n))])
(for/stream ([out (in-stream outputs)])
(for/list ([in (in-stream inputs)] [o out])
(append in (list o))))))
;;; Returns the stream of all Boolean functions of a given arity.
;;;
;;; There are 2^(2^n) Boolean functions of arity n.

16
scribblings/functions.scrbl
View file

@ -1,7 +1,8 @@
#lang scribble/manual
@(require scribble/example racket/sandbox
(for-label typed/racket/base "../functions.rkt" dds/utils
typed/racket/unsafe))
typed/racket/unsafe
(only-in racket stream->list)))
@title[#:tag "functions"]{dds/functions: Formal Functions}
@ -289,6 +290,19 @@ the returned by @racket[table->function/pv] is
(eval:error (my-and #f))
]}
@defproc[(enumerate-boolean-tables [n Integer])
(Sequenceof (Listof (Listof Boolean)))]{
Returns the stream of the truth tables of all Boolean functions of
arity @racket[n].
There are @tt{2^(2^n)} Boolean functions of arity @racket[n].
@examples[#:eval functions-evaluator
(require typed/racket/stream)
(stream->list (enumerate-boolean-tables 1))
]}
@section{Random functions}
@section{Threshold Boolean functions}