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networks: Add enumerate-boolean-tables, enumerate-boolean-functions, and enumerate-boolean-functions/list.

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This commit is contained in:
Sergiu Ivanov 2020-03-19 23:40:08 +01:00
parent 80ef41eaa4
commit 2c79ca3781
2 changed files with 43 additions and 2 deletions
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6
networks-tests.rkt
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@ -218,4 +218,8 @@
(let ([negation (table->function '((#t #f) (#f #t)))] (let ([negation (table->function '((#t #f) (#f #t)))]
[negation/list (table->function/list '((#t #f) (#f #t)))]) [negation/list (table->function/list '((#t #f) (#f #t)))])
(check-true (negation #f)) (check-false (negation #t)) (check-true (negation #f)) (check-false (negation #t))
(check-true (negation/list '(#f))) (check-false (negation/list '(#t))))) (check-true (negation/list '(#f))) (check-false (negation/list '(#t))))
(let ([f1 (car (enumerate-boolean-functions 1))]
[f1/list (car (enumerate-boolean-functions/list 1))])
(check-false (f1 #f)) (check-false (f1 #t))
(check-false (f1/list '(#f))) (check-false (f1/list '(#t)))))

39
networks.rkt
View file

@ -60,7 +60,10 @@
[tabulate (->* (procedure?) () #:rest (listof generic-set?) (listof list?))] [tabulate (->* (procedure?) () #:rest (listof generic-set?) (listof list?))]
[tabulate/boolean (-> procedure-fixed-arity? (listof (listof boolean?)))] [tabulate/boolean (-> procedure-fixed-arity? (listof (listof boolean?)))]
[table->function (-> (listof (*list/c any/c any/c)) procedure?)] [table->function (-> (listof (*list/c any/c any/c)) procedure?)]
[table->function/list (-> (listof (*list/c any/c any/c)) procedure?)]) [table->function/list (-> (listof (*list/c any/c any/c)) procedure?)]
[enumerate-boolean-tables (-> number? (listof (listof (*list/c any/c any/c))))]
[enumerate-boolean-functions (-> number? (listof procedure?))]
[enumerate-boolean-functions/list (-> number? (listof procedure?))])
;; Predicates ;; Predicates
(contract-out [variable? (-> any/c boolean?)] (contract-out [variable? (-> any/c boolean?)]
[state? (-> any/c boolean?)] [state? (-> any/c boolean?)]
@ -435,3 +438,37 @@
(for/hash ([line table]) (for/hash ([line table])
(let-values ([(x fx) (split-at-right line 1)]) (let-values ([(x fx) (split-at-right line 1)])
(values x (car fx)))))) (values x (car fx))))))
;;; Returns the n-th Cartesian power of the Boolean domain: {0,1}^n.
(define (boolean-power-n n) (apply cartesian-product (make-list n '(#f #t))))
;;; Enumerates the truth tables of all Boolean functions of a given
;;; arity.
;;;
;;; /!\ There are 2^(2^n) Boolean functions of arity n.
;;;
;;; TODO: Think about making this function lazy.
(define (enumerate-boolean-tables n)
(let ([inputs (boolean-power-n n)]
[outputs (boolean-power-n (expt 2 n))])
(for/list ([out outputs])
(for/list ([in inputs] [o out])
(append in (list o))))))
;;; Enumerates all Boolean functions of a given arity.
;;;
;;; /!\ There are 2^(2^n) Boolean functions of arity n.
;;;
;;; TODO: Think about making this function lazy.
(define (enumerate-boolean-functions n)
(map table->function (enumerate-boolean-tables n)))
;;; Enumerates all Boolean functions of a given arity. As different
;;; from the functions returned by enumerate-boolean-functions, the
;;; functions take lists of arguments instead of n arguments.
;;;
;;; /!\ There are 2^(2^n) Boolean functions of arity n.
;;;
;;; TODO: Think about making this function lazy.
(define (enumerate-boolean-functions/list n)
(map table->function/list (enumerate-boolean-tables n)))