From 2c79ca37813ca58cc903fff18a8b9261f126dc13 Mon Sep 17 00:00:00 2001
From: Sergiu Ivanov <sivanov@colimite.fr>
Date: Thu, 19 Mar 2020 23:40:08 +0100
Subject: [PATCH] networks: Add enumerate-boolean-tables,
 enumerate-boolean-functions, and enumerate-boolean-functions/list.

---
 networks-tests.rkt |  6 +++++-
 networks.rkt       | 39 ++++++++++++++++++++++++++++++++++++++-
 2 files changed, 43 insertions(+), 2 deletions(-)

diff --git a/networks-tests.rkt b/networks-tests.rkt
index ffc6176..187a073 100644
--- a/networks-tests.rkt
+++ b/networks-tests.rkt
@@ -218,4 +218,8 @@
   (let ([negation (table->function '((#t #f) (#f #t)))]
         [negation/list (table->function/list '((#t #f) (#f #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)))))
diff --git a/networks.rkt b/networks.rkt
index 458196e..535c4e5 100644
--- a/networks.rkt
+++ b/networks.rkt
@@ -60,7 +60,10 @@
                [tabulate (->* (procedure?) () #:rest (listof generic-set?) (listof list?))]
                [tabulate/boolean (-> procedure-fixed-arity? (listof (listof boolean?)))]
                [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
  (contract-out [variable? (-> any/c boolean?)]
                [state? (-> any/c boolean?)]
@@ -435,3 +438,37 @@
    (for/hash ([line table])
      (let-values ([(x fx) (split-at-right line 1)])
        (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)))