networks: Add interaction?.

networks.rkt

@@ -31,6 +31,7 @@
                                             network?)]
                [list-syntactic-interactions (-> network-form? variable? (listof variable?))]
                [build-syntactic-interaction-graph (-> network-form? graph?)]
+               [interaction? (-> network? domain-mapping/c variable? variable? boolean?)]
                [build-all-states (-> domain-mapping/c (listof state?))]
                [make-same-domains (-> (listof variable?) generic-set? domain-mapping/c)]
                [make-boolean-domains (-> (listof variable?) (hash/c variable? (list/c #f #t)))]
@@ -397,7 +398,41 @@
                     #hash((a . 1) (b . 0))
                     #hash((a . 1) (b . 1))))))
 
+;;; Given two variables x and y of a network f, verifies if they
+;;; interact, i.e. that there exists such a state s with the property
+;;; that s' which is s with a different value for x yields such a new
+;;; state f(s') in which the value for y is different from f(s).
+(define (interaction? network doms x y)
+  (define states-not-x (build-all-states (hash-remove doms x)))
+  (define (different-ys-exist? st)
+    (define x-states (for/list ([x-val (in-list (hash-ref doms x))])
+                       (hash-set st x x-val)))
+    (for*/first ([st1 x-states]
+                 [st2 x-states]
+                 #:unless (equal? (hash-ref st1 x) (hash-ref st2 x))
+                 #:unless (equal? ((hash-ref network y) st1)
+                                  ((hash-ref network y) st2)))
+      #t))
+  (for*/first ([st (in-list states-not-x)]
+               #:when (different-ys-exist? st))
+    #t))
 
+(module+ test
+  (test-case "interaction?"
+    (define n-bool (network-form->network
+                    (hash 'x '(not y)
+                          'y 'x
+                          'z '(and y z))))
+    (define bool-doms (make-boolean-domains '(x y z)))
+    (check-true (interaction? n-bool bool-doms 'x 'y))
+    (check-true (interaction? n-bool bool-doms 'y 'x))
+    (check-false (interaction? n-bool bool-doms 'x 'z))
+    (define n-multi (network-form->network
+                     (hash 'x '(max (+ y 1) 2)
+                           'y '(min (- y 1) 0))))
+    (define 123-doms (make-same-domains '(x y) '(0 1 2)))
+    (check-false (interaction? n-multi 123-doms 'x 'y))
+    (check-true (interaction? n-multi 123-doms 'y 'x))))
 
 ;;; ====================
 ;;; Dynamics of networks