networks: Add tabulate and illustrate it in example.

example/example.org

@@ -471,6 +471,44 @@ tab
    [[file:dots/examplehsuRqc.svg]]
    :END:
 
+** Network functions
+ =dds/networks= provides some basic primitives for working with
+   individual functions which may appear in a network model.  Clearly,
+   these primitives can be applied in contexts not necessarily
+   directly related to networks.
+
+   Here's how you can tabulate a function.  The domain of x is {1, 2},
+   and the domain of y is {0, 2, 4}.  The first column in the output
+   corresponds to x, the second to y, and the third corresponds to the
+   value of the function.
+
+   #+BEGIN_SRC racket :results table drawer
+(tabulate (λ (x y) (+ x y)) '(1 2) '(0 2 4))
+   #+END_SRC
+
+   #+RESULTS:
+   :RESULTS:
+   | 1 | 0 | 1 |
+   | 1 | 2 | 3 |
+   | 1 | 4 | 5 |
+   | 2 | 0 | 2 |
+   | 2 | 2 | 4 |
+   | 2 | 4 | 6 |
+   :END:
+
+   Here's how you tabulate a Boolean function:
+   #+BEGIN_SRC racket :results table drawer
+(tabulate/boolean (λ (x y) (and x y)))
+   #+END_SRC
+
+   #+RESULTS:
+   :RESULTS:
+   | #f | #f | #f |
+   | #f | #t | #f |
+   | #t | #f | #f |
+   | #t | #t | #t |
+   :END:
+
 * Reaction systems
   :PROPERTIES:
   :header-args:racket: :prologue "#lang racket\n(require graph (file \"~/Candies/prj/racket/dds/rs.rkt\") (file \"~/Candies/prj/racket/dds/utils.rkt\"))"

networks-tests.rkt

@@ -207,3 +207,11 @@
     (check-equal? (edge-weight gr-complete-bool-ann
                                #hash((a . #f) (b . #t)) #hash((a . #t) (b . #t)))
                   (set (set 'a)))))
+
+(test-case "Functions"
+  (check-equal? (tabulate/domain-list (λ (x y) (and x y)) '((#f #t) (#f #t)))
+                '((#f #f #f) (#f #t #f) (#t #f #f) (#t #t #t)))
+  (check-equal? (tabulate (λ (x y) (and x y)) '(#f #t) '(#f #t))
+                '((#f #f #f) (#f #t #f) (#t #f #f) (#t #t #t)))
+  (check-equal? (tabulate/boolean (lambda (x y) (and x y)))
+                '((#f #f #f) (#f #t #f) (#t #f #f) (#t #t #t))))

networks.rkt

@@ -55,7 +55,10 @@
                [pretty-print-state-graph (-> graph? graph?)]
                [pretty-print-boolean-state-graph (-> graph? graph?)]
                [build-full-boolean-state-graph (-> dynamics? graph?)]
-               [build-full-boolean-state-graph-annotated (-> dynamics? graph?)])
+               [build-full-boolean-state-graph-annotated (-> dynamics? graph?)]
+               [tabulate/domain-list (-> procedure? (listof generic-set?) (listof list?))]
+               [tabulate (->* (procedure?) () #:rest (listof generic-set?) (listof list?))]
+               [tabulate/boolean (-> procedure-fixed-arity? (listof (listof boolean?)))])
  ;; Predicates
  (contract-out [variable? (-> any/c boolean?)]
                [state? (-> any/c boolean?)]
@@ -385,3 +388,24 @@
   (dds-build-state-graph-annotated
    dyn
    (list->set (build-all-boolean-states (hash-keys (dynamics-network dyn))))))
+
+
+;;; =========
+;;; Functions
+;;; =========
+
+;;; Given a function and a list of domains 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.
+(define (tabulate/domain-list func doms)
+  (for/list ([xs (apply cartesian-product doms)])
+    (append xs (list (apply func xs)))))
+
+;;; Like tabulate, but the domains are given as a rest argument.
+(define (tabulate func . doms) (tabulate/domain-list func doms))
+
+;;; Like tabulate, but assumes the domains of all variables of the
+;;; function are Boolean.  func must have a fixed arity.  It is an
+;;; error to supply a function of variable arity.
+(define (tabulate/boolean func)
+  (tabulate/domain-list func (make-list (procedure-arity func) '(#f #t))))