in-solutions

csp/csp/hacs.rkt

@@ -1,6 +1,6 @@
 #lang debug racket
 (require racket/generator graph)
-(provide (all-defined-out))
+(provide (except-out (all-defined-out) define/contract))
 
 (define-syntax-rule (define/contract EXPR CONTRACT . BODY)
   (define EXPR . BODY))
@@ -23,7 +23,7 @@
                     (if (null? argss)
                         (yield (reverse acc))
                         (for ([arg (car argss)])
-                          (loop (cdr argss) (cons arg acc))))))))
+                             (loop (cdr argss) (cons arg acc))))))))
 
 (struct csp (vars constraints) #:mutable #:transparent)
 (define constraints csp-constraints)
@@ -39,7 +39,7 @@
       (raise-argument-error 'constraint "csp" prob))
     ;; apply proc in many-to-many style
     (for/and ([args (in-cartesian (map (λ (name) (find-domain prob name)) (constraint-names const)))])
-      (apply (constraint-proc const) args))))
+             (apply (constraint-proc const) args))))
 
 (define name? symbol?)
 
@@ -100,11 +100,11 @@
   ((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
   (set-csp-constraints! prob (append (constraints prob) 
                                      (for/list ([names (in-list namess)])
-                                       (for ([name (in-list names)])
-                                         (check-name-in-csp! 'add-constraints! prob name))
-                                       (make-constraint names (if proc-name
-                                                                  (procedure-rename proc proc-name)
-                                                                  proc))))))
+                                               (for ([name (in-list names)])
+                                                    (check-name-in-csp! 'add-constraints! prob name))
+                                               (make-constraint names (if proc-name
+                                                                          (procedure-rename proc proc-name)
+                                                                          proc))))))
 
 (define/contract (add-pairwise-constraint! prob proc names [proc-name #false])
   ((csp? procedure? (listof name?)) (name?) . ->* . void?)
@@ -143,7 +143,7 @@
   (check-name-in-csp! 'find-var prob name)
   (for/first ([vr (in-vars prob)]
               #:when (eq? name (var-name vr)))
-    vr))
+             vr))
 
 (define/contract (find-domain prob name)
   (csp? name? . -> . (listof any/c))
@@ -186,20 +186,20 @@
     (ormap assigned? (constraint-names constraint)))
   (make-csp (vars prob)
             (for/list ([const (in-constraints prob)])
-              (cond
-                ;; no point reducing 2-arity functions because they will be consumed by forward checking
-                [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
-                      (partially-assigned? const))
-                 (match-define (constraint cnames proc) const)
-                 ;; pattern is mix of values and boxed symbols (indicating variables to persist)
-                 ;; use boxes here as cheap way to distinguish id symbols from value symbols
-                 (define arity-reduction-pattern (for/list ([cname (in-list cnames)])
-                                                   (if (assigned? cname)
-                                                       (first (find-domain prob cname))
-                                                       (box cname))))
-                 (constraint (filter-not assigned? cnames)
-                             (reduce-function-arity proc arity-reduction-pattern))]
-                [else const]))))
+                      (cond
+                        ;; no point reducing 2-arity functions because they will be consumed by forward checking
+                        [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
+                              (partially-assigned? const))
+                         (match-define (constraint cnames proc) const)
+                         ;; pattern is mix of values and boxed symbols (indicating variables to persist)
+                         ;; use boxes here as cheap way to distinguish id symbols from value symbols
+                         (define arity-reduction-pattern (for/list ([cname (in-list cnames)])
+                                                                   (if (assigned? cname)
+                                                                       (first (find-domain prob cname))
+                                                                       (box cname))))
+                         (constraint (filter-not assigned? cnames)
+                                     (reduce-function-arity proc arity-reduction-pattern))]
+                        [else const]))))
 
 (define nassns 0)
 (define nfchecks 0)
@@ -214,9 +214,9 @@
   (begin0
     (make-csp
      (for/list ([vr (in-vars prob)])
-       (if (eq? name (var-name vr))
-           (assigned-var name (list val))
-           vr))
+               (if (eq? name (var-name vr))
+                   (assigned-var name (list val))
+                   vr))
      (constraints prob))
     (when-debug (set! nassns (add1 nassns)))))
 
@@ -246,7 +246,7 @@
      (for/list ([x (in-list xs)]
                 [val (in-list vals)]
                 #:when (= val target-val))
-       x)]))
+               x)]))
 
 (define/contract (argmax* proc xs)
   (procedure? (listof any/c) . -> . (listof any/c))
@@ -271,7 +271,7 @@
   (csp? var? . -> . natural?)
   (for/sum ([const (in-constraints prob)]
             #:when (memq (var-name var) (constraint-names const)))
-    1))
+           1))
 
 (define/contract (domain-length var)
   (var? . -> . natural?)
@@ -280,7 +280,7 @@
 (define/contract (state-count csp)
   (csp? . -> . natural?)
   (for/product ([vr (in-vars csp)])
-    (domain-length vr)))
+               (domain-length vr)))
 
 (define/contract (mrv-degree-hybrid prob)
   (csp? . -> . (or/c #f var?))
@@ -299,8 +299,8 @@
               [cnames (in-value (constraint-names const))]
               #:when (and (= (length names) (length cnames))
                           (for/and ([name (in-list names)])
-                            (memq name cnames))))
-    const))
+                                   (memq name cnames))))
+             const))
 
 (define (one-arity? const) (= 1 (constraint-arity const)))
 (define (two-arity? const) (= 2 (constraint-arity const)))
@@ -314,7 +314,7 @@
   ((listof (and/c constraint? two-arity?)) . -> . (listof arc?))
   (for*/list ([const (in-list constraints)]
               [name (in-list (constraint-names const))])
-    (arc name const)))
+             (arc name const)))
 
 (require sugar/debug)
 (define/contract (reduce-domain prob ark)
@@ -326,16 +326,16 @@
                    (λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
   (define (satisfies-arc? val)
     (for/or ([other-val (in-list (find-domain prob other-name))])
-      (proc val other-val)))
+            (proc val other-val)))
   (make-csp
    (for/list ([vr (in-vars prob)])
-     (cond
-       [(assigned-var? vr) vr]
-       [(eq? name (var-name vr))
-        (make-var name (match (filter satisfies-arc? (domain vr))
-                         [(? empty?) (backtrack!)]
-                         [vals vals]))]
-       [else vr]))
+             (cond
+               [(assigned-var? vr) vr]
+               [(eq? name (var-name vr))
+                (make-var name (match (filter satisfies-arc? (domain vr))
+                                 [(? empty?) (backtrack!)]
+                                 [vals vals]))]
+               [else vr]))
    (constraints prob)))
 
 (define/contract (terminating-at? arcs name)
@@ -344,7 +344,7 @@
              #:when (and
                      (memq name (constraint-names (arc-const arc)))
                      (not (eq? name (arc-name arc)))))
-    arc))
+            arc))
 
 (define/contract (ac-3 prob ref-name)
   (csp? name? . -> . csp?)
@@ -355,8 +355,8 @@
     (two-arity-constraints->arcs (for/list ([const (in-constraints prob)]
                                             #:when (and (two-arity? const)
                                                         (for/and ([cname (in-list (constraint-names const))])
-                                                          (memq cname checkable-names))))
-                                   const)))
+                                                                 (memq cname checkable-names))))
+                                           const)))
   (for/fold ([prob prob]
              [arcs (sort starting-arcs < #:key (λ (a) (length (find-domain prob (arc-name a)))) #:cache-keys? #true)]
              #:result (prune-singleton-constraints prob))
@@ -386,10 +386,10 @@
         (define new-vals
           (for/list ([val (in-list vals)]
                      #:when (for/and ([const (in-list constraints)])
-                              (match const
-                                  [(constraint (list (== name eq?) _) proc) (proc val ref-val)]
-                                  [(constraint _ proc) (proc ref-val val)])))
-            val))
+                                     (match const
+                                       [(constraint (list (== name eq?) _) proc) (proc val ref-val)]
+                                       [(constraint _ proc) (proc ref-val val)])))
+                    val))
         (checked-variable name new-vals (cons (cons ref-name ref-val) (match vr
                                                                         [(checked-variable _ _ history) history]
                                                                         [_ null])))])]))
@@ -398,15 +398,15 @@
   ((csp?) ((or/c #false name?)) . ->* . csp?)
   (define singleton-var-names (for/list ([vr (in-vars prob)]
                                          #:when (singleton-var? vr))
-                                (var-name vr)))
+                                        (var-name vr)))
   (make-csp
    (vars prob)
    (for/list ([const (in-constraints prob)]
               #:unless (and (two-arity? const)
                             (or (not ref-name) (constraint-relates? const ref-name))
                             (for/and ([cname (in-list (constraint-names const))])
-                              (memq cname singleton-var-names))))
-     const)))
+                                     (memq cname singleton-var-names))))
+             const)))
 
 (define/contract (forward-check prob ref-name)
   (csp? name? . -> . csp?)
@@ -415,7 +415,7 @@
   ;; conflict-set will be empty if there are no empty domains (as we would hope)
   (define conflict-set (for/list ([cvr (in-list checked-vars)]
                                   #:when (empty? (domain cvr)))
-                         (history cvr)))
+                                 (history cvr)))
   ;; for conflict-directed backjumping it's essential to forward-check ALL vars
   ;; (even after an empty domain is generated) and combine their conflicts
   ;; so we can discover the *most recent past var* that could be the culprit.
@@ -432,7 +432,7 @@
   ;; constraint is checkable if all constraint names
   ;; are in target list of names.
   (for/and ([cname (in-list (constraint-names const))])
-    (memq cname names)))
+           (memq cname names)))
 
 (define/contract (constraint-arity const)
   (constraint? . -> . natural?)
@@ -449,21 +449,21 @@
     (partition (λ (const) (and (constraint-checkable? const assigned-varnames)
                                (or (not mandatory-names)
                                    (for/and ([name (in-list mandatory-names)])
-                                     (constraint-relates? const name)))))
+                                            (constraint-relates? const name)))))
                (constraints prob)))
   (cond
     [conflict-count?
      (define conflict-count
        (for/sum ([constraint (in-list checkable-consts)]
                  #:unless (constraint prob))
-         1))
+                1))
      (when-debug (set! nchecks (+ conflict-count nchecks)))
      conflict-count]
     [else
      (for ([(constraint idx) (in-indexed checkable-consts)]
            #:unless (constraint prob))
-       (when-debug (set! nchecks (+ (add1 idx) nchecks)))
-       (backtrack!))
+          (when-debug (set! nchecks (+ (add1 idx) nchecks)))
+          (backtrack!))
      ;; discard checked constraints, since they have no further reason to live
      (make-csp (vars prob) other-consts)]))
 
@@ -475,19 +475,19 @@
       prob
       (make-csp
        (for/list ([vr (in-vars prob)])
-         (match-define (var name vals) vr)
-         (define name-constraints (filter (λ (const) (constraint-relates? const name)) unary-constraints))
-         (make-var name (for/list ([val (in-list vals)]
-                                   #:when (for/and ([const (in-list name-constraints)])
-                                            ((constraint-proc const) val)))
-                          val)))
+                 (match-define (var name vals) vr)
+                 (define name-constraints (filter (λ (const) (constraint-relates? const name)) unary-constraints))
+                 (make-var name (for/list ([val (in-list vals)]
+                                           #:when (for/and ([const (in-list name-constraints)])
+                                                           ((constraint-proc const) val)))
+                                          val)))
        other-constraints)))
 
 (define ((make-hist-proc assocs) . xs)
   (not
    (for/and ([x (in-list xs)]
              [val (in-list (map cdr assocs))])
-     (equal? x val))))
+            (equal? x val))))
 
 (define/contract (backtracking-solver
                   prob
@@ -508,7 +508,7 @@
                     (and (backtrack? exn) (or (let ([bths (backtrack-histories exn)])
                                                 (or (empty? bths) (for*/or ([bth bths]
                                                                             [rec bth])
-                                                                    (eq? name (car rec))))))))
+                                                                           (eq? name (car rec))))))))
                   (for/fold ([conflicts null]
                              #:result (void))
                             ([val (in-list (order-domain-values domain))])
@@ -518,7 +518,7 @@
                                        (append conflicts (remq name (remove-duplicates
                                                                      (for*/list ([bth (in-list bths)]
                                                                                  [rec (in-list bth)])
-                                                                       (car rec)) eq?))))])
+                                                                                (car rec)) eq?))))])
                       (let* ([prob (assign-val prob name val)]
                              ;; reduce constraints before inference,
                              ;; to create more forward-checkable (binary) constraints
@@ -560,9 +560,9 @@
   ((csp?) (integer?) . ->* . generator?)
   (generator ()
              (for ([thread-count (or (current-thread-count) 1)]) ; todo: what is ideal thread count?
-               (make-min-conflcts-thread prob thread-count max-steps))
+                  (make-min-conflcts-thread prob thread-count max-steps))
              (for ([i (in-naturals)])
-               (yield (thread-receive)))))
+                  (yield (thread-receive)))))
 
 (define/contract (optimal-stop-min proc xs)
   (procedure? (listof any/c) . -> . any/c)
@@ -570,7 +570,7 @@
   (define threshold (argmin proc sample))
   (or (for/first ([candidate (in-list candidates)]
                   #:when (<= (proc candidate) threshold))
-        candidate)
+                 candidate)
       (last candidates)))
 
 (define/contract (conflicted-variable-names prob)
@@ -578,7 +578,7 @@
   ;; Return a list of variables in current assignment that are conflicted
   (for/list ([name (in-var-names prob)]
              #:when (positive? (nconflicts prob name)))
-    name))
+            name))
  
 (define/contract (min-conflicts-value prob name vals)
   (csp? name? (listof any/c) . -> . any/c)
@@ -587,7 +587,7 @@
                                  #:cache-keys? #true))
   (for/first ([val (in-list vals-by-conflict)]
               #:unless (equal? val (first (find-domain prob name)))) ;; but change the value
-    val))
+             val))
 
 (define no-value-sig (gensym))
 
@@ -602,11 +602,11 @@
   ((csp?) ((listof name?)) . ->* . (listof (cons/c name? any/c)))
   (define assocs
     (for/list ([vr (in-vars prob)])
-      (match vr
-        [(var name (list val)) (cons name val)])))
+              (match vr
+                [(var name (list val)) (cons name val)])))
   (if keys
       (for/list ([key (in-list keys)])
-        (assq key assocs))
+                (assq key assocs))
       assocs))
 
 (define/contract (combine-csps probs)
@@ -621,45 +621,51 @@
   (make-csp
    (for/list ([vr (in-vars prob)]
               #:when (memq (var-name vr) names))
-     vr)
+             vr)
    (for/list ([const (in-constraints prob)]
               #:when (for/and ([cname (in-list (constraint-names const))])
-                       (memq cname names)))
-     const)))
+                              (memq cname names)))
+             const)))
 
-(define/contract (solve* prob
+(define (decompose-prob prob)
+  ; decompose into independent csps. `cc` determines "connected components"
+  (if (current-decompose)
+      (for/list ([nodeset (in-list (cc (csp->graph prob)))])
+                (extract-subcsp prob nodeset))
+      (list prob)))
+
+(define (make-solution-generator prob)
+  (generator ()
+             (define subprobs (decompose-prob prob))
+             (define solgens (map (current-solver) subprobs))
+             (define solstreams (for/list ([solgen (in-list solgens)])
+                                          (for/stream ([sol (in-producer solgen (void))]) 
+                                                      sol)))
+             (for ([solution-pieces (in-cartesian solstreams)])
+                  (yield (combine-csps solution-pieces)))))
+
+(define-syntax-rule (in-solutions PROB)
+  (in-producer (make-solution-generator PROB) (void)))
+
+(define/contract (solve* prob [max-solutions +inf.0]
                          #:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]
-                         #:solver [solver (or (current-solver) backtracking-solver)]
-                         #:count [max-solutions +inf.0])
-  ((csp?) (#:finish-proc procedure? #:solver procedure? #:count natural?)
-          . ->* . (listof any/c))
+                         #:solver [solver #f])
+  ((csp?) (natural? #:finish-proc procedure? #:solver procedure?) . ->* . (listof any/c))
   (when-debug (reset-nassns!) (reset-nfchecks!) (reset-nchecks!))          
 
-  (define subcsps ; decompose into independent csps. `cc` determines "connected components"
-    (if (current-decompose)
-        (for/list ([nodeset (in-list (cc (csp->graph prob)))])
-          (extract-subcsp prob nodeset))
-        (list prob)))
-
-  (define solgens (map solver subcsps))
-  (define solstreams (for/list ([solgen (in-list solgens)])
-                       (for/stream ([sol (in-producer solgen (void))]) 
-                         sol)))
-  
-  (for/list ([solution-pieces (in-cartesian solstreams)]
-             [idx (in-range max-solutions)])
-    (finish-proc (combine-csps solution-pieces))))
+  (parameterize ([current-solver (or solver (current-solver) backtracking-solver)])
+    (for/list ([sol (in-solutions prob)]
+               [idx (in-range max-solutions)])
+              (finish-proc sol))))
 
 (define/contract (solve prob
                         #:finish-proc [finish-proc (λ (p) (csp->assocs p (map var-name (vars prob))))]
-                        #:solver [solver (or (current-solver) backtracking-solver)]
-                        #:count [max-solutions 1])
-  ((csp?) (#:finish-proc procedure? #:solver procedure? #:count natural?)
+                        #:solver [solver #f])
+  ((csp?) (#:finish-proc procedure? #:solver procedure?)
           . ->* . (or/c #false any/c))
-  (match (solve* prob #:finish-proc finish-proc #:solver solver #:count max-solutions)
+  (match (solve* prob 1 #:finish-proc finish-proc #:solver solver)
     [(list solution) solution]
-    [(list) #false]
-    [(list solutions ...) solutions]))
+    [_ #false]))
 
 (define (<> a b) (not (= a b)))
 (define (neq? a b) (not (eq? a b)))

csp/csp/scribblings/csp.scrbl

@@ -8,7 +8,7 @@
 @(define-syntax-rule (my-examples ARG ...)
 (examples #:label #f #:eval my-eval ARG ...))
 
-@title{Constraint-satisfaction problems}
+@title{Constraint-satisfaction problems (and how to solve them)}
 
 @author[(author+email "Matthew Butterick" "mb@mbtype.com")]
 
@@ -120,11 +120,11 @@ We should use @racket[solve*] with care. It can't finish until the CSP solver e
 (state-count triples)
 ]
 
-It's easy for a CSP to have a state count in the zillions. For this reason we can supply @racket[solve*] with an optional @racket[#:count] argument that will only generate a certain number of solutions: 
+It's easy for a CSP to have a state count in the zillions. For this reason we can supply @racket[solve*] with an optional argument that will only generate a certain number of solutions: 
 
 @examples[#:label #f #:eval my-eval
 (time (solve* triples))
-(time (solve* triples #:count 2))
+(time (solve* triples 2))
 ]
 
 Here, the answers are the same. But the second call to @racket[solve*] finishes sooner, because it quits as soon as it's found two solutions.
@@ -159,7 +159,7 @@ The whole example in one block:
 
 (add-constraint! triples <= '(a b))
 
-(solve* triples #:count 2)
+(solve* triples 2)
 ]
 
 @section{Interlude}
@@ -282,19 +282,21 @@ TK
 }
 
 @defproc[(solve 
-[prob csp?] 
-[#:count count natural? 1])
+[prob csp?] )
 (or/c #false any/c (listof any/c))]{
 TK
 }
 
 @defproc[(solve* 
 [prob csp?] 
-[#:count count natural? +inf.0])
+[count natural? +inf.0])
 (listof any/c)]{
 TK
 }
 
+@defform[(in-solutions prob)]{
+TK
+}
 
 
 @section{Sideshows}