From 6e942167bfbdf266e3402976ae542e1486cd56ed Mon Sep 17 00:00:00 2001 From: Matthew Butterick Date: Sat, 27 Oct 2018 16:02:24 -0700 Subject: [PATCH] in-solutions --- csp/csp/hacs.rkt | 208 +++++++++++++++++----------------- csp/csp/scribblings/csp.scrbl | 16 +-- 2 files changed, 116 insertions(+), 108 deletions(-) diff --git a/csp/csp/hacs.rkt b/csp/csp/hacs.rkt index 13a79541..a967fc3f 100644 --- a/csp/csp/hacs.rkt +++ b/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))) diff --git a/csp/csp/scribblings/csp.scrbl b/csp/csp/scribblings/csp.scrbl index b88585be..f24aff53 100644 --- a/csp/csp/scribblings/csp.scrbl +++ 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}