diff --git a/csp/csp/hacs-smm.rkt b/csp/csp/hacs-smm.rkt deleted file mode 100644 index 58e9ac67..00000000 --- a/csp/csp/hacs-smm.rkt +++ /dev/null @@ -1,47 +0,0 @@ -#lang br -(require "hacs.rkt") - -; SEND -;+ MORE -;------ -; MONEY - -(define $vd +var) - -(define (word-value . xs) - (for/sum ([(x idx) (in-indexed (reverse xs))]) - (* x (expt 10 idx)))) - -(define vs '(s e n d m o r y)) -(define vds (for/list ([k vs]) - ($vd k (range 10)))) - -(define (not= x y) (not (= x y))) - -(define alldiffs - (for/list ([pr (in-combinations vs 2)]) - ($constraint pr not=))) - -(define (smm-func s e n d m o r y) - (= (+ (word-value s e n d) (word-value m o r e)) (word-value m o n e y))) - -(define csp ($csp vds (append - - alldiffs - (list - ($constraint vs smm-func) - ($constraint '(s) positive?) - ($constraint '(m) (λ (x) (= 1 x))) - ($constraint '(d e y) (λ (d e y) (= (modulo (+ d e) 10) y))) - ($constraint '(n d r e y) (λ (n d r e y) - (= (modulo (+ (word-value n d) (word-value r e)) 100) - (word-value e y)))) - ($constraint '(e n d o r y) (λ (e n d o r y) - (= (modulo (+ (word-value e n d) (word-value o r e)) 1000) (word-value n e y)))))))) -(parameterize ([current-select-variable mrv] - [current-order-values lcv] - [current-inference mac]) - (time (solve csp))) -(nassigns csp) -(nchecks csp) -(reset! csp) \ No newline at end of file diff --git a/csp/csp/hacs-test-workbench.rkt b/csp/csp/hacs-test-workbench.rkt index df69806d..e8a05ca8 100644 --- a/csp/csp/hacs-test-workbench.rkt +++ b/csp/csp/hacs-test-workbench.rkt @@ -25,6 +25,7 @@ (list qa qb)) (add-constraint! queens (negate =) (list qa qb))) +(current-multithreaded #t) (time-avg 10 (solve queens)) (parameterize ([current-solver min-conflicts-solver]) - (time-named (solve queens))) \ No newline at end of file + (time-avg 10 (solve queens))) \ No newline at end of file diff --git a/csp/csp/hacs-test.rkt b/csp/csp/hacs-test.rkt index 4c3511b5..73ff798f 100644 --- a/csp/csp/hacs-test.rkt +++ b/csp/csp/hacs-test.rkt @@ -6,72 +6,72 @@ (current-order-values shuffle) (current-random #true) -(check-equal? (first-unassigned-variable ($csp (list ($var 'a (range 3)) ($var 'b (range 3))) null)) - ($var 'a (range 3))) -(check-equal? (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($var 'b (range 3))) null)) - ($var 'b (range 3))) -(check-false (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($avar 'b (range 3))) null))) +(check-equal? (first-unassigned-variable (csp (list (variable 'a (range 3)) (variable 'b (range 3))) null)) + (variable 'a (range 3))) +(check-equal? (first-unassigned-variable (csp (list (avar 'a (range 3)) (variable 'b (range 3))) null)) + (variable 'b (range 3))) +(check-false (first-unassigned-variable (csp (list (avar 'a (range 3)) (avar 'b (range 3))) null))) (check-equal? ;; no forward checking when no constraints - ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2))) null) 'a)) - (list ($avar 'a '(1)) ($var 'b '(0 1)))) + (csp-vars (forward-check (csp (list (avar 'a '(1)) (variable 'b (range 2))) null) 'a)) + (list (avar 'a '(1)) (variable 'b '(0 1)))) (check-equal? - ($csp-vars (forward-check (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(0)) ($var 'c '(0 1 2))) - (list ($constraint '(a c) (negate =)) - ($constraint '(b c) (negate =)))) 'a) 'b)) - (list ($avar 'a '(1)) ($avar 'b '(0)) ($cvar 'c '(2) '(b a)))) + (csp-vars (forward-check (forward-check (csp (list (avar 'a '(1)) (avar 'b '(0)) (variable 'c '(0 1 2))) + (list (constraint '(a c) (negate =)) + (constraint '(b c) (negate =)))) 'a) 'b)) + (list (avar 'a '(1)) (avar 'b '(0)) (cvar 'c '(2) '(b a)))) (check-equal? ;; no inconsistency: b≠c not checked when fc is relative to a - ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2)) ($var 'c '(0))) - (list ($constraint '(a b) (negate =)) - ($constraint '(b c) (negate =)))) 'a)) - (list ($avar 'a '(1)) ($cvar 'b '(0) '(a)) ($var 'c '(0)))) + (csp-vars (forward-check (csp (list (avar 'a '(1)) (variable 'b (range 2)) (variable 'c '(0))) + (list (constraint '(a b) (negate =)) + (constraint '(b c) (negate =)))) 'a)) + (list (avar 'a '(1)) (cvar 'b '(0) '(a)) (variable 'c '(0)))) (check-equal? ;; no inconsistency: a≠b not checked when fc ignores a, which is already assigned - ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c (range 2))) - (list ($constraint '(a b) (negate =)) - ($constraint '(b c) (negate =)))) 'b)) - (list ($avar 'a '(1)) ($avar 'b '(1)) ($cvar 'c '(0) '(b)))) + (csp-vars (forward-check (csp (list (avar 'a '(1)) (avar 'b '(1)) (variable 'c (range 2))) + (list (constraint '(a b) (negate =)) + (constraint '(b c) (negate =)))) 'b)) + (list (avar 'a '(1)) (avar 'b '(1)) (cvar 'c '(0) '(b)))) (check-exn $backtrack? - (λ () ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) - ($var 'b '(1))) - (list ($constraint '(a b) (negate =)))) 'a)))) + (λ () (csp-vars (forward-check (csp (list (avar 'a '(1)) + (variable 'b '(1))) + (list (constraint '(a b) (negate =)))) 'a)))) -(check-equal? ($csp-vars (forward-check ($csp (list ($var 'a '(0)) - ($var 'b (range 3))) - (list ($constraint '(a b) <))) 'a)) - (list ($var 'a '(0)) ($cvar 'b '(1 2) '(a)))) +(check-equal? (csp-vars (forward-check (csp (list (variable 'a '(0)) + (variable 'b (range 3))) + (list (constraint '(a b) <))) 'a)) + (list (variable 'a '(0)) (cvar 'b '(1 2) '(a)))) (check-equal? (parameterize ([current-inference forward-check]) - (length (solve* ($csp (list ($var 'x (range 3)) - ($var 'y (range 3)) - ($var 'z (range 3))) - (list ($constraint '(x y) <>) - ($constraint '(x z) <>) - ($constraint '(y z) <>)))))) 6) + (length (solve* (csp (list (variable 'x (range 3)) + (variable 'y (range 3)) + (variable 'z (range 3))) + (list (constraint '(x y) <>) + (constraint '(x z) <>) + (constraint '(y z) <>)))))) 6) (parameterize ([current-inference forward-check]) (define vds (for/list ([k '(wa nt nsw q t v sa)]) - ($var k '(red green blue)))) + (variable k '(red green blue)))) (define cs (list - ($constraint '(wa nt) neq?) - ($constraint '(wa sa) neq?) - ($constraint '(nt sa) neq?) - ($constraint '(nt q) neq?) - ($constraint '(q sa) neq?) - ($constraint '(q nsw) neq?) - ($constraint '(nsw sa) neq?) - ($constraint '(nsw v) neq?) - ($constraint '(v sa) neq?))) - (define csp ($csp vds cs)) - (check-equal? (length (solve* csp)) 18)) + (constraint '(wa nt) neq?) + (constraint '(wa sa) neq?) + (constraint '(nt sa) neq?) + (constraint '(nt q) neq?) + (constraint '(q sa) neq?) + (constraint '(q nsw) neq?) + (constraint '(nsw sa) neq?) + (constraint '(nsw v) neq?) + (constraint '(v sa) neq?))) + (define aus (csp vds cs)) + (check-equal? (length (solve* aus)) 18)) (define quarters (make-csp)) diff --git a/csp/csp/hacs.rkt b/csp/csp/hacs.rkt index 23a2cc84..8d21eccc 100644 --- a/csp/csp/hacs.rkt +++ b/csp/csp/hacs.rkt @@ -1,5 +1,5 @@ #lang debug racket -(require racket/generator graph sugar/debug) +(require racket/generator graph) (provide (all-defined-out)) (define-syntax when-debug @@ -16,95 +16,97 @@ (if (null? argss) (yield (reverse acc)) (for ([arg (in-list (car argss))]) - (loop (cdr argss) (cons arg acc)))))))) + (loop (cdr argss) (cons arg acc)))))))) -(struct $csp (vars +(struct csp (vars constraints [assignments #:auto] [checks #:auto]) #:mutable #:transparent #:auto-value 0) -(define csp? $csp?) -(define vars $csp-vars) -(define constraints $csp-constraints) -(define-syntax-rule (in-constraints csp) (in-list ($csp-constraints csp))) -(define-syntax-rule (in-vars csp) (in-list ($csp-vars csp))) -(define-syntax-rule (in-var-names csp) (in-list (map $var-name ($csp-vars csp)))) - -(struct $constraint (names proc) #:transparent +(define vars csp-vars) +(define constraints csp-constraints) +(define-syntax-rule (in-constraints csp) (in-list (csp-constraints csp))) +(define-syntax-rule (in-vars csp) (in-list (csp-vars csp))) +(define-syntax-rule (in-variable-names csp) (in-list (map variable-name (csp-vars csp)))) + +(struct constraint (names proc) #:transparent #:property prop:procedure - (λ (constraint csp) - (unless ($csp? csp) - (raise-argument-error '$constraint-proc "$csp" csp)) + (λ (const prob) + (unless (csp? prob) + (raise-argument-error '$constraint-proc "$csp" prob)) ;; apply proc in many-to-many style - (for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))]) - (apply ($constraint-proc constraint) args)))) + (for/and ([args (in-cartesian (map (λ (name) (csp-domain prob name)) (constraint-names const)))]) + (apply (constraint-proc const) args)))) (define (make-constraint [names null] [proc values]) - ($constraint names proc)) + (constraint names proc)) -(define constraint-names $constraint-names) -(define constraint? $constraint?) -(define (csp->graphviz csp) - (define g (csp->graph csp)) +(define (csp->graphviz prob) + (define g (csp->graph prob)) (graphviz g #:colors (coloring/brelaz g))) -(define (csp->graph csp) - (for*/fold ([g (unweighted-graph/undirected (map var-name (vars csp)))]) - ([constraint (in-constraints csp)] +(define (csp->graph prob) + (for*/fold ([gr (unweighted-graph/undirected (map variable-name (vars prob)))]) + ([constraint (in-constraints prob)] [edge (in-combinations (constraint-names constraint) 2)]) - (apply add-edge! g edge) - g)) + (apply add-edge! gr edge) + gr)) -(struct $var (name domain) #:transparent) -(define var? $var?) +(struct variable (name domain) #:transparent) (define name? symbol?) -(define $var-vals $var-domain) -(define var-name $var-name) -(struct $cvar $var (past) #:transparent) -(struct $avar $var () #:transparent) -(define assigned-var? $avar?) +(struct checked-var variable (past) #:transparent) +(define cvar checked-var) +(define cvar? checked-var?) + +(struct assigned-var variable () #:transparent) +(define avar assigned-var) +(define avar? assigned-var?) -(define/contract (make-csp [vars null] [constraints null]) - (() ((listof var?) (listof constraint?)) . ->* . csp?) - ($csp vars constraints)) +(define/contract (make-csp [vars null] [consts null]) + (() ((listof variable?) (listof constraint?)) . ->* . csp?) + (csp vars consts)) -(define/contract (add-vars! csp names-or-procedure [vals-or-procedure empty]) +(define/contract (add-variables! prob names-or-procedure [vals-or-procedure empty]) ((csp? (or/c (listof name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?) - (for/fold ([vars ($csp-vars csp)] - #:result (set-$csp-vars! csp vars)) + (for/fold ([vars (csp-vars prob)] + #:result (set-csp-vars! prob vars)) ([name (in-list (if (procedure? names-or-procedure) (names-or-procedure) names-or-procedure))]) - (when (memq name (map var-name vars)) + (when (memq name (map variable-name vars)) (raise-argument-error 'add-vars! "var that doesn't already exist" name)) - (append vars (list ($var name + (append vars (list (variable name (if (procedure? vals-or-procedure) (vals-or-procedure) vals-or-procedure)))))) -(define/contract (add-var! csp name [vals-or-procedure empty]) +(define add-vars! add-variables!) + +(define/contract (add-variable! prob name [vals-or-procedure empty]) ((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?) - (add-vars! csp (list name) vals-or-procedure)) + (add-vars! prob (list name) vals-or-procedure)) -(define/contract (add-constraints! csp proc namess [proc-name #false]) +(define add-var! add-variable!) + +(define/contract (add-constraints! prob proc namess [proc-name #false]) ((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?) - (set-$csp-constraints! csp (append (constraints csp) - (for/list ([names (in-list namess)]) - (for ([name (in-list names)]) - (check-name-in-csp! 'add-constraints! csp name)) - (make-constraint names (if proc-name - (procedure-rename proc proc-name) - proc)))))) - -(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false]) + (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)))))) + +(define/contract (add-pairwise-constraint! prob proc var-names [proc-name #false]) ((csp? procedure? (listof name?)) (name?) . ->* . void?) - (add-constraints! csp proc (combinations var-names 2) proc-name)) + (add-constraints! prob proc (combinations var-names 2) proc-name)) -(define/contract (add-constraint! csp proc var-names [proc-name #false]) +(define/contract (add-constraint! prob proc names [proc-name #false]) ((csp? procedure? (listof name?)) (name?) . ->* . void?) - (add-constraints! csp proc (list var-names) proc-name)) + (add-constraints! prob proc (list names) proc-name)) (define/contract (alldiff= x y) (any/c any/c . -> . boolean?) @@ -120,37 +122,38 @@ (define current-random (make-parameter #t)) (define current-decompose (make-parameter #t)) -(define/contract (check-name-in-csp! caller csp name) +(define/contract (check-name-in-csp! caller prob name) (symbol? csp? name? . -> . void?) - (define names (map var-name (vars csp))) + (define names (map variable-name (vars prob))) (unless (memq name names) (raise-argument-error caller (format "one of these existing csp var names: ~v" names) name))) -(define/contract (csp-var csp name) - (csp? name? . -> . $var?) - (check-name-in-csp! 'csp-var csp name) - (for/first ([var (in-vars csp)] - #:when (eq? name (var-name var))) - var)) +(define/contract (csp-var prob name) + (csp? name? . -> . variable?) + (check-name-in-csp! 'csp-var prob name) + (for/first ([var (in-vars prob)] + #:when (eq? name (variable-name var))) + var)) -(define/contract ($csp-vals csp name) +(define/contract (csp-domain prob name) (csp? name? . -> . (listof any/c)) - (check-name-in-csp! 'csp-vals csp name) - ($var-domain (csp-var csp name))) + (check-name-in-csp! 'csp-vals prob name) + (variable-domain (csp-var prob name))) (define order-domain-values values) -(define/contract (assigned-name? csp name) +(define/contract (assigned-name? prob name) (csp? name? . -> . any/c) - (for/or ([var (in-vars csp)] + (for/or ([var (in-vars prob)] #:when (assigned-var? var)) - (eq? name (var-name var)))) + (eq? name (variable-name var)))) -(define (reduce-function-arity proc pattern) +(define/contract (reduce-function-arity proc pattern) + (procedure? (listof any/c) . -> . procedure?) (unless (match (procedure-arity proc) [(arity-at-least val) (<= val (length pattern))] [(? number? val) (= val (length pattern))]) - (raise-argument-error 'reduce-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern)) + (raise-argument-error 'reduce-function-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern)) (define reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc)))) (define-values (boxed-id-names vals) (partition box? pattern)) (define new-arity (length boxed-id-names)) @@ -168,80 +171,82 @@ (values (cons (car vals) acc) xs (cdr vals)))))) reduced-arity-name)) -(define/contract (reduce-constraint-arity csp [minimum-arity 3]) +(define/contract (reduce-constraint-arity prob [minimum-arity 3]) ((csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . csp?) - (let ([assigned-name? (curry assigned-name? csp)]) + (let ([assigned-name? (curry assigned-name? prob)]) (define (partially-assigned? constraint) - (ormap assigned-name? ($constraint-names constraint))) - (make-csp (vars csp) - (for/list ([constraint (in-constraints csp)]) - (cond - [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity constraint))) - (partially-assigned? constraint)) - (match-define ($constraint cnames proc) constraint) - ($constraint (filter-not assigned-name? cnames) - ;; 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 - (let ([reduce-arity-pattern (for/list ([cname (in-list cnames)]) - (if (assigned-name? cname) - (first ($csp-vals csp cname)) - (box cname)))]) - (reduce-function-arity proc reduce-arity-pattern)))] - [else constraint]))))) + (ormap assigned-name? (constraint-names constraint))) + (make-csp (vars prob) + (for/list ([const (in-constraints prob)]) + (cond + [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const))) + (partially-assigned? const)) + (match-define (constraint cnames proc) const) + (constraint (filter-not assigned-name? cnames) + ;; pattern is mix of values and boxed symbols (indicating variables to persist) + ;; use boxes here as cheap way to distinguish id symbols from value symbols + (let ([reduce-arity-pattern (for/list ([cname (in-list cnames)]) + (if (assigned-name? cname) + (first (csp-domain prob cname)) + (box cname)))]) + (reduce-function-arity proc reduce-arity-pattern)))] + [else const]))))) (define nassns 0) + (define (reset-assns!) (set! nassns 0)) -(define/contract (assign-val csp name val) + +(define/contract (assign-val prob name val) (csp? name? any/c . -> . csp?) (when-debug (set! nassns (add1 nassns))) (make-csp - (for/list ([var (vars csp)]) - (if (eq? name (var-name var)) - ($avar name (list val)) - var)) - (constraints csp))) + (for/list ([var (vars prob)]) + (if (eq? name (variable-name var)) + (assigned-var name (list val)) + var)) + (constraints prob))) -(define/contract (unassigned-vars csp) - (csp? . -> . (listof (and/c $var? (not/c assigned-var?)))) - (filter-not assigned-var? (vars csp))) +(define/contract (unassigned-vars prob) + (csp? . -> . (listof (and/c variable? (not/c assigned-var?)))) + (filter-not assigned-var? (vars prob))) (define/contract (first-unassigned-variable csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) + (csp? . -> . (or/c #false (and/c variable? (not/c assigned-var?)))) (match (unassigned-vars csp) [(? empty?) #false] [(cons x _) x])) -(define/contract (minimum-remaining-values csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) - (match (unassigned-vars csp) +(define/contract (minimum-remaining-values prob) + (csp? . -> . (or/c #false (and/c variable? (not/c assigned-var?)))) + (match (unassigned-vars prob) [(? empty?) #false] - [xs (argmin (λ (var) (length ($var-domain var))) xs)])) + [xs (argmin (λ (var) (length (variable-domain var))) xs)])) (define mrv minimum-remaining-values) -(define/contract (var-degree csp var) - (csp? $var? . -> . exact-nonnegative-integer?) - (for/sum ([constraint (in-constraints csp)] - #:when (memq (var-name var) ($constraint-names constraint))) - 1)) +(define/contract (var-degree prob var) + (csp? variable? . -> . exact-nonnegative-integer?) + (for/sum ([const (in-constraints prob)] + #:when (memq (variable-name var) (constraint-names const))) + 1)) -(define/contract (blended-variable-selector csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) - (define uvars (unassigned-vars csp)) +(define/contract (blended-variable-selector prob) + (csp? . -> . (or/c #false (and/c variable? (not/c assigned-var?)))) + (define uvars (unassigned-vars prob)) (cond [(empty? uvars) #false] [(findf singleton-var? uvars)] - [else (first (let* ([uvars-by-mrv (sort uvars < #:key (λ (var) (length ($var-domain var))))] - [uvars-by-degree (sort uvars-by-mrv > #:key (λ (var) (var-degree csp var)))]) + [else (first (let* ([uvars-by-mrv (sort uvars < #:key (λ (var) (length (variable-domain var))))] + [uvars-by-degree (sort uvars-by-mrv > #:key (λ (var) (var-degree prob var)))]) uvars-by-degree))])) (define/contract (remaining-values var) - ($var? . -> . exact-nonnegative-integer?) - (length ($var-vals var))) + (variable? . -> . exact-nonnegative-integer?) + (length (variable-domain var))) -(define/contract (mrv-degree-hybrid csp) - (csp? . -> . (or/c #f $var?)) - (define uvars (unassigned-vars csp)) +(define/contract (mrv-degree-hybrid prob) + (csp? . -> . (or/c #f variable?)) + (define uvars (unassigned-vars prob)) (cond [(empty? uvars) #false] [else @@ -251,66 +256,66 @@ [(list winning-uvar) winning-uvar] [(list mrv-uvars ...) ;; use degree as tiebreaker for mrv - (define degrees (map (λ (var) (var-degree csp var)) mrv-uvars)) + (define degrees (map (λ (var) (var-degree prob var)) mrv-uvars)) (define max-degree (apply max degrees)) ;; use random tiebreaker for degree (random-pick (for/list ([var (in-list mrv-uvars)] [degree (in-list degrees)] #:when (= max-degree degree)) - var))])])) + var))])])) (define first-domain-value values) -(define (no-inference csp name) csp) +(define (no-inference prob name) prob) (define/contract (relating-only constraints names) - ((listof $constraint?) (listof name?) . -> . (listof $constraint?)) - (for*/list ([constraint (in-list constraints)] - [cnames (in-value ($constraint-names constraint))] + ((listof constraint?) (listof name?) . -> . (listof constraint?)) + (for*/list ([const (in-list constraints)] + [cnames (in-value (constraint-names const))] #:when (and (= (length names) (length cnames)) (for/and ([name (in-list names)]) - (memq name cnames)))) - constraint)) + (memq name cnames)))) + const)) -(define (binary-constraint? constraint) - (= 2 (constraint-arity constraint))) +(define (binary-constraint? const) + (= 2 (constraint-arity const))) -(define (constraint-relates? constraint name) - (memq name ($constraint-names constraint))) +(define (constraint-relates? const name) + (memq name (constraint-names const))) (define nfchecks 0) (define (reset-nfcs!) (set! nfchecks 0)) -(define/contract (forward-check csp aname) +(define/contract (forward-check prob ref-name) (csp? name? . -> . csp?) - (define aval (first ($csp-vals csp aname))) + (define aval (first (csp-domain prob ref-name))) (define (check-var var) (match var ;; don't check against assigned vars, or the reference var ;; (which is probably assigned but maybe not) - [(? (λ (x) (or (assigned-var? x) (eq? (var-name x) aname)))) var] - [($var name vals) - (match ((constraints csp) . relating-only . (list aname name)) + [(? (λ (x) (or (assigned-var? x) (eq? (variable-name x) ref-name)))) var] + [(variable name vals) + (match ((constraints prob) . relating-only . (list ref-name name)) [(? empty?) var] [constraints (define new-vals (for/list ([val (in-list vals)] #:when (for/and ([constraint (in-list constraints)]) - (let ([proc ($constraint-proc constraint)]) - (if (eq? name (first ($constraint-names constraint))) - (proc val aval) - (proc aval val))))) - val)) - ($cvar name new-vals (cons aname (if ($cvar? var) - ($cvar-past var) + (let ([proc (constraint-proc constraint)]) + (if (eq? name (first (constraint-names constraint))) + (proc val aval) + (proc aval val))))) + val)) + (checked-var name new-vals (cons ref-name (if (checked-var? var) + (checked-var-past var) null)))])])) - (define checked-vars (map check-var (vars csp))) + (define checked-vars (map check-var (vars prob))) (when-debug (set! nfchecks (+ (length checked-vars) nchecks))) ;; conflict-set will be empty if there are no empty domains (define conflict-set (for*/list ([var (in-list checked-vars)] - #:when (empty? ($var-domain var)) - [name (in-list ($cvar-past var))]) - name)) + #:when (empty? (variable-domain var)) + [name (in-list (checked-var-past var))]) + name)) ;; 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. @@ -321,87 +326,89 @@ ;; Discard constraints that have produced singleton domains ;; (they have no further use) (define nonsingleton-constraints - (for/list ([constraint (in-constraints csp)] + (for/list ([const (in-constraints prob)] #:unless (and - (binary-constraint? constraint) - (constraint-relates? constraint aname) - (let ([other-name (first (remq aname ($constraint-names constraint)))]) - (singleton-var? (csp-var csp other-name))))) - constraint)) + (binary-constraint? const) + (constraint-relates? const ref-name) + (let ([other-name (first (remq ref-name (constraint-names const)))]) + (singleton-var? (csp-var prob other-name))))) + const)) (make-csp checked-vars nonsingleton-constraints)) (define/contract (constraint-checkable? c names) - ($constraint? (listof name?) . -> . any/c) + (constraint? (listof name?) . -> . any/c) ;; constraint is checkable if all constraint names ;; are in target list of names. - (for/and ([cname (in-list ($constraint-names c))]) - (memq cname names))) + (for/and ([cname (in-list (constraint-names c))]) + (memq cname names))) -(define/contract (constraint-arity constraint) - ($constraint? . -> . exact-nonnegative-integer?) - (length ($constraint-names constraint))) +(define/contract (constraint-arity const) + (constraint? . -> . exact-nonnegative-integer?) + (length (constraint-names const))) (define (singleton-var? var) - (= 1 (length ($var-domain var)))) + (= 1 (length (variable-domain var)))) (define nchecks 0) (define (reset-nchecks!) (set! nchecks 0)) -(define/contract (check-constraints csp [mandatory-names #f] #:conflicts [conflict-count? #f]) +(define/contract (check-constraints prob [mandatory-names #f] #:conflicts [conflict-count? #f]) ((csp?) ((listof name?) #:conflicts boolean?) . ->* . (or/c csp? exact-nonnegative-integer?)) ;; this time, we're not limited to assigned variables ;; (that is, vars that have been deliberately assigned in the backtrack process thus far) ;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking) - (define singleton-varnames (for/list ([var (in-vars csp)] + (define singleton-varnames (for/list ([var (in-vars prob)] #:when (singleton-var? var)) - (var-name var))) - (define-values (checkable-constraints other-constraints) + (variable-name var))) + (define-values (checkable-consts other-consts) (partition (λ (c) (and (constraint-checkable? c singleton-varnames) (or (not mandatory-names) (for/and ([name (in-list mandatory-names)]) - (constraint-relates? c name))))) - (constraints csp))) + (constraint-relates? c name))))) + (constraints prob))) (cond - [conflict-count? (define conflict-count - (for/sum ([constraint (in-list checkable-constraints)] - #:unless (constraint csp)) - 1)) - (when-debug (set! nchecks (+ conflict-count nchecks))) - conflict-count] - [else (for ([(constraint idx) (in-indexed (sort checkable-constraints < #:key constraint-arity))] - #:unless (constraint csp)) - (when-debug (set! nchecks (+ (add1 idx) nchecks))) - (backtrack!)) - ;; discard checked constraints, since they have no further reason to live - (make-csp (vars csp) other-constraints)])) - -(define/contract (make-nodes-consistent csp) + [conflict-count? + (define conflict-count + (for/sum ([constraint (in-list checkable-consts)] + #:unless (constraint prob)) + 1)) + (when-debug (set! nchecks (+ conflict-count nchecks))) + conflict-count] + [else + (for ([(constraint idx) (in-indexed (sort checkable-consts < #:key constraint-arity))] + #:unless (constraint prob)) + (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)])) + +(define/contract (make-nodes-consistent prob) (csp? . -> . csp?) ;; todo: why does this function slow down searches? (make-csp - (for/list ([var (in-vars csp)]) - (match-define ($var name vals) var) - (define procs (for*/list ([constraint (in-constraints csp)] - [cnames (in-value ($constraint-names constraint))] - #:when (and (= 1 (length cnames)) (eq? name (car cnames)))) - ($constraint-proc constraint))) - ($var name - (for*/fold ([vals vals]) - ([proc (in-list procs)]) - (filter proc vals)))) - (constraints csp))) + (for/list ([var (in-vars prob)]) + (match-define (variable name vals) var) + (define procs (for*/list ([const (in-constraints prob)] + [cnames (in-value (constraint-names const))] + #:when (and (= 1 (length cnames)) (eq? name (car cnames)))) + (constraint-proc const))) + (variable name + (for*/fold ([vals vals]) + ([proc (in-list procs)]) + (filter proc vals)))) + (constraints prob))) (define/contract (backtracking-solver - csp + prob #:select-variable [select-unassigned-variable (or (current-select-variable) first-unassigned-variable)] #:order-values [order-domain-values (or (current-order-values) first-domain-value)] #:inference [inference (or (current-inference) no-inference)]) ((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?) (generator () - (let loop ([csp csp]) - (match (select-unassigned-variable csp) - [#false (yield csp)] - [($var name domain) + (let loop ([prob prob]) + (match (select-unassigned-variable prob) + [#false (yield prob)] + [(variable name domain) (define (wants-backtrack? exn) (and ($backtrack? exn) (or (let ([btns ($backtrack-names exn)]) (or (empty? btns) (memq name btns)))))) @@ -410,83 +417,91 @@ ([val (in-list (order-domain-values domain))]) (with-handlers ([wants-backtrack? (λ (bt) (append conflicts (remq name ($backtrack-names bt))))]) - (let* ([csp (assign-val csp name val)] + (let* ([prob (assign-val prob name val)] ;; reduce constraints before inference, ;; to create more forward-checkable (binary) constraints - [csp (reduce-constraint-arity csp)] - [csp (inference csp name)] - [csp (check-constraints csp)]) - (loop csp))) + [prob (reduce-constraint-arity prob)] + [prob (inference prob name)] + [prob (check-constraints prob)]) + (loop prob))) conflicts)])))) (define (random-pick xs) (list-ref xs (random (length xs)))) -(define (assign-random-vals csp) - (for/fold ([new-csp csp]) - ([name (in-var-names csp)]) - (assign-val new-csp name (random-pick ($csp-vals csp name))))) +(define (assign-random-vals prob) + (for/fold ([new-csp prob]) + ([name (in-variable-names prob)]) + (assign-val new-csp name (random-pick (csp-domain prob name))))) -(define (make-min-conflcts-thread csp0 thread-count max-steps [main-thread (current-thread)]) +(define (make-min-conflcts-thread prob-start thread-count max-steps [main-thread (current-thread)]) (thread (λ () (let loop () ;; Generate a complete assignment for all variables (probably with conflicts) - (for/fold ([csp (assign-random-vals csp0)]) + (for/fold ([prob (assign-random-vals prob-start)]) ([nth-step (in-range max-steps)]) ;; Now repeatedly choose a random conflicted variable and change it - (match (conflicted-var-names csp) - [(? empty?) (thread-send main-thread csp) (loop)] + (match (conflicted-variable-names prob) + [(? empty?) (thread-send main-thread prob) (loop)] [names (define name (random-pick names)) - (define val (min-conflicts-value csp name ($csp-vals csp0 name))) - (assign-val csp name val)])))))) + (define val (min-conflicts-value prob name (csp-domain prob-start name))) + (assign-val prob name val)])))))) -(define/contract (min-conflicts-solver csp [max-steps 100]) - (($csp?) (integer?) . ->* . generator?) - ;; Solve a CSP by stochastic hillclimbing on the number of conflicts. +(define/contract (min-conflicts-solver prob [max-steps 100]) + ((csp?) (integer?) . ->* . generator?) (generator () (for ([thread-count 4]) ; todo: what is ideal thread count? - (make-min-conflcts-thread csp thread-count max-steps)) + (make-min-conflcts-thread prob thread-count max-steps)) (for ([i (in-naturals)]) - (yield (thread-receive))))) - -(define/contract (conflicted-var-names csp) - ($csp? . -> . (listof name?)) + (yield (thread-receive))))) + +(define/contract (optimal-stop-min proc xs) + (procedure? (listof any/c) . -> . any/c) + (define-values (sample candidates) (split-at xs (inexact->exact (floor (* .458 (length xs)))))) + (define threshold (argmin proc sample)) + (or (for/first ([c (in-list candidates)] + #:when (<= (proc c) threshold)) + c) + (last candidates))) + +(define/contract (conflicted-variable-names prob) + (csp? . -> . (listof name?)) ;; Return a list of variables in current assignment that are conflicted - (for/list ([name (in-var-names csp)] - #:when (positive? (nconflicts csp name))) - name)) + (for/list ([name (in-variable-names prob)] + #:when (positive? (nconflicts prob name))) + name)) -(define/contract (min-conflicts-value csp name vals) - ($csp? name? (listof any/c) . -> . any/c) +(define/contract (min-conflicts-value prob name vals) + (csp? name? (listof any/c) . -> . any/c) ;; Return the value that will give var the least number of conflicts - (define vals-by-conflict (sort vals < #:key (λ (val) (nconflicts csp name val)) + (define vals-by-conflict (sort vals < #:key (λ (val) (nconflicts prob name val)) #:cache-keys? #true)) (for/first ([val (in-list vals-by-conflict)] - #:unless (equal? val (first ($csp-vals csp name)))) ;; but change the value - val)) + #:unless (equal? val (first (csp-domain prob name)))) ;; but change the value + val)) (define no-value-sig (gensym)) -(define/contract (nconflicts csp name [val no-value-sig]) - (($csp? name?) (any/c) . ->* . exact-nonnegative-integer?) +(define/contract (nconflicts prob name [val no-value-sig]) + ((csp? name?) (any/c) . ->* . exact-nonnegative-integer?) ;; How many conflicts var: val assignment has with other variables. (check-constraints (if (eq? val no-value-sig) - csp - (assign-val csp name val)) (list name) #:conflicts #true)) + prob + (assign-val prob name val)) (list name) #:conflicts #true)) -(define/contract (csp->assocs csp) +(define/contract (csp->assocs prob) (csp? . -> . (listof (cons/c name? any/c))) - (for/list ([var (in-vars csp)]) - (match var - [($var name (list val)) (cons name val)]))) + (for/list ([var (in-vars prob)]) + (match var + [(variable name (list val)) (cons name val)]))) -(define/contract (combine-csps csps) - ((listof $csp?) . -> . $csp?) +(define/contract (combine-csps probs) + ((listof csp?) . -> . csp?) (make-csp - (apply append (map $csp-vars csps)) - (apply append (map $csp-constraints csps)))) + (apply append (map csp-vars probs)) + (apply append (map csp-constraints probs)))) (define/contract (make-cartesian-generator solgens) ((listof generator?) . -> . generator?) @@ -500,18 +515,18 @@ (for ([sol (in-stream (car solstreams))]) (loop (cdr solstreams) (cons sol sols))))))) -(define/contract (extract-subcsp csp names) - ($csp? (listof name?) . -> . $csp?) +(define/contract (extract-subcsp prob names) + (csp? (listof name?) . -> . csp?) (make-csp - (for/list ([var (in-vars csp)] - #:when (memq (var-name var) names)) - var) - (for/list ([constraint (in-constraints csp)] - #:when (for/and ([cname (in-list ($constraint-names constraint))]) - (memq cname names))) - constraint))) - -(define/contract (solve* csp + (for/list ([var (in-vars prob)] + #:when (memq (variable-name var) names)) + var) + (for/list ([const (in-constraints prob)] + #:when (for/and ([cname (in-list (constraint-names const))]) + (memq cname names))) + const))) + +(define/contract (solve* prob #:finish-proc [finish-proc csp->assocs] #:solver [solver (or (current-solver) backtracking-solver)] #:limit [max-solutions +inf.0]) @@ -521,21 +536,21 @@ (define subcsps ; decompose into independent csps. `cc` determines "connected components" (if (current-decompose) - (for/list ([nodeset (in-list (cc (csp->graph csp)))]) - (extract-subcsp csp nodeset)) - (list csp))) + (for/list ([nodeset (in-list (cc (csp->graph prob)))]) + (extract-subcsp prob nodeset)) + (list prob))) (for/list ([solution (in-producer (make-cartesian-generator (map solver subcsps)) (void))] [idx (in-range max-solutions)]) - (finish-proc solution))) + (finish-proc solution))) -(define/contract (solve csp +(define/contract (solve prob #:finish-proc [finish-proc csp->assocs] #:solver [solver (or (current-solver) backtracking-solver)] #:limit [max-solutions 1]) ((csp?) (#:finish-proc procedure? #:solver procedure? #:limit exact-nonnegative-integer?) . ->* . (or/c #false any/c)) - (match (solve* csp #:finish-proc finish-proc #:solver solver #:limit max-solutions) + (match (solve* prob #:finish-proc finish-proc #:solver solver #:limit max-solutions) [(list solution) solution] [(list solutions ...) solutions] [else #false])) diff --git a/csp/csp/info.rkt b/csp/csp/info.rkt new file mode 100644 index 00000000..9debf269 --- /dev/null +++ b/csp/csp/info.rkt @@ -0,0 +1,3 @@ +#lang info + +(define scribblings '(("scribblings/csp.scrbl" (multi-page)))) diff --git a/csp/csp/main.rkt b/csp/csp/main.rkt index f4d54358..334cb23a 100644 --- a/csp/csp/main.rkt +++ b/csp/csp/main.rkt @@ -1,4 +1,4 @@ #lang racket/base -(require "port/main.rkt") -(provide (all-from-out "port/main.rkt")) +(require "hacs.rkt") +(provide (all-from-out "hacs.rkt")) diff --git a/csp/csp/scribblings/csp.scrbl b/csp/csp/scribblings/csp.scrbl index 158d5897..6216c9da 100644 --- a/csp/csp/scribblings/csp.scrbl +++ b/csp/csp/scribblings/csp.scrbl @@ -5,15 +5,15 @@ @(define my-eval (make-base-eval)) @(my-eval `(require csp)) - -@title{csp} +@title{Constraint-satisfaction problems} @author[(author+email "Matthew Butterick" "mb@mbtype.com")] - @defmodule[csp] -A simple hyphenation engine that uses the Knuth–Liang hyphenation algorithm originally developed for TeX. I have added little to their work. Accordingly, I take little credit. +@margin-note{This package is in development. I make no commitment to maintaining the public interface documented below.} + +A simple solver for constraint-satisfaction problems. @section{Installation} diff --git a/csp/hacs-test-workbench.rkt b/csp/hacs-test-workbench.rkt deleted file mode 100644 index e8a05ca8..00000000 --- a/csp/hacs-test-workbench.rkt +++ /dev/null @@ -1,31 +0,0 @@ -#lang debug racket -(require sugar/debug "hacs.rkt") - -(current-inference forward-check) -(current-select-variable mrv) -(current-order-values shuffle) -(current-random #true) - -;; queens problem -;; place queens on chessboard so they do not intersect - -(define board-size 8) - -(define queens (make-csp)) -(define qs (for/list ([q board-size]) (string->symbol (format "q~a" q)))) -(define rows (range (length qs))) -(add-vars! queens qs rows) -(define (q-col q) (string->number (string-trim (symbol->string q) "q"))) -(for* ([qs (in-combinations qs 2)]) - (match-define (list qa qb) qs) - (match-define (list qa-col qb-col) (map q-col qs)) - (add-constraint! queens - (λ (qa-row qb-row) - (not (= (abs (- qa-row qb-row)) (abs (- (q-col qa) (q-col qb)))))) ; same diag? - (list qa qb)) - (add-constraint! queens (negate =) (list qa qb))) - -(current-multithreaded #t) -(time-avg 10 (solve queens)) -(parameterize ([current-solver min-conflicts-solver]) - (time-avg 10 (solve queens))) \ No newline at end of file diff --git a/csp/hacs.rkt b/csp/hacs.rkt deleted file mode 100644 index b9b85cbc..00000000 --- a/csp/hacs.rkt +++ /dev/null @@ -1,557 +0,0 @@ -#lang debug racket -(require racket/generator graph sugar/debug) -(provide (all-defined-out)) - -(define-syntax when-debug - (let () - (define debug #f) - (if debug - (make-rename-transformer #'begin) - (λ (stx) (syntax-case stx () - [(_ . rest) #'(void)]))))) - -(define-syntax-rule (in-cartesian x) - (in-generator (let ([argss x]) - (let loop ([argss argss][acc empty]) - (if (null? argss) - (yield (reverse acc)) - (for ([arg (in-list (car argss))]) - (loop (cdr argss) (cons arg acc)))))))) - -(struct $csp (vars - constraints - [assignments #:auto] - [checks #:auto]) #:mutable #:transparent - #:auto-value 0) -(define csp? $csp?) -(define vars $csp-vars) -(define constraints $csp-constraints) -(define-syntax-rule (in-constraints csp) (in-list ($csp-constraints csp))) -(define-syntax-rule (in-vars csp) (in-list ($csp-vars csp))) -(define-syntax-rule (in-var-names csp) (in-list (map $var-name ($csp-vars csp)))) - -(struct $constraint (names proc) #:transparent - #:property prop:procedure - (λ (constraint csp) - (unless ($csp? csp) - (raise-argument-error '$constraint-proc "$csp" csp)) - ;; apply proc in many-to-many style - (for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))]) - (apply ($constraint-proc constraint) args)))) - -(define (make-constraint [names null] [proc values]) - ($constraint names proc)) - -(define constraint-names $constraint-names) -(define constraint? $constraint?) - -(define (csp->graphviz csp) - (define g (csp->graph csp)) - (graphviz g #:colors (coloring/brelaz g))) - -(define (csp->graph csp) - (for*/fold ([g (unweighted-graph/undirected (map var-name (vars csp)))]) - ([constraint (in-constraints csp)] - [edge (in-combinations (constraint-names constraint) 2)]) - (apply add-edge! g edge) - g)) - -(struct $var (name domain) #:transparent) -(define var? $var?) -(define name? symbol?) -(define $var-vals $var-domain) -(define var-name $var-name) - -(struct $cvar $var (past) #:transparent) -(struct $avar $var () #:transparent) -(define assigned-var? $avar?) - -(define/contract (make-csp [vars null] [constraints null]) - (() ((listof var?) (listof constraint?)) . ->* . csp?) - ($csp vars constraints)) - -(define/contract (add-vars! csp names-or-procedure [vals-or-procedure empty]) - ((csp? (or/c (listof name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?) - (for/fold ([vars ($csp-vars csp)] - #:result (set-$csp-vars! csp vars)) - ([name (in-list (if (procedure? names-or-procedure) - (names-or-procedure) - names-or-procedure))]) - (when (memq name (map var-name vars)) - (raise-argument-error 'add-vars! "var that doesn't already exist" name)) - (append vars (list ($var name - (if (procedure? vals-or-procedure) - (vals-or-procedure) - vals-or-procedure)))))) - -(define/contract (add-var! csp name [vals-or-procedure empty]) - ((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?) - (add-vars! csp (list name) vals-or-procedure)) - -(define/contract (add-constraints! csp proc namess [proc-name #false]) - ((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?) - (set-$csp-constraints! csp (append (constraints csp) - (for/list ([names (in-list namess)]) - (for ([name (in-list names)]) - (check-name-in-csp! 'add-constraints! csp name)) - (make-constraint names (if proc-name - (procedure-rename proc proc-name) - proc)))))) - -(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false]) - ((csp? procedure? (listof name?)) (name?) . ->* . void?) - (add-constraints! csp proc (combinations var-names 2) proc-name)) - -(define/contract (add-constraint! csp proc var-names [proc-name #false]) - ((csp? procedure? (listof name?)) (name?) . ->* . void?) - (add-constraints! csp proc (list var-names) proc-name)) - -(define/contract (alldiff= x y) - (any/c any/c . -> . boolean?) - (not (= x y))) - -(struct $backtrack (names) #:transparent) -(define (backtrack! [names null]) (raise ($backtrack names))) - -(define current-select-variable (make-parameter #f)) -(define current-order-values (make-parameter #f)) -(define current-inference (make-parameter #f)) -(define current-solver (make-parameter #f)) -(define current-random (make-parameter #t)) -(define current-decompose (make-parameter #t)) -(define current-multithreaded (make-parameter #t)) - -(define/contract (check-name-in-csp! caller csp name) - (symbol? csp? name? . -> . void?) - (define names (map var-name (vars csp))) - (unless (memq name names) - (raise-argument-error caller (format "one of these existing csp var names: ~v" names) name))) - -(define/contract (csp-var csp name) - (csp? name? . -> . $var?) - (check-name-in-csp! 'csp-var csp name) - (for/first ([var (in-vars csp)] - #:when (eq? name (var-name var))) - var)) - -(define/contract ($csp-vals csp name) - (csp? name? . -> . (listof any/c)) - (check-name-in-csp! 'csp-vals csp name) - ($var-domain (csp-var csp name))) - -(define order-domain-values values) - -(define/contract (assigned-name? csp name) - (csp? name? . -> . any/c) - (for/or ([var (in-vars csp)] - #:when (assigned-var? var)) - (eq? name (var-name var)))) - -(define (reduce-function-arity proc pattern) - (unless (match (procedure-arity proc) - [(arity-at-least val) (<= val (length pattern))] - [(? number? val) (= val (length pattern))]) - (raise-argument-error 'reduce-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern)) - (define reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc)))) - (define-values (boxed-id-names vals) (partition box? pattern)) - (define new-arity (length boxed-id-names)) - (procedure-rename - (λ xs - (unless (= (length xs) new-arity) - (apply raise-arity-error reduced-arity-name new-arity xs)) - (apply proc (for/fold ([acc empty] - [xs xs] - [vals vals] - #:result (reverse acc)) - ([pat-item (in-list pattern)]) - (if (box? pat-item) - (values (cons (car xs) acc) (cdr xs) vals) - (values (cons (car vals) acc) xs (cdr vals)))))) - reduced-arity-name)) - -(define/contract (reduce-constraint-arity csp [minimum-arity 3]) - ((csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . csp?) - (let ([assigned-name? (curry assigned-name? csp)]) - (define (partially-assigned? constraint) - (ormap assigned-name? ($constraint-names constraint))) - (make-csp (vars csp) - (for/list ([constraint (in-constraints csp)]) - (cond - [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity constraint))) - (partially-assigned? constraint)) - (match-define ($constraint cnames proc) constraint) - ($constraint (filter-not assigned-name? cnames) - ;; 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 - (let ([reduce-arity-pattern (for/list ([cname (in-list cnames)]) - (if (assigned-name? cname) - (first ($csp-vals csp cname)) - (box cname)))]) - (reduce-function-arity proc reduce-arity-pattern)))] - [else constraint]))))) - -(define nassns 0) -(define (reset-assns!) (set! nassns 0)) -(define/contract (assign-val csp name val) - (csp? name? any/c . -> . csp?) - (when-debug (set! nassns (add1 nassns))) - (make-csp - (for/list ([var (vars csp)]) - (if (eq? name (var-name var)) - ($avar name (list val)) - var)) - (constraints csp))) - -(define/contract (unassigned-vars csp) - (csp? . -> . (listof (and/c $var? (not/c assigned-var?)))) - (filter-not assigned-var? (vars csp))) - -(define/contract (first-unassigned-variable csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) - (match (unassigned-vars csp) - [(? empty?) #false] - [(cons x _) x])) - -(define/contract (minimum-remaining-values csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) - (match (unassigned-vars csp) - [(? empty?) #false] - [xs (argmin (λ (var) (length ($var-domain var))) xs)])) - -(define mrv minimum-remaining-values) - -(define/contract (var-degree csp var) - (csp? $var? . -> . exact-nonnegative-integer?) - (for/sum ([constraint (in-constraints csp)] - #:when (memq (var-name var) ($constraint-names constraint))) - 1)) - -(define/contract (blended-variable-selector csp) - (csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) - (define uvars (unassigned-vars csp)) - (cond - [(empty? uvars) #false] - [(findf singleton-var? uvars)] - [else (first (let* ([uvars-by-mrv (sort uvars < #:key (λ (var) (length ($var-domain var))))] - [uvars-by-degree (sort uvars-by-mrv > #:key (λ (var) (var-degree csp var)))]) - uvars-by-degree))])) - -(define/contract (remaining-values var) - ($var? . -> . exact-nonnegative-integer?) - (length ($var-vals var))) - -(define/contract (mrv-degree-hybrid csp) - (csp? . -> . (or/c #f $var?)) - (define uvars (unassigned-vars csp)) - (cond - [(empty? uvars) #false] - [else - ;; minimum remaining values (MRV) rule - (define mrv-arg (argmin remaining-values uvars)) - (match (filter (λ (var) (= (remaining-values mrv-arg) (remaining-values var))) uvars) - [(list winning-uvar) winning-uvar] - [(list mrv-uvars ...) - ;; use degree as tiebreaker for mrv - (define degrees (map (λ (var) (var-degree csp var)) mrv-uvars)) - (define max-degree (apply max degrees)) - ;; use random tiebreaker for degree - (random-pick (for/list ([var (in-list mrv-uvars)] - [degree (in-list degrees)] - #:when (= max-degree degree)) - var))])])) - -(define first-domain-value values) - -(define (no-inference csp name) csp) - -(define/contract (relating-only constraints names) - ((listof $constraint?) (listof name?) . -> . (listof $constraint?)) - (for*/list ([constraint (in-list constraints)] - [cnames (in-value ($constraint-names constraint))] - #:when (and (= (length names) (length cnames)) - (for/and ([name (in-list names)]) - (memq name cnames)))) - constraint)) - -(define (binary-constraint? constraint) - (= 2 (constraint-arity constraint))) - -(define (constraint-relates? constraint name) - (memq name ($constraint-names constraint))) - -(define nfchecks 0) -(define (reset-nfcs!) (set! nfchecks 0)) - -(define/contract (forward-check csp aname) - (csp? name? . -> . csp?) - (define aval (first ($csp-vals csp aname))) - (define (check-var var) - (match var - ;; don't check against assigned vars, or the reference var - ;; (which is probably assigned but maybe not) - [(? (λ (x) (or (assigned-var? x) (eq? (var-name x) aname)))) var] - [($var name vals) - (match ((constraints csp) . relating-only . (list aname name)) - [(? empty?) var] - [constraints - (define new-vals - (for/list ([val (in-list vals)] - #:when (for/and ([constraint (in-list constraints)]) - (let ([proc ($constraint-proc constraint)]) - (if (eq? name (first ($constraint-names constraint))) - (proc val aval) - (proc aval val))))) - val)) - ($cvar name new-vals (cons aname (if ($cvar? var) - ($cvar-past var) - null)))])])) - (define checked-vars (map check-var (vars csp))) - (when-debug (set! nfchecks (+ (length checked-vars) nchecks))) - ;; conflict-set will be empty if there are no empty domains - (define conflict-set (for*/list ([var (in-list checked-vars)] - #:when (empty? ($var-domain var)) - [name (in-list ($cvar-past var))]) - name)) - ;; 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. - ;; If we just bail out at the first conflict, we may backjump too far based on its history - ;; (and thereby miss parts of the search tree) - (when (pair? conflict-set) - (backtrack! conflict-set)) - ;; Discard constraints that have produced singleton domains - ;; (they have no further use) - (define nonsingleton-constraints - (for/list ([constraint (in-constraints csp)] - #:unless (and - (binary-constraint? constraint) - (constraint-relates? constraint aname) - (let ([other-name (first (remq aname ($constraint-names constraint)))]) - (singleton-var? (csp-var csp other-name))))) - constraint)) - (make-csp checked-vars nonsingleton-constraints)) - -(define/contract (constraint-checkable? c names) - ($constraint? (listof name?) . -> . any/c) - ;; constraint is checkable if all constraint names - ;; are in target list of names. - (for/and ([cname (in-list ($constraint-names c))]) - (memq cname names))) - -(define/contract (constraint-arity constraint) - ($constraint? . -> . exact-nonnegative-integer?) - (length ($constraint-names constraint))) - -(define (singleton-var? var) - (= 1 (length ($var-domain var)))) - -(define nchecks 0) -(define (reset-nchecks!) (set! nchecks 0)) -(define/contract (check-constraints csp [mandatory-names #f] #:conflicts [conflict-count? #f]) - ((csp?) ((listof name?) #:conflicts boolean?) . ->* . (or/c csp? exact-nonnegative-integer?)) - ;; this time, we're not limited to assigned variables - ;; (that is, vars that have been deliberately assigned in the backtrack process thus far) - ;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking) - (define singleton-varnames (for/list ([var (in-vars csp)] - #:when (singleton-var? var)) - (var-name var))) - (define-values (checkable-constraints other-constraints) - (partition (λ (c) (and (constraint-checkable? c singleton-varnames) - (or (not mandatory-names) - (for/and ([name (in-list mandatory-names)]) - (constraint-relates? c name))))) - (constraints csp))) - (cond - [conflict-count? (define conflict-count - (for/sum ([constraint (in-list checkable-constraints)] - #:unless (constraint csp)) - 1)) - (when-debug (set! nchecks (+ conflict-count nchecks))) - conflict-count] - [else (for ([(constraint idx) (in-indexed (sort checkable-constraints < #:key constraint-arity))] - #:unless (constraint csp)) - (when-debug (set! nchecks (+ (add1 idx) nchecks))) - (backtrack!)) - ;; discard checked constraints, since they have no further reason to live - (make-csp (vars csp) other-constraints)])) - -(define/contract (make-nodes-consistent csp) - (csp? . -> . csp?) - ;; todo: why does this function slow down searches? - (make-csp - (for/list ([var (in-vars csp)]) - (match-define ($var name vals) var) - (define procs (for*/list ([constraint (in-constraints csp)] - [cnames (in-value ($constraint-names constraint))] - #:when (and (= 1 (length cnames)) (eq? name (car cnames)))) - ($constraint-proc constraint))) - ($var name - (for*/fold ([vals vals]) - ([proc (in-list procs)]) - (filter proc vals)))) - (constraints csp))) - -(define/contract (backtracking-solver - csp - #:select-variable [select-unassigned-variable - (or (current-select-variable) first-unassigned-variable)] - #:order-values [order-domain-values (or (current-order-values) first-domain-value)] - #:inference [inference (or (current-inference) no-inference)]) - ((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?) - (generator () - (let loop ([csp csp]) - (match (select-unassigned-variable csp) - [#false (yield csp)] - [($var name domain) - (define (wants-backtrack? exn) - (and ($backtrack? exn) (or (let ([btns ($backtrack-names exn)]) - (or (empty? btns) (memq name btns)))))) - (for/fold ([conflicts null] - #:result (void)) - ([val (in-list (order-domain-values domain))]) - (with-handlers ([wants-backtrack? - (λ (bt) (append conflicts (remq name ($backtrack-names bt))))]) - (let* ([csp (assign-val csp name val)] - ;; reduce constraints before inference, - ;; to create more forward-checkable (binary) constraints - [csp (reduce-constraint-arity csp)] - [csp (inference csp name)] - [csp (check-constraints csp)]) - (loop csp))) - conflicts)])))) - -(define (random-pick xs) - (list-ref xs (random (length xs)))) - -(define (assign-random-vals csp) - (for/fold ([new-csp csp]) - ([name (in-var-names csp)]) - (assign-val new-csp name (random-pick ($csp-vals csp name))))) - -(define (make-min-conflcts-thread csp0 thread-count max-steps [main-thread (current-thread)]) - (thread - (λ () - (let loop () - ;; Generate a complete assignment for all variables (probably with conflicts) - (for/fold ([csp (assign-random-vals csp0)]) - ([nth-step (in-range max-steps)]) - ;; Now repeatedly choose a random conflicted variable and change it - (match (conflicted-var-names csp) - [(? empty?) (thread-send main-thread csp) (loop)] - [names - (define name (random-pick names)) - (define val (min-conflicts-value csp name ($csp-vals csp0 name))) - (assign-val csp name val)])))))) - -(define/contract (min-conflicts-solver csp [max-steps 100]) - (($csp?) (integer?) . ->* . generator?) - ;; Solve a CSP by stochastic hillclimbing on the number of conflicts. - (generator () - (for ([thread-count (if (current-multithreaded) 4 1)]) ; todo: what is ideal thread count? - (make-min-conflcts-thread csp thread-count max-steps)) - (for ([i (in-naturals)]) - (yield (thread-receive))))) - -(define/contract (conflicted-var-names csp) - ($csp? . -> . (listof name?)) - ;; Return a list of variables in current assignment that are conflicted - (for/list ([name (in-var-names csp)] - #:when (positive? (nconflicts csp name))) - name)) - -(define/contract (optimal-stop-min proc xs) - (procedure? (listof any/c) . -> . any/c) - (define-values (sample candidates) (split-at xs (inexact->exact (floor (* .458 (length xs)))))) - (define threshold (argmin proc sample)) - (or (for/first ([c (in-list candidates)] - #:when (<= (proc c) threshold)) - c) - (last candidates))) - - -(define/contract (min-conflicts-value csp name vals) - ($csp? name? (listof any/c) . -> . any/c) - ;; Return the value that will give var the least number of conflicts - #;(optimal-stop-min (λ (val) (nconflicts csp name val)) vals) - (define vals-by-conflict (sort vals < #:key (λ (val) (nconflicts csp name val)) - #:cache-keys? #true)) - (for/first ([val (in-list vals-by-conflict)] - #:unless (equal? val (first ($csp-vals csp name)))) ;; but change the value - val)) - -(define no-value-sig (gensym)) - -(define/contract (nconflicts csp name [val no-value-sig]) - (($csp? name?) (any/c) . ->* . exact-nonnegative-integer?) - ;; How many conflicts var: val assignment has with other variables. - (check-constraints (if (eq? val no-value-sig) - csp - (assign-val csp name val)) (list name) #:conflicts #true)) - -(define/contract (csp->assocs csp) - (csp? . -> . (listof (cons/c name? any/c))) - (for/list ([var (in-vars csp)]) - (match var - [($var name (list val)) (cons name val)]))) - -(define/contract (combine-csps csps) - ((listof $csp?) . -> . $csp?) - (make-csp - (apply append (map $csp-vars csps)) - (apply append (map $csp-constraints csps)))) - -(define/contract (make-cartesian-generator solgens) - ((listof generator?) . -> . generator?) - (generator () - (define solstreams (for/list ([solgen (in-list solgens)]) - (for/stream ([sol (in-producer solgen (void))]) - sol))) - (let loop ([solstreams solstreams][sols empty]) - (if (null? solstreams) - (yield (combine-csps (reverse sols))) - (for ([sol (in-stream (car solstreams))]) - (loop (cdr solstreams) (cons sol sols))))))) - -(define/contract (extract-subcsp csp names) - ($csp? (listof name?) . -> . $csp?) - (make-csp - (for/list ([var (in-vars csp)] - #:when (memq (var-name var) names)) - var) - (for/list ([constraint (in-constraints csp)] - #:when (for/and ([cname (in-list ($constraint-names constraint))]) - (memq cname names))) - constraint))) - -(define/contract (solve* csp - #:finish-proc [finish-proc csp->assocs] - #:solver [solver (or (current-solver) backtracking-solver)] - #:limit [max-solutions +inf.0]) - ((csp?) (#:finish-proc procedure? #:solver procedure? #:limit exact-nonnegative-integer?) - . ->* . (listof any/c)) - (when-debug (reset-assns!) (reset-nfcs!) (reset-nchecks!)) - - (define subcsps ; decompose into independent csps. `cc` determines "connected components" - (if (current-decompose) - (for/list ([nodeset (in-list (cc (csp->graph csp)))]) - (extract-subcsp csp nodeset)) - (list csp))) - - (for/list ([solution (in-producer (make-cartesian-generator (map solver subcsps)) (void))] - [idx (in-range max-solutions)]) - (finish-proc solution))) - -(define/contract (solve csp - #:finish-proc [finish-proc csp->assocs] - #:solver [solver (or (current-solver) backtracking-solver)] - #:limit [max-solutions 1]) - ((csp?) (#:finish-proc procedure? #:solver procedure? #:limit exact-nonnegative-integer?) - . ->* . (or/c #false any/c)) - (match (solve* csp #:finish-proc finish-proc #:solver solver #:limit max-solutions) - [(list solution) solution] - [(list solutions ...) solutions] - [else #false])) - -(define (<> a b) (not (= a b))) -(define (neq? a b) (not (eq? a b))) - diff --git a/csp/info.rkt b/csp/info.rkt index 5b7681d8..2e2dc245 100644 --- a/csp/info.rkt +++ b/csp/info.rkt @@ -1,6 +1,4 @@ #lang info (define collection 'multi) (define deps '(("base" #:version "6.0") "sugar" "rackunit-lib" "debug" "graph")) -(define update-implies '("sugar")) -(define scribblings '(("csp/scribblings/csp.scrbl" (multi-page)))) -;(define compile-omit-paths '("tests" "raco.rkt")) \ No newline at end of file +(define update-implies '("sugar")) \ No newline at end of file