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Matthew Butterick 6 years ago
parent d418d1ca0c
commit 6f1db5fd55
10 changed files with 327 additions and 945 deletions
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47
csp/csp/hacs-smm.rkt
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@ -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)

3
csp/csp/hacs-test-workbench.rkt
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@ -25,6 +25,7 @@
(list qa qb)) (list qa qb))
(add-constraint! queens (negate =) (list qa qb))) (add-constraint! queens (negate =) (list qa qb)))
(current-multithreaded #t)
(time-avg 10 (solve queens)) (time-avg 10 (solve queens))
(parameterize ([current-solver min-conflicts-solver]) (parameterize ([current-solver min-conflicts-solver])
(time-named (solve queens))) (time-avg 10 (solve queens)))

88
csp/csp/hacs-test.rkt
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@ -6,72 +6,72 @@
(current-order-values shuffle) (current-order-values shuffle)
(current-random #true) (current-random #true)
(check-equal? (first-unassigned-variable ($csp (list ($var 'a (range 3)) ($var 'b (range 3))) null)) (check-equal? (first-unassigned-variable (csp (list (variable 'a (range 3)) (variable 'b (range 3))) null))
($var 'a (range 3))) (variable 'a (range 3)))
(check-equal? (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($var 'b (range 3))) null)) (check-equal? (first-unassigned-variable (csp (list (avar 'a (range 3)) (variable 'b (range 3))) null))
($var 'b (range 3))) (variable 'b (range 3)))
(check-false (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($avar 'b (range 3))) null))) (check-false (first-unassigned-variable (csp (list (avar 'a (range 3)) (avar 'b (range 3))) null)))
(check-equal? (check-equal?
;; no forward checking when no constraints ;; no forward checking when no constraints
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2))) null) 'a)) (csp-vars (forward-check (csp (list (avar 'a '(1)) (variable 'b (range 2))) null) 'a))
(list ($avar 'a '(1)) ($var 'b '(0 1)))) (list (avar 'a '(1)) (variable 'b '(0 1))))
(check-equal? (check-equal?
($csp-vars (forward-check (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(0)) ($var 'c '(0 1 2))) (csp-vars (forward-check (forward-check (csp (list (avar 'a '(1)) (avar 'b '(0)) (variable 'c '(0 1 2)))
(list ($constraint '(a c) (negate =)) (list (constraint '(a c) (negate =))
($constraint '(b c) (negate =)))) 'a) 'b)) (constraint '(b c) (negate =)))) 'a) 'b))
(list ($avar 'a '(1)) ($avar 'b '(0)) ($cvar 'c '(2) '(b a)))) (list (avar 'a '(1)) (avar 'b '(0)) (cvar 'c '(2) '(b a))))
(check-equal? (check-equal?
;; no inconsistency: b≠c not checked when fc is relative to a ;; no inconsistency: b≠c not checked when fc is relative to a
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2)) ($var 'c '(0))) (csp-vars (forward-check (csp (list (avar 'a '(1)) (variable 'b (range 2)) (variable 'c '(0)))
(list ($constraint '(a b) (negate =)) (list (constraint '(a b) (negate =))
($constraint '(b c) (negate =)))) 'a)) (constraint '(b c) (negate =)))) 'a))
(list ($avar 'a '(1)) ($cvar 'b '(0) '(a)) ($var 'c '(0)))) (list (avar 'a '(1)) (cvar 'b '(0) '(a)) (variable 'c '(0))))
(check-equal? (check-equal?
;; no inconsistency: a≠b not checked when fc ignores a, which is already assigned ;; no inconsistency: a≠b not checked when fc ignores a, which is already assigned
($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c (range 2))) (csp-vars (forward-check (csp (list (avar 'a '(1)) (avar 'b '(1)) (variable 'c (range 2)))
(list ($constraint '(a b) (negate =)) (list (constraint '(a b) (negate =))
($constraint '(b c) (negate =)))) 'b)) (constraint '(b c) (negate =)))) 'b))
(list ($avar 'a '(1)) ($avar 'b '(1)) ($cvar 'c '(0) '(b)))) (list (avar 'a '(1)) (avar 'b '(1)) (cvar 'c '(0) '(b))))
(check-exn $backtrack? (check-exn $backtrack?
(λ () ($csp-vars (forward-check ($csp (list ($avar 'a '(1)) (λ () (csp-vars (forward-check (csp (list (avar 'a '(1))
($var 'b '(1))) (variable 'b '(1)))
(list ($constraint '(a b) (negate =)))) 'a)))) (list (constraint '(a b) (negate =)))) 'a))))
(check-equal? ($csp-vars (forward-check ($csp (list ($var 'a '(0)) (check-equal? (csp-vars (forward-check (csp (list (variable 'a '(0))
($var 'b (range 3))) (variable 'b (range 3)))
(list ($constraint '(a b) <))) 'a)) (list (constraint '(a b) <))) 'a))
(list ($var 'a '(0)) ($cvar 'b '(1 2) '(a)))) (list (variable 'a '(0)) (cvar 'b '(1 2) '(a))))
(check-equal? (check-equal?
(parameterize ([current-inference forward-check]) (parameterize ([current-inference forward-check])
(length (solve* ($csp (list ($var 'x (range 3)) (length (solve* (csp (list (variable 'x (range 3))
($var 'y (range 3)) (variable 'y (range 3))
($var 'z (range 3))) (variable 'z (range 3)))
(list ($constraint '(x y) <>) (list (constraint '(x y) <>)
($constraint '(x z) <>) (constraint '(x z) <>)
($constraint '(y z) <>)))))) 6) (constraint '(y z) <>)))))) 6)
(parameterize ([current-inference forward-check]) (parameterize ([current-inference forward-check])
(define vds (for/list ([k '(wa nt nsw q t v sa)]) (define vds (for/list ([k '(wa nt nsw q t v sa)])
($var k '(red green blue)))) (variable k '(red green blue))))
(define cs (list (define cs (list
($constraint '(wa nt) neq?) (constraint '(wa nt) neq?)
($constraint '(wa sa) neq?) (constraint '(wa sa) neq?)
($constraint '(nt sa) neq?) (constraint '(nt sa) neq?)
($constraint '(nt q) neq?) (constraint '(nt q) neq?)
($constraint '(q sa) neq?) (constraint '(q sa) neq?)
($constraint '(q nsw) neq?) (constraint '(q nsw) neq?)
($constraint '(nsw sa) neq?) (constraint '(nsw sa) neq?)
($constraint '(nsw v) neq?) (constraint '(nsw v) neq?)
($constraint '(v sa) neq?))) (constraint '(v sa) neq?)))
(define csp ($csp vds cs)) (define aus (csp vds cs))
(check-equal? (length (solve* csp)) 18)) (check-equal? (length (solve* aus)) 18))
(define quarters (make-csp)) (define quarters (make-csp))

527
csp/csp/hacs.rkt
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@ -1,5 +1,5 @@
#lang debug racket #lang debug racket
(require racket/generator graph sugar/debug) (require racket/generator graph)
(provide (all-defined-out)) (provide (all-defined-out))
(define-syntax when-debug (define-syntax when-debug
@ -16,95 +16,97 @@
(if (null? argss) (if (null? argss)
(yield (reverse acc)) (yield (reverse acc))
(for ([arg (in-list (car argss))]) (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 constraints
[assignments #:auto] [assignments #:auto]
[checks #:auto]) #:mutable #:transparent [checks #:auto]) #:mutable #:transparent
#:auto-value 0) #:auto-value 0)
(define csp? $csp?) (define vars csp-vars)
(define vars $csp-vars) (define constraints csp-constraints)
(define constraints $csp-constraints) (define-syntax-rule (in-constraints csp) (in-list (csp-constraints csp)))
(define-syntax-rule (in-constraints csp) (in-list ($csp-constraints csp))) (define-syntax-rule (in-vars csp) (in-list (csp-vars csp)))
(define-syntax-rule (in-vars csp) (in-list ($csp-vars csp))) (define-syntax-rule (in-variable-names csp) (in-list (map variable-name (csp-vars csp))))
(define-syntax-rule (in-var-names csp) (in-list (map $var-name ($csp-vars csp))))
(struct constraint (names proc) #:transparent
(struct $constraint (names proc) #:transparent
#:property prop:procedure #:property prop:procedure
(λ (constraint csp) (λ (const prob)
(unless ($csp? csp) (unless (csp? prob)
(raise-argument-error '$constraint-proc "$csp" csp)) (raise-argument-error '$constraint-proc "$csp" prob))
;; apply proc in many-to-many style ;; apply proc in many-to-many style
(for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))]) (for/and ([args (in-cartesian (map (λ (name) (csp-domain prob name)) (constraint-names const)))])
(apply ($constraint-proc constraint) args)))) (apply (constraint-proc const) args))))
(define (make-constraint [names null] [proc values]) (define (make-constraint [names null] [proc values])
($constraint names proc)) (constraint names proc))
(define constraint-names $constraint-names)
(define constraint? $constraint?)
(define (csp->graphviz csp) (define (csp->graphviz prob)
(define g (csp->graph csp)) (define g (csp->graph prob))
(graphviz g #:colors (coloring/brelaz g))) (graphviz g #:colors (coloring/brelaz g)))
(define (csp->graph csp) (define (csp->graph prob)
(for*/fold ([g (unweighted-graph/undirected (map var-name (vars csp)))]) (for*/fold ([gr (unweighted-graph/undirected (map variable-name (vars prob)))])
([constraint (in-constraints csp)] ([constraint (in-constraints prob)]
[edge (in-combinations (constraint-names constraint) 2)]) [edge (in-combinations (constraint-names constraint) 2)])
(apply add-edge! g edge) (apply add-edge! gr edge)
g)) gr))
(struct $var (name domain) #:transparent) (struct variable (name domain) #:transparent)
(define var? $var?)
(define name? symbol?) (define name? symbol?)
(define $var-vals $var-domain)
(define var-name $var-name)
(struct $cvar $var (past) #:transparent) (struct checked-var variable (past) #:transparent)
(struct $avar $var () #:transparent) (define cvar checked-var)
(define assigned-var? $avar?) (define cvar? checked-var?)
(struct assigned-var variable () #:transparent)
(define avar assigned-var)
(define avar? assigned-var?)
(define/contract (make-csp [vars null] [constraints null]) (define/contract (make-csp [vars null] [consts null])
(() ((listof var?) (listof constraint?)) . ->* . csp?) (() ((listof variable?) (listof constraint?)) . ->* . csp?)
($csp vars constraints)) (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?) ((csp? (or/c (listof name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
(for/fold ([vars ($csp-vars csp)] (for/fold ([vars (csp-vars prob)]
#:result (set-$csp-vars! csp vars)) #:result (set-csp-vars! prob vars))
([name (in-list (if (procedure? names-or-procedure) ([name (in-list (if (procedure? names-or-procedure)
(names-or-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)) (raise-argument-error 'add-vars! "var that doesn't already exist" name))
(append vars (list ($var name (append vars (list (variable name
(if (procedure? vals-or-procedure) (if (procedure? vals-or-procedure)
(vals-or-procedure) (vals-or-procedure)
vals-or-procedure)))))) vals-or-procedure))))))
(define/contract (add-var! csp name [vals-or-procedure empty]) (define add-vars! add-variables!)
(define/contract (add-variable! prob name [vals-or-procedure empty])
((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?) ((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
(add-vars! csp (list name) vals-or-procedure)) (add-vars! prob (list name) vals-or-procedure))
(define/contract (add-constraints! csp proc namess [proc-name #false]) (define add-var! add-variable!)
(define/contract (add-constraints! prob proc namess [proc-name #false])
((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?) ((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
(set-$csp-constraints! csp (append (constraints csp) (set-csp-constraints! prob (append (constraints prob)
(for/list ([names (in-list namess)]) (for/list ([names (in-list namess)])
(for ([name (in-list names)]) (for ([name (in-list names)])
(check-name-in-csp! 'add-constraints! csp name)) (check-name-in-csp! 'add-constraints! prob name))
(make-constraint names (if proc-name (make-constraint names (if proc-name
(procedure-rename proc proc-name) (procedure-rename proc proc-name)
proc)))))) proc))))))
(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false]) (define/contract (add-pairwise-constraint! prob proc var-names [proc-name #false])
((csp? procedure? (listof name?)) (name?) . ->* . void?) ((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?) ((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) (define/contract (alldiff= x y)
(any/c any/c . -> . boolean?) (any/c any/c . -> . boolean?)
@ -120,37 +122,38 @@
(define current-random (make-parameter #t)) (define current-random (make-parameter #t))
(define current-decompose (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?) (symbol? csp? name? . -> . void?)
(define names (map var-name (vars csp))) (define names (map variable-name (vars prob)))
(unless (memq name names) (unless (memq name names)
(raise-argument-error caller (format "one of these existing csp var names: ~v" names) name))) (raise-argument-error caller (format "one of these existing csp var names: ~v" names) name)))
(define/contract (csp-var csp name) (define/contract (csp-var prob name)
(csp? name? . -> . $var?) (csp? name? . -> . variable?)
(check-name-in-csp! 'csp-var csp name) (check-name-in-csp! 'csp-var prob name)
(for/first ([var (in-vars csp)] (for/first ([var (in-vars prob)]
#:when (eq? name (var-name var))) #:when (eq? name (variable-name var)))
var)) var))
(define/contract ($csp-vals csp name) (define/contract (csp-domain prob name)
(csp? name? . -> . (listof any/c)) (csp? name? . -> . (listof any/c))
(check-name-in-csp! 'csp-vals csp name) (check-name-in-csp! 'csp-vals prob name)
($var-domain (csp-var csp name))) (variable-domain (csp-var prob name)))
(define order-domain-values values) (define order-domain-values values)
(define/contract (assigned-name? csp name) (define/contract (assigned-name? prob name)
(csp? name? . -> . any/c) (csp? name? . -> . any/c)
(for/or ([var (in-vars csp)] (for/or ([var (in-vars prob)]
#:when (assigned-var? var)) #: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) (unless (match (procedure-arity proc)
[(arity-at-least val) (<= val (length pattern))] [(arity-at-least val) (<= val (length pattern))]
[(? number? 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 reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc))))
(define-values (boxed-id-names vals) (partition box? pattern)) (define-values (boxed-id-names vals) (partition box? pattern))
(define new-arity (length boxed-id-names)) (define new-arity (length boxed-id-names))
@ -168,80 +171,82 @@
(values (cons (car vals) acc) xs (cdr vals)))))) (values (cons (car vals) acc) xs (cdr vals))))))
reduced-arity-name)) 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?) ((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) (define (partially-assigned? constraint)
(ormap assigned-name? ($constraint-names constraint))) (ormap assigned-name? (constraint-names constraint)))
(make-csp (vars csp) (make-csp (vars prob)
(for/list ([constraint (in-constraints csp)]) (for/list ([const (in-constraints prob)])
(cond (cond
[(and (or (not minimum-arity) (<= minimum-arity (constraint-arity constraint))) [(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
(partially-assigned? constraint)) (partially-assigned? const))
(match-define ($constraint cnames proc) constraint) (match-define (constraint cnames proc) const)
($constraint (filter-not assigned-name? cnames) (constraint (filter-not assigned-name? cnames)
;; pattern is mix of values and boxed symbols (indicating variables to persist) ;; 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 ;; use boxes here as cheap way to distinguish id symbols from value symbols
(let ([reduce-arity-pattern (for/list ([cname (in-list cnames)]) (let ([reduce-arity-pattern (for/list ([cname (in-list cnames)])
(if (assigned-name? cname) (if (assigned-name? cname)
(first ($csp-vals csp cname)) (first (csp-domain prob cname))
(box cname)))]) (box cname)))])
(reduce-function-arity proc reduce-arity-pattern)))] (reduce-function-arity proc reduce-arity-pattern)))]
[else constraint]))))) [else const])))))
(define nassns 0) (define nassns 0)
(define (reset-assns!) (set! nassns 0)) (define (reset-assns!) (set! nassns 0))
(define/contract (assign-val csp name val)
(define/contract (assign-val prob name val)
(csp? name? any/c . -> . csp?) (csp? name? any/c . -> . csp?)
(when-debug (set! nassns (add1 nassns))) (when-debug (set! nassns (add1 nassns)))
(make-csp (make-csp
(for/list ([var (vars csp)]) (for/list ([var (vars prob)])
(if (eq? name (var-name var)) (if (eq? name (variable-name var))
($avar name (list val)) (assigned-var name (list val))
var)) var))
(constraints csp))) (constraints prob)))
(define/contract (unassigned-vars csp) (define/contract (unassigned-vars prob)
(csp? . -> . (listof (and/c $var? (not/c assigned-var?)))) (csp? . -> . (listof (and/c variable? (not/c assigned-var?))))
(filter-not assigned-var? (vars csp))) (filter-not assigned-var? (vars prob)))
(define/contract (first-unassigned-variable csp) (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) (match (unassigned-vars csp)
[(? empty?) #false] [(? empty?) #false]
[(cons x _) x])) [(cons x _) x]))
(define/contract (minimum-remaining-values csp) (define/contract (minimum-remaining-values prob)
(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) (csp? . -> . (or/c #false (and/c variable? (not/c assigned-var?))))
(match (unassigned-vars csp) (match (unassigned-vars prob)
[(? empty?) #false] [(? empty?) #false]
[xs (argmin (λ (var) (length ($var-domain var))) xs)])) [xs (argmin (λ (var) (length (variable-domain var))) xs)]))
(define mrv minimum-remaining-values) (define mrv minimum-remaining-values)
(define/contract (var-degree csp var) (define/contract (var-degree prob var)
(csp? $var? . -> . exact-nonnegative-integer?) (csp? variable? . -> . exact-nonnegative-integer?)
(for/sum ([constraint (in-constraints csp)] (for/sum ([const (in-constraints prob)]
#:when (memq (var-name var) ($constraint-names constraint))) #:when (memq (variable-name var) (constraint-names const)))
1)) 1))
(define/contract (blended-variable-selector csp) (define/contract (blended-variable-selector prob)
(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?)))) (csp? . -> . (or/c #false (and/c variable? (not/c assigned-var?))))
(define uvars (unassigned-vars csp)) (define uvars (unassigned-vars prob))
(cond (cond
[(empty? uvars) #false] [(empty? uvars) #false]
[(findf singleton-var? uvars)] [(findf singleton-var? uvars)]
[else (first (let* ([uvars-by-mrv (sort uvars < #:key (λ (var) (length ($var-domain 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 csp var)))]) [uvars-by-degree (sort uvars-by-mrv > #:key (λ (var) (var-degree prob var)))])
uvars-by-degree))])) uvars-by-degree))]))
(define/contract (remaining-values var) (define/contract (remaining-values var)
($var? . -> . exact-nonnegative-integer?) (variable? . -> . exact-nonnegative-integer?)
(length ($var-vals var))) (length (variable-domain var)))
(define/contract (mrv-degree-hybrid csp) (define/contract (mrv-degree-hybrid prob)
(csp? . -> . (or/c #f $var?)) (csp? . -> . (or/c #f variable?))
(define uvars (unassigned-vars csp)) (define uvars (unassigned-vars prob))
(cond (cond
[(empty? uvars) #false] [(empty? uvars) #false]
[else [else
@ -251,66 +256,66 @@
[(list winning-uvar) winning-uvar] [(list winning-uvar) winning-uvar]
[(list mrv-uvars ...) [(list mrv-uvars ...)
;; use degree as tiebreaker for mrv ;; 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)) (define max-degree (apply max degrees))
;; use random tiebreaker for degree ;; use random tiebreaker for degree
(random-pick (for/list ([var (in-list mrv-uvars)] (random-pick (for/list ([var (in-list mrv-uvars)]
[degree (in-list degrees)] [degree (in-list degrees)]
#:when (= max-degree degree)) #:when (= max-degree degree))
var))])])) var))])]))
(define first-domain-value values) (define first-domain-value values)
(define (no-inference csp name) csp) (define (no-inference prob name) prob)
(define/contract (relating-only constraints names) (define/contract (relating-only constraints names)
((listof $constraint?) (listof name?) . -> . (listof $constraint?)) ((listof constraint?) (listof name?) . -> . (listof constraint?))
(for*/list ([constraint (in-list constraints)] (for*/list ([const (in-list constraints)]
[cnames (in-value ($constraint-names constraint))] [cnames (in-value (constraint-names const))]
#:when (and (= (length names) (length cnames)) #:when (and (= (length names) (length cnames))
(for/and ([name (in-list names)]) (for/and ([name (in-list names)])
(memq name cnames)))) (memq name cnames))))
constraint)) const))
(define (binary-constraint? constraint) (define (binary-constraint? const)
(= 2 (constraint-arity constraint))) (= 2 (constraint-arity const)))
(define (constraint-relates? constraint name) (define (constraint-relates? const name)
(memq name ($constraint-names constraint))) (memq name (constraint-names const)))
(define nfchecks 0) (define nfchecks 0)
(define (reset-nfcs!) (set! nfchecks 0)) (define (reset-nfcs!) (set! nfchecks 0))
(define/contract (forward-check csp aname) (define/contract (forward-check prob ref-name)
(csp? name? . -> . csp?) (csp? name? . -> . csp?)
(define aval (first ($csp-vals csp aname))) (define aval (first (csp-domain prob ref-name)))
(define (check-var var) (define (check-var var)
(match var (match var
;; don't check against assigned vars, or the reference var ;; don't check against assigned vars, or the reference var
;; (which is probably assigned but maybe not) ;; (which is probably assigned but maybe not)
[(? (λ (x) (or (assigned-var? x) (eq? (var-name x) aname)))) var] [(? (λ (x) (or (assigned-var? x) (eq? (variable-name x) ref-name)))) var]
[($var name vals) [(variable name vals)
(match ((constraints csp) . relating-only . (list aname name)) (match ((constraints prob) . relating-only . (list ref-name name))
[(? empty?) var] [(? empty?) var]
[constraints [constraints
(define new-vals (define new-vals
(for/list ([val (in-list vals)] (for/list ([val (in-list vals)]
#:when (for/and ([constraint (in-list constraints)]) #:when (for/and ([constraint (in-list constraints)])
(let ([proc ($constraint-proc constraint)]) (let ([proc (constraint-proc constraint)])
(if (eq? name (first ($constraint-names constraint))) (if (eq? name (first (constraint-names constraint)))
(proc val aval) (proc val aval)
(proc aval val))))) (proc aval val)))))
val)) val))
($cvar name new-vals (cons aname (if ($cvar? var) (checked-var name new-vals (cons ref-name (if (checked-var? var)
($cvar-past var) (checked-var-past var)
null)))])])) 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))) (when-debug (set! nfchecks (+ (length checked-vars) nchecks)))
;; conflict-set will be empty if there are no empty domains ;; conflict-set will be empty if there are no empty domains
(define conflict-set (for*/list ([var (in-list checked-vars)] (define conflict-set (for*/list ([var (in-list checked-vars)]
#:when (empty? ($var-domain var)) #:when (empty? (variable-domain var))
[name (in-list ($cvar-past var))]) [name (in-list (checked-var-past var))])
name)) name))
;; for conflict-directed backjumping it's essential to forward-check ALL vars ;; for conflict-directed backjumping it's essential to forward-check ALL vars
;; (even after an empty domain is generated) and combine their conflicts ;; (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. ;; 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 ;; Discard constraints that have produced singleton domains
;; (they have no further use) ;; (they have no further use)
(define nonsingleton-constraints (define nonsingleton-constraints
(for/list ([constraint (in-constraints csp)] (for/list ([const (in-constraints prob)]
#:unless (and #:unless (and
(binary-constraint? constraint) (binary-constraint? const)
(constraint-relates? constraint aname) (constraint-relates? const ref-name)
(let ([other-name (first (remq aname ($constraint-names constraint)))]) (let ([other-name (first (remq ref-name (constraint-names const)))])
(singleton-var? (csp-var csp other-name))))) (singleton-var? (csp-var prob other-name)))))
constraint)) const))
(make-csp checked-vars nonsingleton-constraints)) (make-csp checked-vars nonsingleton-constraints))
(define/contract (constraint-checkable? c names) (define/contract (constraint-checkable? c names)
($constraint? (listof name?) . -> . any/c) (constraint? (listof name?) . -> . any/c)
;; constraint is checkable if all constraint names ;; constraint is checkable if all constraint names
;; are in target list of names. ;; are in target list of names.
(for/and ([cname (in-list ($constraint-names c))]) (for/and ([cname (in-list (constraint-names c))])
(memq cname names))) (memq cname names)))
(define/contract (constraint-arity constraint) (define/contract (constraint-arity const)
($constraint? . -> . exact-nonnegative-integer?) (constraint? . -> . exact-nonnegative-integer?)
(length ($constraint-names constraint))) (length (constraint-names const)))
(define (singleton-var? var) (define (singleton-var? var)
(= 1 (length ($var-domain var)))) (= 1 (length (variable-domain var))))
(define nchecks 0) (define nchecks 0)
(define (reset-nchecks!) (set! 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?)) ((csp?) ((listof name?) #:conflicts boolean?) . ->* . (or/c csp? exact-nonnegative-integer?))
;; this time, we're not limited to assigned variables ;; this time, we're not limited to assigned variables
;; (that is, vars that have been deliberately assigned in the backtrack process thus far) ;; (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) ;; 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)) #:when (singleton-var? var))
(var-name var))) (variable-name var)))
(define-values (checkable-constraints other-constraints) (define-values (checkable-consts other-consts)
(partition (λ (c) (and (constraint-checkable? c singleton-varnames) (partition (λ (c) (and (constraint-checkable? c singleton-varnames)
(or (not mandatory-names) (or (not mandatory-names)
(for/and ([name (in-list mandatory-names)]) (for/and ([name (in-list mandatory-names)])
(constraint-relates? c name))))) (constraint-relates? c name)))))
(constraints csp))) (constraints prob)))
(cond (cond
[conflict-count? (define conflict-count [conflict-count?
(for/sum ([constraint (in-list checkable-constraints)] (define conflict-count
#:unless (constraint csp)) (for/sum ([constraint (in-list checkable-consts)]
1)) #:unless (constraint prob))
(when-debug (set! nchecks (+ conflict-count nchecks))) 1))
conflict-count] (when-debug (set! nchecks (+ conflict-count nchecks)))
[else (for ([(constraint idx) (in-indexed (sort checkable-constraints < #:key constraint-arity))] conflict-count]
#:unless (constraint csp)) [else
(when-debug (set! nchecks (+ (add1 idx) nchecks))) (for ([(constraint idx) (in-indexed (sort checkable-consts < #:key constraint-arity))]
(backtrack!)) #:unless (constraint prob))
;; discard checked constraints, since they have no further reason to live (when-debug (set! nchecks (+ (add1 idx) nchecks)))
(make-csp (vars csp) other-constraints)])) (backtrack!))
;; discard checked constraints, since they have no further reason to live
(define/contract (make-nodes-consistent csp) (make-csp (vars prob) other-consts)]))
(define/contract (make-nodes-consistent prob)
(csp? . -> . csp?) (csp? . -> . csp?)
;; todo: why does this function slow down searches? ;; todo: why does this function slow down searches?
(make-csp (make-csp
(for/list ([var (in-vars csp)]) (for/list ([var (in-vars prob)])
(match-define ($var name vals) var) (match-define (variable name vals) var)
(define procs (for*/list ([constraint (in-constraints csp)] (define procs (for*/list ([const (in-constraints prob)]
[cnames (in-value ($constraint-names constraint))] [cnames (in-value (constraint-names const))]
#:when (and (= 1 (length cnames)) (eq? name (car cnames)))) #:when (and (= 1 (length cnames)) (eq? name (car cnames))))
($constraint-proc constraint))) (constraint-proc const)))
($var name (variable name
(for*/fold ([vals vals]) (for*/fold ([vals vals])
([proc (in-list procs)]) ([proc (in-list procs)])
(filter proc vals)))) (filter proc vals))))
(constraints csp))) (constraints prob)))
(define/contract (backtracking-solver (define/contract (backtracking-solver
csp prob
#:select-variable [select-unassigned-variable #:select-variable [select-unassigned-variable
(or (current-select-variable) first-unassigned-variable)] (or (current-select-variable) first-unassigned-variable)]
#:order-values [order-domain-values (or (current-order-values) first-domain-value)] #:order-values [order-domain-values (or (current-order-values) first-domain-value)]
#:inference [inference (or (current-inference) no-inference)]) #:inference [inference (or (current-inference) no-inference)])
((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?) ((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
(generator () (generator ()
(let loop ([csp csp]) (let loop ([prob prob])
(match (select-unassigned-variable csp) (match (select-unassigned-variable prob)
[#false (yield csp)] [#false (yield prob)]
[($var name domain) [(variable name domain)
(define (wants-backtrack? exn) (define (wants-backtrack? exn)
(and ($backtrack? exn) (or (let ([btns ($backtrack-names exn)]) (and ($backtrack? exn) (or (let ([btns ($backtrack-names exn)])
(or (empty? btns) (memq name btns)))))) (or (empty? btns) (memq name btns))))))
@ -410,83 +417,91 @@
([val (in-list (order-domain-values domain))]) ([val (in-list (order-domain-values domain))])
(with-handlers ([wants-backtrack? (with-handlers ([wants-backtrack?
(λ (bt) (append conflicts (remq name ($backtrack-names bt))))]) (λ (bt) (append conflicts (remq name ($backtrack-names bt))))])
(let* ([csp (assign-val csp name val)] (let* ([prob (assign-val prob name val)]
;; reduce constraints before inference, ;; reduce constraints before inference,
;; to create more forward-checkable (binary) constraints ;; to create more forward-checkable (binary) constraints
[csp (reduce-constraint-arity csp)] [prob (reduce-constraint-arity prob)]
[csp (inference csp name)] [prob (inference prob name)]
[csp (check-constraints csp)]) [prob (check-constraints prob)])
(loop csp))) (loop prob)))
conflicts)])))) conflicts)]))))
(define (random-pick xs) (define (random-pick xs)
(list-ref xs (random (length xs)))) (list-ref xs (random (length xs))))
(define (assign-random-vals csp) (define (assign-random-vals prob)
(for/fold ([new-csp csp]) (for/fold ([new-csp prob])
([name (in-var-names csp)]) ([name (in-variable-names prob)])
(assign-val new-csp name (random-pick ($csp-vals csp name))))) (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 (thread
(λ () (λ ()
(let loop () (let loop ()
;; Generate a complete assignment for all variables (probably with conflicts) ;; 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)]) ([nth-step (in-range max-steps)])
;; Now repeatedly choose a random conflicted variable and change it ;; Now repeatedly choose a random conflicted variable and change it
(match (conflicted-var-names csp) (match (conflicted-variable-names prob)
[(? empty?) (thread-send main-thread csp) (loop)] [(? empty?) (thread-send main-thread prob) (loop)]
[names [names
(define name (random-pick names)) (define name (random-pick names))
(define val (min-conflicts-value csp name ($csp-vals csp0 name))) (define val (min-conflicts-value prob name (csp-domain prob-start name)))
(assign-val csp name val)])))))) (assign-val prob name val)]))))))
(define/contract (min-conflicts-solver csp [max-steps 100]) (define/contract (min-conflicts-solver prob [max-steps 100])
(($csp?) (integer?) . ->* . generator?) ((csp?) (integer?) . ->* . generator?)
;; Solve a CSP by stochastic hillclimbing on the number of conflicts.
(generator () (generator ()
(for ([thread-count 4]) ; todo: what is ideal thread count? (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)]) (for ([i (in-naturals)])
(yield (thread-receive))))) (yield (thread-receive)))))
(define/contract (conflicted-var-names csp) (define/contract (optimal-stop-min proc xs)
($csp? . -> . (listof name?)) (procedure? (listof any/c) . -> . any/c)
(define-values (sample candidates) (split-at xs (inexact->exact (floor (* .458 (length xs))))))
(define threshold (argmin proc sample))
(or (for/first ([c (in-list candidates)]
#:when (<= (proc c) threshold))
c)
(last candidates)))
(define/contract (conflicted-variable-names prob)
(csp? . -> . (listof name?))
;; Return a list of variables in current assignment that are conflicted ;; Return a list of variables in current assignment that are conflicted
(for/list ([name (in-var-names csp)] (for/list ([name (in-variable-names prob)]
#:when (positive? (nconflicts csp name))) #:when (positive? (nconflicts prob name)))
name)) name))
(define/contract (min-conflicts-value csp name vals) (define/contract (min-conflicts-value prob name vals)
($csp? name? (listof any/c) . -> . any/c) (csp? name? (listof any/c) . -> . any/c)
;; Return the value that will give var the least number of conflicts ;; 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)) #:cache-keys? #true))
(for/first ([val (in-list vals-by-conflict)] (for/first ([val (in-list vals-by-conflict)]
#:unless (equal? val (first ($csp-vals csp name)))) ;; but change the value #:unless (equal? val (first (csp-domain prob name)))) ;; but change the value
val)) val))
(define no-value-sig (gensym)) (define no-value-sig (gensym))
(define/contract (nconflicts csp name [val no-value-sig]) (define/contract (nconflicts prob name [val no-value-sig])
(($csp? name?) (any/c) . ->* . exact-nonnegative-integer?) ((csp? name?) (any/c) . ->* . exact-nonnegative-integer?)
;; How many conflicts var: val assignment has with other variables. ;; How many conflicts var: val assignment has with other variables.
(check-constraints (if (eq? val no-value-sig) (check-constraints (if (eq? val no-value-sig)
csp prob
(assign-val csp name val)) (list name) #:conflicts #true)) (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))) (csp? . -> . (listof (cons/c name? any/c)))
(for/list ([var (in-vars csp)]) (for/list ([var (in-vars prob)])
(match var (match var
[($var name (list val)) (cons name val)]))) [(variable name (list val)) (cons name val)])))
(define/contract (combine-csps csps) (define/contract (combine-csps probs)
((listof $csp?) . -> . $csp?) ((listof csp?) . -> . csp?)
(make-csp (make-csp
(apply append (map $csp-vars csps)) (apply append (map csp-vars probs))
(apply append (map $csp-constraints csps)))) (apply append (map csp-constraints probs))))
(define/contract (make-cartesian-generator solgens) (define/contract (make-cartesian-generator solgens)
((listof generator?) . -> . generator?) ((listof generator?) . -> . generator?)
@ -500,18 +515,18 @@
(for ([sol (in-stream (car solstreams))]) (for ([sol (in-stream (car solstreams))])
(loop (cdr solstreams) (cons sol sols))))))) (loop (cdr solstreams) (cons sol sols)))))))
(define/contract (extract-subcsp csp names) (define/contract (extract-subcsp prob names)
($csp? (listof name?) . -> . $csp?) (csp? (listof name?) . -> . csp?)
(make-csp (make-csp
(for/list ([var (in-vars csp)] (for/list ([var (in-vars prob)]
#:when (memq (var-name var) names)) #:when (memq (variable-name var) names))
var) var)
(for/list ([constraint (in-constraints csp)] (for/list ([const (in-constraints prob)]
#:when (for/and ([cname (in-list ($constraint-names constraint))]) #:when (for/and ([cname (in-list (constraint-names const))])
(memq cname names))) (memq cname names)))
constraint))) const)))
(define/contract (solve* csp (define/contract (solve* prob
#:finish-proc [finish-proc csp->assocs] #:finish-proc [finish-proc csp->assocs]
#:solver [solver (or (current-solver) backtracking-solver)] #:solver [solver (or (current-solver) backtracking-solver)]
#:limit [max-solutions +inf.0]) #:limit [max-solutions +inf.0])
@ -521,21 +536,21 @@
(define subcsps ; decompose into independent csps. `cc` determines "connected components" (define subcsps ; decompose into independent csps. `cc` determines "connected components"
(if (current-decompose) (if (current-decompose)
(for/list ([nodeset (in-list (cc (csp->graph csp)))]) (for/list ([nodeset (in-list (cc (csp->graph prob)))])
(extract-subcsp csp nodeset)) (extract-subcsp prob nodeset))
(list csp))) (list prob)))
(for/list ([solution (in-producer (make-cartesian-generator (map solver subcsps)) (void))] (for/list ([solution (in-producer (make-cartesian-generator (map solver subcsps)) (void))]
[idx (in-range max-solutions)]) [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] #:finish-proc [finish-proc csp->assocs]
#:solver [solver (or (current-solver) backtracking-solver)] #:solver [solver (or (current-solver) backtracking-solver)]
#:limit [max-solutions 1]) #:limit [max-solutions 1])
((csp?) (#:finish-proc procedure? #:solver procedure? #:limit exact-nonnegative-integer?) ((csp?) (#:finish-proc procedure? #:solver procedure? #:limit exact-nonnegative-integer?)
. ->* . (or/c #false any/c)) . ->* . (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 solution) solution]
[(list solutions ...) solutions] [(list solutions ...) solutions]
[else #false])) [else #false]))

3
csp/csp/info.rkt
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@ -0,0 +1,3 @@
#lang info
(define scribblings '(("scribblings/csp.scrbl" (multi-page))))

4
csp/csp/main.rkt
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@ -1,4 +1,4 @@
#lang racket/base #lang racket/base
(require "port/main.rkt") (require "hacs.rkt")
(provide (all-from-out "port/main.rkt")) (provide (all-from-out "hacs.rkt"))

8
csp/csp/scribblings/csp.scrbl
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@ -5,15 +5,15 @@
@(define my-eval (make-base-eval)) @(define my-eval (make-base-eval))
@(my-eval `(require csp)) @(my-eval `(require csp))
@title{Constraint-satisfaction problems}
@title{csp}
@author[(author+email "Matthew Butterick" "mb@mbtype.com")] @author[(author+email "Matthew Butterick" "mb@mbtype.com")]
@defmodule[csp] @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} @section{Installation}

31
csp/hacs-test-workbench.rkt
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@ -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)))

557
csp/hacs.rkt
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@ -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)))

4
csp/info.rkt
Unescape Escape View File

@ -1,6 +1,4 @@
#lang info #lang info
(define collection 'multi) (define collection 'multi)
(define deps '(("base" #:version "6.0") "sugar" "rackunit-lib" "debug" "graph")) (define deps '(("base" #:version "6.0") "sugar" "rackunit-lib" "debug" "graph"))
(define update-implies '("sugar")) (define update-implies '("sugar"))
(define scribblings '(("csp/scribblings/csp.scrbl" (multi-page))))
;(define compile-omit-paths '("tests" "raco.rkt"))
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