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ac-3 etc

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Matthew Butterick 6 years ago
parent 558c905393
commit 7ef8d6937e
4 changed files with 218 additions and 138 deletions
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4
csp/csp/csp.rkt
Unescape Escape View File

@ -177,7 +177,9 @@
(define/contract (terminating-at arcs name)
((listof $arc?) $var-name? . -> . (listof $arc?))
(for/list ([arc (in-list arcs)]
#:when (eq? name (second ($constraint-names ($arc-constraint arc)))))
#:when (and
(memq name ($constraint-names ($arc-constraint arc)))
(not (eq? name ($arc-name arc)))))
arc))
(define/contract (constraint-assigned? csp constraint)

53
csp/csp/hacs-test-workbench.rkt
Unescape Escape View File

@ -6,26 +6,33 @@
(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)))
(define (word-value . xs)
(for/sum ([(x idx) (in-indexed (reverse xs))])
(* x (expt 10 idx))))
(define smm (make-csp))
(define vs '(s e n d m o r y))
(add-vars! smm vs (λ () (range 10)))
(add-constraint! smm positive? '(s))
(add-constraint! smm positive? '(m))
(add-constraint! smm (λ (d e y) (= (modulo (+ d e) 10) y)) '(d e y))
(add-constraint! smm (λ (n d r e y)
(= (modulo (+ (word-value n d) (word-value r e)) 100)
(word-value e y))) '(n d r e y))
(add-constraint! smm (λ (e n d o r y)
(= (modulo (+ (word-value e n d) (word-value o r e)) 1000) (word-value n e y))) '(e n d o r y))
(add-constraint! smm (λ (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))) '(s e n d m o r y))
(add-pairwise-constraint! smm alldiff= '(s e n d m o r y))
(parameterize ([current-select-variable mrv-degree-hybrid]
[current-node-consistency make-nodes-consistent]) ; todo: why is plain mrv so bad on this problem?
(time-named (solve smm)))
nassns
nfchecks
nchecks

4
csp/csp/hacs-test.rkt
Unescape Escape View File

@ -5,6 +5,8 @@
(current-select-variable mrv-degree-hybrid)
(current-order-values shuffle)
(current-random #true)
(current-node-consistency #f)
(current-arity-reduction #t)
(check-equal? (first-unassigned-variable (csp (list (var 'a (range 3)) (var 'b (range 3))) null))
(var 'a (range 3)))
@ -287,7 +289,7 @@
((nationality-4 . spaniard) (color-4 . ivory) (drink-4 . orange-juice) (smoke-4 . luckystrike) (pet-4 . dogs))))
(module+ main
(when-debug
(begin
(define-syntax n (λ (stx) #'10))
(time-avg n (void (solve quarters)))
(time-avg n (void (solve* xsum)))

295
csp/csp/hacs.rkt
Unescape Escape View File

@ -4,7 +4,7 @@
(define-syntax when-debug
(let ()
(define debug #f)
(define debug #t)
(if debug
(make-rename-transformer #'begin)
(λ (stx) (syntax-case stx ()
@ -16,24 +16,23 @@
(if (null? argss)
(yield (reverse acc))
(for ([arg (car argss)])
(loop (cdr argss) (cons arg acc))))))))
(loop (cdr argss) (cons arg acc))))))))
(struct csp (vars constraints [assignments #:auto] [checks #:auto])
#:mutable #:transparent #:auto-value 0)
(struct csp (vars constraints) #:mutable #:transparent)
(define constraints csp-constraints)
(define vars csp-vars)
(define-syntax-rule (in-constraints csp) (in-list (csp-constraints csp)))
(define-syntax-rule (in-vars csp) (in-list (vars csp)))
(define-syntax-rule (in-variable-names csp) (in-list (map var-name (vars csp))))
(define-syntax-rule (in-var-names csp) (in-list (map var-name (vars csp))))
(struct constraint (names proc) #:transparent
#:property prop:procedure
(λ (const prob)
(unless (csp? prob)
(raise-argument-error 'constraint-proc "csp" prob))
(raise-argument-error 'constraint "csp" prob))
;; apply proc in many-to-many style
(for/and ([args (in-cartesian (map (λ (name) (find-domain prob name)) (constraint-names const)))])
(apply (constraint-proc const) args))))
(apply (constraint-proc const) args))))
(define name? symbol?)
@ -92,15 +91,15 @@
((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
(set-csp-constraints! prob (append (constraints prob)
(for/list ([names (in-list namess)])
(for ([name (in-list names)])
(check-name-in-csp! 'add-constraints! prob name))
(make-constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(for ([name (in-list names)])
(check-name-in-csp! 'add-constraints! prob name))
(make-constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(define/contract (add-pairwise-constraint! prob proc var-names [proc-name #false])
(define/contract (add-pairwise-constraint! prob proc names [proc-name #false])
((csp? procedure? (listof name?)) (name?) . ->* . void?)
(add-constraints! prob proc (combinations var-names 2) proc-name))
(add-constraints! prob proc (combinations names 2) proc-name))
(define/contract (add-constraint! prob proc names [proc-name #false])
((csp? procedure? (listof name?)) (name?) . ->* . void?)
@ -120,6 +119,8 @@
(define current-random (make-parameter #t))
(define current-decompose (make-parameter #t))
(define current-thread-count (make-parameter 4))
(define current-node-consistency (make-parameter #f))
(define current-arity-reduction (make-parameter #t))
(define/contract (check-name-in-csp! caller prob name)
(symbol? csp? name? . -> . void?)
@ -132,7 +133,7 @@
(check-name-in-csp! 'find-var prob name)
(for/first ([vr (in-vars prob)]
#:when (eq? name (var-name vr)))
vr))
vr))
(define/contract (find-domain prob name)
(csp? name? . -> . (listof any/c))
@ -145,7 +146,7 @@
(csp? name? . -> . any/c)
(for/or ([vr (in-vars prob)]
#:when (assigned-var? vr))
(eq? name (var-name vr))))
(eq? name (var-name vr))))
(define/contract (reduce-function-arity proc pattern)
(procedure? (listof any/c) . -> . procedure?)
@ -177,31 +178,27 @@
(ormap assigned? (constraint-names constraint)))
(make-csp (vars prob)
(for/list ([const (in-constraints prob)])
(cond
;; no point reducing 2-arity functions because they will be consumed by forward checking
[(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
(partially-assigned? const))
(match-define (constraint cnames proc) const)
;; pattern is mix of values and boxed symbols (indicating variables to persist)
;; use boxes here as cheap way to distinguish id symbols from value symbols
(define reduce-arity-pattern (for/list ([cname (in-list cnames)])
(if (assigned? cname)
(first (find-domain prob cname))
(box cname))))
(constraint (filter-not assigned? cnames)
(reduce-function-arity proc reduce-arity-pattern))]
[else const]))))
(cond
;; no point reducing 2-arity functions because they will be consumed by forward checking
[(and (or (not minimum-arity) (<= minimum-arity (constraint-arity const)))
(partially-assigned? const))
(match-define (constraint cnames proc) const)
;; pattern is mix of values and boxed symbols (indicating variables to persist)
;; use boxes here as cheap way to distinguish id symbols from value symbols
(define arity-reduction-pattern (for/list ([cname (in-list cnames)])
(if (assigned? cname)
(first (find-domain prob cname))
(box cname))))
(constraint (filter-not assigned? cnames)
(reduce-function-arity proc arity-reduction-pattern))]
[else const]))))
(define nassns 0)
(define (reset-assns!) (set! nassns 0))
(define nfchecks 0)
(define (reset-nfcs!) (set! nfchecks 0))
(define nchecks 0)
(define (reset-nassns!) (set! nassns 0))
(define (reset-nfchecks!) (set! nfchecks 0))
(define (reset-nchecks!) (set! nchecks 0))
(define/contract (assign-val prob name val)
@ -209,9 +206,9 @@
(when-debug (set! nassns (add1 nassns)))
(make-csp
(for/list ([vr (in-vars prob)])
(if (eq? name (var-name vr))
(assigned-var name (list val))
vr))
(if (eq? name (var-name vr))
(assigned-var name (list val))
vr))
(constraints prob)))
(define/contract (unassigned-vars prob)
@ -236,7 +233,7 @@
(csp? var? . -> . natural?)
(for/sum ([const (in-constraints prob)]
#:when (memq (var-name var) (constraint-names const)))
1))
1))
(define/contract (domain-length var)
(var? . -> . natural?)
@ -259,7 +256,7 @@
(random-pick (for/list ([uv (in-list mrv-uvars)]
[degree (in-list degrees)]
#:when (= max-degree degree))
uv))])]))
uv))])]))
(define first-domain-value values)
@ -271,44 +268,122 @@
[cnames (in-value (constraint-names const))]
#:when (and (= (length names) (length cnames))
(for/and ([name (in-list names)])
(memq name cnames))))
const))
(memq name cnames))))
const))
(define (one-arity? const) (= 1 (constraint-arity const)))
(define (two-arity? const) (= 2 (constraint-arity const)))
(define (constraint-relates? const name)
(memq name (constraint-names const)))
(struct arc (name const) #:transparent)
(define/contract (two-arity-constraints->arcs constraints)
((listof (and/c constraint? two-arity?)) . -> . (listof arc?))
(for*/list ([const (in-list constraints)]
[name (in-list (constraint-names const))])
(arc name const)))
(require sugar/debug)
(define/contract (reduce-domain prob ark)
(csp? arc? . -> . csp?)
(match-define (arc name (constraint names constraint-proc)) ark)
(match-define (list other-name) (remove name names))
(define proc (if (eq? name (first names)) ; name is on left
constraint-proc ; so val stays on left
(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
(define (satisfies-arc? val)
(for/or ([other-val (in-list (find-domain prob other-name))])
(proc val other-val)))
(make-csp
(for/list ([vr (in-vars prob)])
(cond
[(assigned-var? vr) vr]
[(eq? name (var-name vr))
(var name (match (filter satisfies-arc? (domain vr))
[(? empty?) (backtrack!)]
[vals vals]))]
[else vr]))
(constraints prob)))
(define/contract (terminating-at? arcs name)
((listof arc?) name? . -> . (listof arc?))
(for/list ([arc (in-list arcs)]
#:when (and
(memq name (constraint-names (arc-const arc)))
(not (eq? name (arc-name arc)))))
arc))
(define/contract (ac-3 prob . _)
((csp?) (any/c) . ->* . csp?)
;; csp is arc-consistent if every pair of variables (x y)
;; has values in their domain that satisfy every binary constraint
(define starting-arcs (two-arity-constraints->arcs (filter two-arity? (constraints prob))))
(for/fold ([prob prob]
[arcs starting-arcs]
#:result (prune-singleton-constraints prob))
([i (in-naturals)]
#:break (empty? arcs))
(length starting-arcs)
(match-define (cons (arc name proc) other-arcs) arcs)
(length other-arcs)
(define reduced-csp (reduce-domain prob (arc name proc)))
(values reduced-csp (if (= (length (find-domain prob name)) (length (find-domain reduced-csp name)))
;; revision did not reduce the domain, so keep going
other-arcs
;; revision reduced the domain, so supplement the list of arcs
(remove-duplicates (append (starting-arcs . terminating-at? . name) other-arcs))))))
(define/contract (forward-check-var prob ref-name vr)
(csp? name? var? . -> . var?)
(cond
;; don't check against assigned vars, or the reference var
;; (which is probably assigned but maybe not)
[(assigned-var? vr) vr]
[(eq? (var-name vr) ref-name) vr]
[else
(match-define (var name vals) vr)
(match ((constraints prob) . relating-only . (list ref-name name))
[(? empty?) vr]
[constraints
(define new-vals
(for/list ([val (in-list vals)]
#:when (for/and ([const (in-list constraints)])
(let ([proc (constraint-proc const)]
[ref-val (first (find-domain prob ref-name))])
(if (eq? name (first (constraint-names const)))
(proc val ref-val)
(proc ref-val val)))))
val))
(checked-variable name new-vals (cons ref-name (match vr
[(checked-variable _ _ history) history]
[else null])))])]))
(define/contract (prune-singleton-constraints prob [ref-name #false])
((csp?) ((or/c #false name?)) . ->* . csp?)
(define singleton-var-names (for/list ([vr (in-vars prob)]
#:when (singleton-var? vr))
(var-name vr)))
(make-csp
(vars prob)
(for/list ([const (in-constraints prob)]
#:unless (and (two-arity? const)
(or (not ref-name) (constraint-relates? const ref-name))
(for/and ([cname (in-list (constraint-names const))])
(memq cname singleton-var-names))))
const)))
(define/contract (forward-check prob ref-name)
(csp? name? . -> . csp?)
(define aval (first (find-domain prob ref-name)))
(define (check-var vr)
(match vr
;; 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) ref-name)))) vr]
[(var name vals)
(match ((constraints prob) . relating-only . (list ref-name name))
[(? empty?) vr]
[constraints
(define new-vals
(for/list ([val (in-list vals)]
#:when (for/and ([const (in-list constraints)])
(let ([proc (constraint-proc const)])
(if (eq? name (first (constraint-names const)))
(proc val aval)
(proc aval val)))))
val))
(checked-variable name new-vals (cons ref-name (match vr
[(checked-variable _ _ history) history]
[else null])))])]))
(define checked-vars (map check-var (vars prob)))
(define checked-vars (map (λ (vr) (forward-check-var prob ref-name vr)) (vars prob)))
(when-debug (set! nfchecks (+ (length checked-vars) nchecks)))
;; conflict-set will be empty if there are no empty domains (as we would hope)
(define conflict-set (for*/list ([cvr (in-list checked-vars)]
#:when (empty? (domain cvr))
[name (in-list (history cvr))])
name))
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.
@ -318,27 +393,21 @@
(backtrack! conflict-set))
;; Discard constraints that have produced singleton domains
;; (they have no further use)
(define nonsingleton-constraints
(for/list ([const (in-constraints prob)]
#:unless (and (two-arity? const)
(constraint-relates? const ref-name)
(let ([other-name (first (remq ref-name (constraint-names const)))])
(singleton-var? (find-var prob other-name)))))
const))
(make-csp checked-vars nonsingleton-constraints))
(prune-singleton-constraints (make-csp checked-vars (constraints prob)) ref-name))
(define/contract (constraint-checkable? const 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 const))])
(memq cname names)))
(memq cname names)))
(define/contract (constraint-arity const)
(constraint? . -> . natural?)
(length (constraint-names const)))
(define (singleton-var? var)
(define/contract (singleton-var? var)
(var? . -> . boolean?)
(= 1 (domain-length var)))
(define/contract (check-constraints prob [mandatory-names #f] #:conflicts [conflict-count? #f])
@ -348,44 +417,43 @@
;; 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 ([vr (in-vars prob)]
#:when (singleton-var? vr))
(var-name vr)))
(var-name vr)))
(define-values (checkable-consts other-consts)
(partition (λ (const) (and (constraint-checkable? const singleton-varnames)
(or (not mandatory-names)
(for/and ([name (in-list mandatory-names)])
(constraint-relates? const name)))))
(constraint-relates? const name)))))
(constraints prob)))
(cond
[conflict-count?
(define conflict-count
(for/sum ([constraint (in-list checkable-consts)]
#:unless (constraint prob))
1))
1))
(when-debug (set! nchecks (+ conflict-count nchecks)))
conflict-count]
[else
(for ([(constraint idx) (in-indexed checkable-consts)]
#:unless (constraint prob))
(when-debug (set! nchecks (+ (add1 idx) nchecks)))
(backtrack!))
(when-debug (set! nchecks (+ (add1 idx) nchecks)))
(backtrack!))
;; discard checked constraints, since they have no further reason to live
(make-csp (vars prob) other-consts)]))
(define/contract (make-nodes-consistent prob)
(csp? . -> . csp?)
;; todo: why does this function slow down searches?
(make-csp
(for/list ([vr (in-vars prob)])
(match-define (var name vals) vr)
(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)))
(var name
(for*/fold ([vals vals])
([proc (in-list procs)])
(filter proc vals))))
(constraints prob)))
(define-values (unary-constraints other-constraints)
(partition one-arity? (constraints prob)))
(if (empty? unary-constraints)
prob
(make-csp
(for/list ([vr (in-vars prob)])
(match-define (var name vals) vr)
(var name (for/fold ([vals vals])
([const (in-list unary-constraints)]
#:when (constraint-relates? const name))
(filter (constraint-proc const) vals))))
other-constraints)))
(define/contract (backtracking-solver
prob
@ -395,7 +463,8 @@
#:inference [inference (or (current-inference) no-inference)])
((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
(generator ()
(let loop ([prob prob])
(define reduce-arity-proc (if (current-arity-reduction) reduce-constraint-arity values))
(let loop ([prob ((if (current-node-consistency) make-nodes-consistent values) prob)])
(match (select-unassigned-variable prob)
[#false (yield prob)]
[(var name domain)
@ -410,7 +479,7 @@
(let* ([prob (assign-val prob name val)]
;; reduce constraints before inference,
;; to create more forward-checkable (binary) constraints
[prob (reduce-constraint-arity prob)]
[prob (reduce-arity-proc prob)]
[prob (inference prob name)]
[prob (check-constraints prob)])
(loop prob)))
@ -421,7 +490,7 @@
(define (assign-random-vals prob)
(for/fold ([new-csp prob])
([name (in-variable-names prob)])
([name (in-var-names prob)])
(assign-val new-csp name (random-pick (find-domain prob name)))))
(define (make-min-conflcts-thread prob-start thread-count max-steps [main-thread (current-thread)])
@ -443,9 +512,9 @@
((csp?) (integer?) . ->* . generator?)
(generator ()
(for ([thread-count (or (current-thread-count) 1)]) ; todo: what is ideal thread count?
(make-min-conflcts-thread prob thread-count max-steps))
(make-min-conflcts-thread prob thread-count max-steps))
(for ([i (in-naturals)])
(yield (thread-receive)))))
(yield (thread-receive)))))
(define/contract (optimal-stop-min proc xs)
(procedure? (listof any/c) . -> . any/c)
@ -453,15 +522,15 @@
(define threshold (argmin proc sample))
(or (for/first ([candidate (in-list candidates)]
#:when (<= (proc candidate) threshold))
candidate)
candidate)
(last candidates)))
(define/contract (conflicted-variable-names prob)
(csp? . -> . (listof name?))
;; Return a list of variables in current assignment that are conflicted
(for/list ([name (in-variable-names prob)]
(for/list ([name (in-var-names prob)]
#:when (positive? (nconflicts prob name)))
name))
name))
(define/contract (min-conflicts-value prob name vals)
(csp? name? (listof any/c) . -> . any/c)
@ -470,7 +539,7 @@
#:cache-keys? #true))
(for/first ([val (in-list vals-by-conflict)]
#:unless (equal? val (first (find-domain prob name)))) ;; but change the value
val))
val))
(define no-value-sig (gensym))
@ -484,8 +553,8 @@
(define/contract (csp->assocs prob)
(csp? . -> . (listof (cons/c name? any/c)))
(for/list ([vr (in-vars prob)])
(match vr
[(var name (list val)) (cons name val)])))
(match vr
[(var name (list val)) (cons name val)])))
(define/contract (combine-csps probs)
((listof csp?) . -> . csp?)
@ -499,11 +568,11 @@
(make-csp
(for/list ([vr (in-vars prob)]
#:when (memq (var-name vr) names))
vr)
vr)
(for/list ([const (in-constraints prob)]
#:when (for/and ([cname (in-list (constraint-names const))])
(memq cname names)))
const)))
(memq cname names)))
const)))
(define/contract (solve* prob
#:finish-proc [finish-proc csp->assocs]
@ -511,22 +580,22 @@
#:limit [max-solutions +inf.0])
((csp?) (#:finish-proc procedure? #:solver procedure? #:limit natural?)
. ->* . (listof any/c))
(when-debug (reset-assns!) (reset-nfcs!) (reset-nchecks!))
(when-debug (reset-nassns!) (reset-nfchecks!) (reset-nchecks!))
(define subcsps ; decompose into independent csps. `cc` determines "connected components"
(if (current-decompose)
(for/list ([nodeset (in-list (cc (csp->graph prob)))])
(extract-subcsp prob nodeset))
(extract-subcsp prob nodeset))
(list prob)))
(define solgens (map solver subcsps))
(define solstreams (for/list ([solgen (in-list solgens)])
(for/stream ([sol (in-producer solgen (void))])
sol)))
(for/stream ([sol (in-producer solgen (void))])
sol)))
(for/list ([solution-pieces (in-cartesian solstreams)]
[idx (in-range max-solutions)])
(finish-proc (combine-csps solution-pieces))))
(finish-proc (combine-csps solution-pieces))))
(define/contract (solve prob
#:finish-proc [finish-proc csp->assocs]

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