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Matthew Butterick 6 years ago
parent 8c8c51fe84
commit 667ccecda2
1 changed files with 107 additions and 90 deletions
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197
csp/hacs.rkt
Unescape Escape View File

@ -12,6 +12,12 @@
(struct $csp ([vars #:mutable]
[constraints #:mutable]) #:transparent)
(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)))
(struct $constraint (names proc) #:transparent
#:property prop:procedure
(λ (constraint csp)
@ -21,24 +27,29 @@
(for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))])
(apply ($constraint-proc constraint) args))))
(define (make-constraint [names null] [proc values])
($constraint names proc))
(struct $var (name domain) #:transparent)
(define $var-name? symbol?)
(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? $avar?)
(define (make-csp [vds null] [constraints null])
($csp vds constraints))
(define (make-csp [vars null] [constraints null])
($csp vars constraints))
(define/contract (add-vars! csp names-or-procedure [vals-or-procedure empty])
(($csp? (or/c (listof $var-name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
((csp? (or/c (listof name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
(for/fold ([vars ($csp-vars csp)]
#:result (set-$csp-vars! csp vars))
([name (in-list (if (procedure? names-or-procedure)
(names-or-procedure)
names-or-procedure))])
(when (memq name (map $var-name vars))
(when (memq name (map var-name vars))
(raise-argument-error 'add-vars! "var that doesn't already exist" name))
(append vars (list ($var name
(if (procedure? vals-or-procedure)
@ -46,25 +57,25 @@
vals-or-procedure))))))
(define/contract (add-var! csp name [vals-or-procedure empty])
(($csp? $var-name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
(add-vars! csp (list name) vals-or-procedure))
(define/contract (add-constraints! csp proc namess [proc-name #false])
(($csp? procedure? (listof (listof $var-name?))) ((or/c #false $var-name?)) . ->* . void?)
(set-$csp-constraints! csp (append ($csp-constraints csp)
((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
(set-$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))
($constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(make-constraint names (if proc-name
(procedure-rename proc proc-name)
proc))))))
(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
(($csp? procedure? (listof $var-name?)) ($var-name?) . ->* . void?)
((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 $var-name?)) ($var-name?) . ->* . void?)
((csp? procedure? (listof name?)) (name?) . ->* . void?)
(add-constraints! csp proc (list var-names) proc-name))
(define/contract (alldiff= x y)
@ -74,6 +85,7 @@
(struct inconsistency-signal (csp) #:transparent)
(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))
@ -82,28 +94,30 @@
(define current-shuffle (make-parameter #t))
(define/contract (check-name-in-csp! caller csp name)
(symbol? $csp? $var-name? . -> . void?)
(define names (map $var-name ($csp-vars csp)))
(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? $var-name? . -> . $var?)
(check-name-in-csp! '$csp-var csp name)
(for/first ([var (in-list ($csp-vars csp))]
#:when (eq? name ($var-name var)))
(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? $var-name? . -> . (listof any/c))
(check-name-in-csp! '$csp-vals csp name)
($var-domain ($csp-var 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? $var-name? . -> . boolean?)
(and (memq name (map $var-name (filter $avar? ($csp-vars csp)))) #true))
(csp? name? . -> . any/c)
(for/first ([var (in-vars csp)]
#:when (assigned-var? var))
(eq? name (var-name var))))
(define (reduce-arity proc pattern)
(unless (match (procedure-arity proc)
@ -112,11 +126,10 @@
(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 id-names (map unbox boxed-id-names))
(define new-arity (length id-names))
(define new-arity (length boxed-id-names))
(procedure-rename
(λ xs
(unless (= (length xs) new-arity)
(unless (= (length xs) new-arity)
(apply raise-arity-error reduced-arity-name new-arity xs))
(apply proc (for/fold ([acc empty]
[xs xs]
@ -129,47 +142,44 @@
reduced-arity-name))
(define/contract (reduce-constraint-arity csp [minimum-arity 3])
(($csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . $csp?)
((csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . csp?)
(let ([assigned-name? (curry assigned-name? csp)])
(define (partially-assigned? constraint)
(ormap assigned-name? ($constraint-names constraint)))
($csp ($csp-vars csp)
(for/list ([constraint (in-list ($csp-constraints csp))])
(cond
[(and (if minimum-arity (<= minimum-arity (constraint-arity constraint)) #true)
(partially-assigned? constraint))
(match-define ($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-arity proc reduce-arity-pattern)))]
[else constraint])))))
(make-csp (vars csp)
(for/list ([constraint (in-constraints csp)])
(cond
[(and (if minimum-arity (<= minimum-arity (constraint-arity constraint)) #true)
(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 ($csp-vals csp cname))
(box cname)))])
(reduce-arity proc reduce-arity-pattern)))]
[else constraint])))))
(define/contract (assign-val csp name val)
($csp? $var-name? any/c . -> . $csp?)
(define assigned-csp ($csp
(for/list ([var ($csp-vars csp)])
(if (eq? name ($var-name var))
($avar name (list val))
var))
($csp-constraints csp)))
assigned-csp)
(csp? name? any/c . -> . csp?)
(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 $avar?))))
(for/list ([var (in-list ($csp-vars csp))]
#:unless ($avar? var))
var))
(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 $avar?))))
(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
(match (unassigned-vars csp)
[(? empty?) #false]
[xs (first xs)]))
[(cons x _) x]))
(define/contract (argmin-random-tie proc xs)
(procedure? (non-empty-listof any/c) . -> . any/c)
@ -180,21 +190,22 @@
(first xs)))
(define/contract (minimum-remaining-values csp)
($csp? . -> . (or/c #false (and/c $var? (not/c $avar?))))
(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
(match (unassigned-vars csp)
[(? empty?) #false]
[xs (argmin-random-tie (λ (var) (length ($var-domain var))) xs)]))
(define mrv minimum-remaining-values)
(define/contract (var-degree csp var)
($csp? $var? . -> . exact-nonnegative-integer?)
(for/sum ([constraint (in-list ($csp-constraints csp))]
#:when (memq ($var-name var) ($constraint-names constraint)))
(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 $avar?))))
(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
(define uvars (unassigned-vars csp))
(cond
[(empty? uvars) #false]
@ -208,7 +219,7 @@
(length ($var-vals var)))
(define/contract (mrv-degree-hybrid csp)
($csp? . -> . (or/c #f $var?))
(csp? . -> . (or/c #f $var?))
(define uvars (unassigned-vars csp))
(cond
[(empty? uvars) #false]
@ -228,7 +239,7 @@
(define (no-inference csp name) csp)
(define/contract (relating-only constraints names)
((listof $constraint?) (listof $var-name?) . -> . (listof $constraint?))
((listof $constraint?) (listof name?) . -> . (listof $constraint?))
(for*/list ([constraint (in-list constraints)]
[cnames (in-value ($constraint-names constraint))]
#:when (and (= (length names) (length cnames))
@ -236,16 +247,22 @@
(memq name cnames))))
constraint))
(define (binary-constraint? constraint)
(= 2 (constraint-arity constraint)))
(define (constraint-relates? constraint name)
(and (memq name ($constraint-names constraint)) #true))
(define/contract (forward-check csp aname)
($csp? $var-name? . -> . $csp?)
(csp? name? . -> . csp?)
(define aval (first ($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 ($avar? x) (eq? ($var-name x) aname)))) var]
[(? (λ (x) (or (assigned-var? x) (eq? (var-name x) aname)))) var]
[($var name vals)
(match (($csp-constraints csp) . relating-only . (list aname name))
(match ((constraints csp) . relating-only . (list aname name))
[(? empty?) var]
[constraints
(define new-vals
@ -259,7 +276,7 @@
($cvar name new-vals (cons aname (if ($cvar? var)
($cvar-past var)
null)))])]))
(define checked-vars (map check-var ($csp-vars csp)))
(define checked-vars (map check-var (vars csp)))
;; conflict-set will be empty if there are no empty domains
(define conflict-set (for*/list ([var (in-list checked-vars)]
#:when (empty? ($var-domain var))
@ -271,21 +288,21 @@
;; If we just bail out at the first conflict, we may backjump too far based on its history
;; (and thereby miss parts of the search tree)
(when (pair? conflict-set)
(raise ($backtrack conflict-set)))
(backtrack! conflict-set))
;; Discard constraints that have produced singleton domains
;; (they have no further use)
(define nonsingleton-constraints
(for/list ([constraint (in-list ($csp-constraints csp))]
(for/list ([constraint (in-constraints csp)]
#:unless (and
(= 2 (constraint-arity constraint)) ; binary constraint
(memq aname ($constraint-names constraint)) ; includes target name
(binary-constraint? constraint)
(constraint-relates? constraint aname)
(let ([other-name (first (remq aname ($constraint-names constraint)))]) ; and something else
(= (length ($csp-vals csp other-name)) 1)))) ; that has only one value
constraint))
($csp checked-vars nonsingleton-constraints))
(make-csp checked-vars nonsingleton-constraints))
(define/contract (constraint-checkable? c names)
($constraint? (listof $var-name?) . -> . boolean?)
($constraint? (listof name?) . -> . boolean?)
(and (for/and ([cname (in-list ($constraint-names c))])
(memq cname names))
#true))
@ -298,27 +315,27 @@
(= 1 (length ($var-domain var))))
(define/contract (check-constraints csp)
($csp? . -> . $csp?)
(csp? . -> . csp?)
;; this time, we're not limited to assigned variables
;; (that is, vars that have been deliberately assigned in the backtrack process thus far)
;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking)
(define singleton-varnames (for/list ([var (in-list ($csp-vars csp))]
(define singleton-varnames (for/list ([var (in-vars csp)]
#:when (singleton-var? var))
($var-name var)))
(var-name var)))
(define-values (checkable-constraints other-constraints)
(partition (λ (c) (constraint-checkable? c singleton-varnames)) ($csp-constraints csp)))
(partition (λ (c) (constraint-checkable? c singleton-varnames)) (constraints csp)))
(for ([constraint (in-list (sort checkable-constraints < #:key constraint-arity))]
#:unless (constraint csp))
(raise ($backtrack null)))
($csp ($csp-vars csp) other-constraints))
(backtrack!))
(make-csp (vars csp) other-constraints))
(define/contract (make-nodes-consistent csp)
($csp? . -> . $csp?)
(csp? . -> . csp?)
;; todo: why does this function slow down searches?
($csp
(for/list ([var (in-list ($csp-vars csp))])
(for/list ([var (in-vars csp)])
(match-define ($var name vals) var)
(define procs (for*/list ([constraint (in-list ($csp-constraints csp))]
(define procs (for*/list ([constraint (in-constraints csp)]
[cnames (in-value ($constraint-names constraint))]
#:when (and (= 1 (length cnames)) (eq? name (car cnames))))
($constraint-proc constraint)))
@ -326,7 +343,7 @@
(for*/fold ([vals vals])
([proc (in-list procs)])
(filter proc vals))))
($csp-constraints csp)))
(constraints csp)))
(define/contract (backtracking-solver
csp
@ -334,7 +351,7 @@
(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)])
(($csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
(generator ()
(let loop ([csp csp])
(match (select-unassigned-variable csp)
@ -360,8 +377,8 @@
;; todo: min-conflicts solver
(define/contract ($csp-assocs csp)
($csp? . -> . (listof (cons/c $var-name? any/c)))
(for/list ([var (in-list ($csp-vars csp))])
(csp? . -> . (listof (cons/c name? any/c)))
(for/list ([var (in-vars csp)])
(match var
[($var name domain) (cons name (first domain))])))
@ -369,7 +386,7 @@
#:finish-proc [finish-proc $csp-assocs]
#:solver [solver (or (current-solver) backtracking-solver)]
#:count [max-solutions +inf.0])
(($csp?) (#:finish-proc procedure? #:solver procedure? #:count integer?) . ->* . (listof any/c))
((csp?) (#:finish-proc procedure? #:solver procedure? #:count integer?) . ->* . (listof any/c))
(for/list ([solution (in-producer (solver csp) (void))]
[idx (in-range max-solutions)])
(finish-proc solution)))
@ -377,7 +394,7 @@
(define/contract (solve csp
#:finish-proc [finish-proc $csp-assocs]
#:solver [solver (or (current-solver) backtracking-solver)])
(($csp?) (#:finish-proc procedure? #:solver procedure?) . ->* . (or/c #false any/c))
((csp?) (#:finish-proc procedure? #:solver procedure?) . ->* . (or/c #false any/c))
(match (solve* csp #:finish-proc finish-proc #:solver solver #:count 1)
[(list solution) solution]
[else #false]))

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