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#lang debug racket
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(require racket/generator graph sugar/debug)
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(provide (all-defined-out))
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(define-syntax when-debug
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(let ()
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(define debug #f)
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(if debug
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(make-rename-transformer #'begin)
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(λ (stx) (syntax-case stx ()
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[(_ . rest) #'(void)])))))
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(define-syntax-rule (in-cartesian x)
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(in-generator (let ([argss x])
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(let loop ([argss argss][acc empty])
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(if (null? argss)
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(yield (reverse acc))
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(for ([arg (in-list (car argss))])
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(loop (cdr argss) (cons arg acc))))))))
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(struct $csp (vars
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constraints
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[assignments #:auto]
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[checks #:auto]) #:mutable #:transparent
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#:auto-value 0)
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(define csp? $csp?)
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(define vars $csp-vars)
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(define constraints $csp-constraints)
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(define-syntax-rule (in-constraints csp) (in-list ($csp-constraints csp)))
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(define-syntax-rule (in-vars csp) (in-list ($csp-vars csp)))
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(define-syntax-rule (in-var-names csp) (in-list (map $var-name ($csp-vars csp))))
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(struct $constraint (names proc) #:transparent
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#:property prop:procedure
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(λ (constraint csp)
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(unless ($csp? csp)
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(raise-argument-error '$constraint-proc "$csp" csp))
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;; apply proc in many-to-many style
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(for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))])
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(apply ($constraint-proc constraint) args))))
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(define (make-constraint [names null] [proc values])
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($constraint names proc))
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(define constraint-names $constraint-names)
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(define constraint? $constraint?)
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(define (csp->graphviz csp)
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(define g (csp->graph csp))
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(graphviz g #:colors (coloring/brelaz g)))
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(define (csp->graph csp)
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(for*/fold ([g (unweighted-graph/undirected (map var-name (vars csp)))])
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([constraint (in-constraints csp)]
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[edge (in-combinations (constraint-names constraint) 2)])
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(apply add-edge! g edge)
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g))
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(struct $var (name domain) #:transparent)
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(define var? $var?)
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(define name? symbol?)
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(define $var-vals $var-domain)
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(define var-name $var-name)
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(struct $cvar $var (past) #:transparent)
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(struct $avar $var () #:transparent)
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(define assigned-var? $avar?)
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(define/contract (make-csp [vars null] [constraints null])
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(() ((listof var?) (listof constraint?)) . ->* . csp?)
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($csp vars constraints))
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(define/contract (add-vars! csp names-or-procedure [vals-or-procedure empty])
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((csp? (or/c (listof name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(for/fold ([vars ($csp-vars csp)]
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#:result (set-$csp-vars! csp vars))
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([name (in-list (if (procedure? names-or-procedure)
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(names-or-procedure)
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names-or-procedure))])
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(when (memq name (map var-name vars))
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(raise-argument-error 'add-vars! "var that doesn't already exist" name))
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(append vars (list ($var name
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(if (procedure? vals-or-procedure)
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(vals-or-procedure)
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vals-or-procedure))))))
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(define/contract (add-var! csp name [vals-or-procedure empty])
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((csp? name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(add-vars! csp (list name) vals-or-procedure))
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(define/contract (add-constraints! csp proc namess [proc-name #false])
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((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
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(set-$csp-constraints! csp (append (constraints csp)
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(for/list ([names (in-list namess)])
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(for ([name (in-list names)])
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(check-name-in-csp! 'add-constraints! csp name))
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(make-constraint names (if proc-name
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(procedure-rename proc proc-name)
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proc))))))
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(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
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((csp? procedure? (listof name?)) (name?) . ->* . void?)
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(add-constraints! csp proc (combinations var-names 2) proc-name))
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(define/contract (add-constraint! csp proc var-names [proc-name #false])
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((csp? procedure? (listof name?)) (name?) . ->* . void?)
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(add-constraints! csp proc (list var-names) proc-name))
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(define/contract (alldiff= x y)
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(any/c any/c . -> . boolean?)
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(not (= x y)))
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(struct $backtrack (names) #:transparent)
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(define (backtrack! [names null]) (raise ($backtrack names)))
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(define current-select-variable (make-parameter #f))
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(define current-order-values (make-parameter #f))
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(define current-inference (make-parameter #f))
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(define current-solver (make-parameter #f))
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(define current-random (make-parameter #t))
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(define current-decompose (make-parameter #t))
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(define/contract (check-name-in-csp! caller csp name)
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(symbol? csp? name? . -> . void?)
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(define names (map var-name (vars csp)))
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(unless (memq name names)
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(raise-argument-error caller (format "one of these existing csp var names: ~v" names) name)))
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(define/contract (csp-var csp name)
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(csp? name? . -> . $var?)
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(check-name-in-csp! 'csp-var csp name)
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(for/first ([var (in-vars csp)]
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#:when (eq? name (var-name var)))
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var))
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(define/contract ($csp-vals csp name)
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(csp? name? . -> . (listof any/c))
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(check-name-in-csp! 'csp-vals csp name)
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($var-domain (csp-var csp name)))
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(define order-domain-values values)
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(define/contract (assigned-name? csp name)
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(csp? name? . -> . any/c)
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(for/or ([var (in-vars csp)]
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#:when (assigned-var? var))
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(eq? name (var-name var))))
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(define (reduce-function-arity proc pattern)
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(unless (match (procedure-arity proc)
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[(arity-at-least val) (<= val (length pattern))]
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[(? number? val) (= val (length pattern))])
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(raise-argument-error 'reduce-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern))
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(define reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc))))
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(define-values (boxed-id-names vals) (partition box? pattern))
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(define new-arity (length boxed-id-names))
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(procedure-rename
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(λ xs
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(unless (= (length xs) new-arity)
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(apply raise-arity-error reduced-arity-name new-arity xs))
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(apply proc (for/fold ([acc empty]
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[xs xs]
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[vals vals]
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#:result (reverse acc))
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([pat-item (in-list pattern)])
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(if (box? pat-item)
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(values (cons (car xs) acc) (cdr xs) vals)
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(values (cons (car vals) acc) xs (cdr vals))))))
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reduced-arity-name))
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(define/contract (reduce-constraint-arity csp [minimum-arity 3])
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((csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . csp?)
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(let ([assigned-name? (curry assigned-name? csp)])
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(define (partially-assigned? constraint)
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(ormap assigned-name? ($constraint-names constraint)))
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(make-csp (vars csp)
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(for/list ([constraint (in-constraints csp)])
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(cond
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[(and (or (not minimum-arity) (<= minimum-arity (constraint-arity constraint)))
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(partially-assigned? constraint))
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(match-define ($constraint cnames proc) constraint)
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($constraint (filter-not assigned-name? cnames)
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;; pattern is mix of values and boxed symbols (indicating variables to persist)
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;; use boxes here as cheap way to distinguish id symbols from value symbols
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(let ([reduce-arity-pattern (for/list ([cname (in-list cnames)])
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(if (assigned-name? cname)
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(first ($csp-vals csp cname))
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(box cname)))])
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(reduce-function-arity proc reduce-arity-pattern)))]
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[else constraint])))))
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(define nassns 0)
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(define (reset-assns!) (set! nassns 0))
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(define/contract (assign-val csp name val)
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(csp? name? any/c . -> . csp?)
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(when-debug (set! nassns (add1 nassns)))
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(make-csp
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(for/list ([var (vars csp)])
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(if (eq? name (var-name var))
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($avar name (list val))
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var))
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(constraints csp)))
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(define/contract (unassigned-vars csp)
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(csp? . -> . (listof (and/c $var? (not/c assigned-var?))))
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(filter-not assigned-var? (vars csp)))
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(define/contract (first-unassigned-variable csp)
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(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
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(match (unassigned-vars csp)
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[(? empty?) #false]
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[(cons x _) x]))
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(define/contract (minimum-remaining-values csp)
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(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
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(match (unassigned-vars csp)
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[(? empty?) #false]
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[xs (argmin (λ (var) (length ($var-domain var))) xs)]))
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(define mrv minimum-remaining-values)
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(define/contract (var-degree csp var)
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(csp? $var? . -> . exact-nonnegative-integer?)
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(for/sum ([constraint (in-constraints csp)]
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#:when (memq (var-name var) ($constraint-names constraint)))
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1))
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(define/contract (blended-variable-selector csp)
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(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
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(define uvars (unassigned-vars csp))
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(cond
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[(empty? uvars) #false]
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[(findf singleton-var? uvars)]
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[else (first (let* ([uvars-by-mrv (sort uvars < #:key (λ (var) (length ($var-domain var))))]
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[uvars-by-degree (sort uvars-by-mrv > #:key (λ (var) (var-degree csp var)))])
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uvars-by-degree))]))
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(define/contract (remaining-values var)
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($var? . -> . exact-nonnegative-integer?)
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(length ($var-vals var)))
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(define/contract (mrv-degree-hybrid csp)
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(csp? . -> . (or/c #f $var?))
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(define uvars (unassigned-vars csp))
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(cond
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[(empty? uvars) #false]
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[else
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;; minimum remaining values (MRV) rule
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(define mrv-arg (argmin remaining-values uvars))
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(match (filter (λ (var) (= (remaining-values mrv-arg) (remaining-values var))) uvars)
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[(list winning-uvar) winning-uvar]
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[(list mrv-uvars ...)
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;; use degree as tiebreaker for mrv
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(define degrees (map (λ (var) (var-degree csp var)) mrv-uvars))
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(define max-degree (apply max degrees))
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;; use random tiebreaker for degree
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(random-pick (for/list ([var (in-list mrv-uvars)]
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[degree (in-list degrees)]
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#:when (= max-degree degree))
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var))])]))
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(define first-domain-value values)
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(define (no-inference csp name) csp)
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(define/contract (relating-only constraints names)
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((listof $constraint?) (listof name?) . -> . (listof $constraint?))
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(for*/list ([constraint (in-list constraints)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (= (length names) (length cnames))
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(for/and ([name (in-list names)])
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(memq name cnames))))
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constraint))
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(define (binary-constraint? constraint)
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(= 2 (constraint-arity constraint)))
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(define (constraint-relates? constraint name)
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(memq name ($constraint-names constraint)))
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(define nfchecks 0)
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(define (reset-nfcs!) (set! nfchecks 0))
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(define/contract (forward-check csp aname)
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(csp? name? . -> . csp?)
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(define aval (first ($csp-vals csp aname)))
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(define (check-var var)
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(match var
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;; don't check against assigned vars, or the reference var
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;; (which is probably assigned but maybe not)
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[(? (λ (x) (or (assigned-var? x) (eq? (var-name x) aname)))) var]
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[($var name vals)
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(match ((constraints csp) . relating-only . (list aname name))
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[(? empty?) var]
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[constraints
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(define new-vals
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(for/list ([val (in-list vals)]
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#:when (for/and ([constraint (in-list constraints)])
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(let ([proc ($constraint-proc constraint)])
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(if (eq? name (first ($constraint-names constraint)))
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(proc val aval)
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(proc aval val)))))
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val))
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($cvar name new-vals (cons aname (if ($cvar? var)
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($cvar-past var)
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null)))])]))
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(define checked-vars (map check-var (vars csp)))
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(when-debug (set! nfchecks (+ (length checked-vars) nchecks)))
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;; conflict-set will be empty if there are no empty domains
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(define conflict-set (for*/list ([var (in-list checked-vars)]
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#:when (empty? ($var-domain var))
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[name (in-list ($cvar-past var))])
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name))
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;; for conflict-directed backjumping it's essential to forward-check ALL vars
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;; (even after an empty domain is generated) and combine their conflicts
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;; so we can discover the *most recent past var* that could be the culprit.
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;; If we just bail out at the first conflict, we may backjump too far based on its history
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;; (and thereby miss parts of the search tree)
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(when (pair? conflict-set)
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(backtrack! conflict-set))
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;; Discard constraints that have produced singleton domains
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;; (they have no further use)
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(define nonsingleton-constraints
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(for/list ([constraint (in-constraints csp)]
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#:unless (and
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(binary-constraint? constraint)
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(constraint-relates? constraint aname)
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(let ([other-name (first (remq aname ($constraint-names constraint)))])
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(singleton-var? (csp-var csp other-name)))))
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constraint))
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(make-csp checked-vars nonsingleton-constraints))
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(define/contract (constraint-checkable? c names)
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($constraint? (listof name?) . -> . any/c)
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;; constraint is checkable if all constraint names
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;; are in target list of names.
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(for/and ([cname (in-list ($constraint-names c))])
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(memq cname names)))
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(define/contract (constraint-arity constraint)
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($constraint? . -> . exact-nonnegative-integer?)
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(length ($constraint-names constraint)))
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(define (singleton-var? var)
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(= 1 (length ($var-domain var))))
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(define nchecks 0)
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(define (reset-nchecks!) (set! nchecks 0))
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(define/contract (check-constraints csp [mandatory-names #f] #:conflicts [conflict-count? #f])
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((csp?) ((listof name?) #:conflicts boolean?) . ->* . (or/c csp? exact-nonnegative-integer?))
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;; this time, we're not limited to assigned variables
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;; (that is, vars that have been deliberately assigned in the backtrack process thus far)
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;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking)
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(define singleton-varnames (for/list ([var (in-vars csp)]
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#:when (singleton-var? var))
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(var-name var)))
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(define-values (checkable-constraints other-constraints)
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(partition (λ (c) (and (constraint-checkable? c singleton-varnames)
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(or (not mandatory-names)
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(for/and ([name (in-list mandatory-names)])
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(constraint-relates? c name)))))
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(constraints csp)))
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(cond
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[conflict-count? (define conflict-count
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(for/sum ([constraint (in-list checkable-constraints)]
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#:unless (constraint csp))
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1))
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(when-debug (set! nchecks (+ conflict-count nchecks)))
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conflict-count]
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[else (for ([(constraint idx) (in-indexed (sort checkable-constraints < #:key constraint-arity))]
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#:unless (constraint csp))
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(when-debug (set! nchecks (+ (add1 idx) nchecks)))
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(backtrack!))
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;; discard checked constraints, since they have no further reason to live
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(make-csp (vars csp) other-constraints)]))
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(define/contract (make-nodes-consistent csp)
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(csp? . -> . csp?)
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;; todo: why does this function slow down searches?
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(make-csp
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(for/list ([var (in-vars csp)])
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(match-define ($var name vals) var)
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(define procs (for*/list ([constraint (in-constraints csp)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (= 1 (length cnames)) (eq? name (car cnames))))
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($constraint-proc constraint)))
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($var name
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(for*/fold ([vals vals])
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([proc (in-list procs)])
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(filter proc vals))))
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(constraints csp)))
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(define/contract (backtracking-solver
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csp
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#:select-variable [select-unassigned-variable
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(or (current-select-variable) first-unassigned-variable)]
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#:order-values [order-domain-values (or (current-order-values) first-domain-value)]
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#:inference [inference (or (current-inference) no-inference)])
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((csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
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(generator ()
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(let loop ([csp csp])
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(match (select-unassigned-variable csp)
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[#false (yield csp)]
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[($var name domain)
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(define (wants-backtrack? exn)
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(and ($backtrack? exn) (or (let ([btns ($backtrack-names exn)])
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(or (empty? btns) (memq name btns))))))
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(for/fold ([conflicts null]
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#:result (void))
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([val (in-list (order-domain-values domain))])
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(with-handlers ([wants-backtrack?
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(λ (bt) (append conflicts (remq name ($backtrack-names bt))))])
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(let* ([csp (assign-val csp name val)]
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;; reduce constraints before inference,
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|
;; to create more forward-checkable (binary) constraints
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|
[csp (reduce-constraint-arity csp)]
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[csp (inference csp name)]
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[csp (check-constraints csp)])
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(loop csp)))
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|
conflicts)]))))
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(define (random-pick xs)
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(list-ref xs (random (length xs))))
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(define (assign-random-vals csp)
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(for/fold ([new-csp csp])
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([name (in-var-names csp)])
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(assign-val new-csp name (random-pick ($csp-vals csp name)))))
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|
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(define (make-min-conflcts-thread csp0 thread-count max-steps [main-thread (current-thread)])
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|
(thread
|
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|
(λ ()
|
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|
(let loop ()
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|
;; Generate a complete assignment for all variables (probably with conflicts)
|
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|
(for/fold ([csp (assign-random-vals csp0)])
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|
([nth-step (in-range max-steps)])
|
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|
;; Now repeatedly choose a random conflicted variable and change it
|
|
|
(match (conflicted-var-names csp)
|
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|
[(? empty?) (thread-send main-thread csp) (loop)]
|
|
|
[names
|
|
|
(define name (random-pick names))
|
|
|
(define val (min-conflicts-value csp name ($csp-vals csp0 name)))
|
|
|
(assign-val csp name val)]))))))
|
|
|
|
|
|
(define/contract (min-conflicts-solver csp [max-steps 100])
|
|
|
(($csp?) (integer?) . ->* . generator?)
|
|
|
;; Solve a CSP by stochastic hillclimbing on the number of conflicts.
|
|
|
(generator ()
|
|
|
(for ([thread-count 4]) ; todo: what is ideal thread count?
|
|
|
(make-min-conflcts-thread csp thread-count max-steps))
|
|
|
(for ([i (in-naturals)])
|
|
|
(yield (thread-receive)))))
|
|
|
|
|
|
(define/contract (conflicted-var-names csp)
|
|
|
($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 (min-conflicts-value csp name vals)
|
|
|
($csp? name? (listof any/c) . -> . any/c)
|
|
|
;; Return the value that will give var the least number of conflicts
|
|
|
(define vals-by-conflict (sort vals < #:key (λ (val) (nconflicts csp name val))
|
|
|
#:cache-keys? #true))
|
|
|
(for/first ([val (in-list vals-by-conflict)]
|
|
|
#:unless (equal? val (first ($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 $csp-constraints csps))))
|
|
|
|
|
|
(define/contract (make-cartesian-generator solgens)
|
|
|
((listof generator?) . -> . generator?)
|
|
|
(generator ()
|
|
|
(define solcache (make-hasheqv))
|
|
|
(let loop ([solgens solgens][idx 0][sols empty])
|
|
|
(match solgens
|
|
|
[(? empty?) (yield (combine-csps (reverse sols)))]
|
|
|
[(cons solgen rest)
|
|
|
(cond
|
|
|
[(eq? (generator-state solgen) 'done)
|
|
|
(for ([sol (in-list (reverse (hash-ref solcache idx)))])
|
|
|
(loop rest (add1 idx) (cons sol sols)))]
|
|
|
[else
|
|
|
(for ([sol (in-producer solgen (void))])
|
|
|
(hash-update! solcache idx (λ (vals) (cons sol vals)) null)
|
|
|
(loop rest (add1 idx) (cons sol sols)))])]))))
|
|
|
|
|
|
(define/contract (extract-subcsp csp names)
|
|
|
($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)))
|
|
|
|