569 lines
18 KiB
Racket
569 lines
18 KiB
Racket
#lang racket/base
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(require racket/set)
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(require racket/match)
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(require (only-in racket/port call-with-output-string))
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(require (only-in racket/class object?))
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(require rackunit)
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;; TODO: proper exports
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(provide ror
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pattern->matcher
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?)
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(define-syntax-rule (define-singleton-struct singleton-name struct-name print-representation)
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(begin
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(struct struct-name ()
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#:transparent
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#:property prop:custom-write
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(lambda (v port mode) (display print-representation port)))
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(define singleton-name (struct-name))))
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;; Unicode angle brackets: 〈, 〉
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;; A Sigma is, roughly, a token in a value being matched. It is one of:
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;; - a struct-type, signifying the start of a struct.
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;; - start-of-pair, signifying the start of a pair.
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;; - start-of-vector, signifying the start of a vector.
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;; - end-of-sequence, signifying the notional close-paren at the end of a compound.
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;; - any other value, representing itself.
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(define-singleton-struct SOP start-of-pair "<pair")
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(define-singleton-struct SOV start-of-vector "<vector")
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(define-singleton-struct EOS end-of-sequence ">")
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;; A Pattern is an atom, the special wildcard value, or a Racket
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;; compound (struct, pair, or vector) containing Patterns.
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(define-singleton-struct ? wildcard "★") ;; alternative printing: ¿
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;; A Matcher is either
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;; - #f, indicating no further matches possible
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;; - a Set of Any, representing a successful match (if the end of the input has been reached)
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;; - a Hashtable mapping (Sigma or wildcard) to Matcher
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;; - a (wildcard-sequence Matcher)
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;; If, in a hashtable matcher, a wild key is present, it is intended
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;; to catch all and ONLY those keys not otherwise present in the
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;; table.
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(struct wildcard-sequence (matcher) #:transparent)
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(define (rnull) #f)
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(define (rempty? r) (not r))
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(define (rvalue v) (set v))
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(define (rseq e r) (if (rempty? r) r (hash e r)))
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(define (rwild r) (rseq ? r))
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(define (rwildseq r) (if (rempty? r) r (wildcard-sequence r)))
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(define (rseq* x . xs)
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(let walk ((xs (cons x xs)))
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(match xs
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[(list r) r]
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[(cons e xs1) (rseq e (walk xs1))])))
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;; Any -> Boolean
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;; Racket objects are structures, so we reject them explicitly for
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;; now, leaving them opaque to unification.
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(define (non-object-struct? x)
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(and (struct? x)
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(not (object? x))))
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(define (pattern->matcher v p)
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(let walk ((p p) (acc (rseq EOS (rvalue v))))
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(match p
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[(== ?) (rwild acc)]
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[(cons p1 p2) (rseq SOP (walk p1 (walk p2 (rseq EOS acc))))]
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[(vector ps ...) (rseq SOV (foldr walk (rseq EOS acc) ps))]
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[(? non-object-struct?)
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(define-values (t skipped?) (struct-info p))
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(when skipped? (error 'pattern->matcher "Cannot reflect on struct instance ~v" p))
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(define fs (cdr (vector->list (struct->vector p))))
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(rseq t (foldr walk (rseq EOS acc) fs))]
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;; TODO: consider options for treating hash tables as compounds rather than (useless) atoms
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[(? hash?) (error 'pattern->matcher "Cannot match on hash tables at present")]
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[other (rseq other acc)])))
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(module+ test
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(define (E . vs) (hash EOS (apply set vs)))
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(check-equal? (pattern->matcher 'A 123) (hash 123 (E 'A)))
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(check-equal? (pattern->matcher 'A (cons 1 2)) (hash SOP (hash 1 (hash 2 (hash EOS (E 'A))))))
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(check-equal? (pattern->matcher 'A (cons ? 2)) (hash SOP (hash ? (hash 2 (hash EOS (E 'A))))))
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(check-equal? (pattern->matcher 'A SOP) (hash struct:start-of-pair (hash EOS (E 'A))))
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(check-equal? (pattern->matcher 'A ?) (hash ? (E 'A)))
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)
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(define (rlookup r key)
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(hash-ref r key (lambda () #f)))
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(define (rupdate r key k)
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(if (rempty? k)
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(and r (hash-remove r key))
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(hash-set (or r (hash)) key k)))
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(define (key-open? k)
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(or (eq? k SOP)
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(eq? k SOV)
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(struct-type? k)))
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(define (key-close? k)
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(eq? k EOS))
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(define (key-normal? k)
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(not (or (key-open? k)
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(key-close? k))))
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(define (expand-wildseq r)
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(ror (rwild (rwildseq r))
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(rseq EOS r)))
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(define ror
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(let ()
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(define (merge o1 o2)
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(match* (o1 o2)
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[(#f #f) #f]
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[(#f r) r]
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[(r #f) r]
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[(r1 r2) (walk r1 r2)]))
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(define (walk re1 re2)
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(match* (re1 re2)
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[((wildcard-sequence r1) (wildcard-sequence r2)) (rwildseq (walk r1 r2))]
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[((wildcard-sequence r1) r2) (walk (expand-wildseq r1) r2)]
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[(r1 (wildcard-sequence r2)) (walk (expand-wildseq r2) r1)]
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[((? set? v1) (? set? v2)) (set-union v1 v2)]
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[((? hash? h1) (? hash? h2))
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(define w (merge (rlookup h1 ?) (rlookup h2 ?)))
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(cond
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[w (merge/wildcard w h1 h2)]
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[(< (hash-count h2) (hash-count h1)) (merge/no-wildcard h2 h1)]
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[else (merge/no-wildcard h1 h2)])]))
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(define (merge/wildcard w h1 h2)
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(for/fold [(acc (rwild w))]
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[(key (set-remove (set-union (hash-keys h1) (hash-keys h2)) ?))]
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(define k (merge (rlookup h1 key) (rlookup h2 key)))
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(rupdate acc
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key
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(cond
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[(key-open? key) (merge (rwildseq w) k)]
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[(key-close? key) (if (wildcard-sequence? w)
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(merge (wildcard-sequence-matcher w) k)
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k)]
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[else (merge w k)]))))
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(define (merge/no-wildcard h1 h2)
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(for/fold [(acc h2)] [((key k1) (in-hash h1))]
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(define k (merge k1 (rlookup h2 key)))
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(rupdate acc key k)))
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(lambda (re1 re2)
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(match* (re1 re2)
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[(#f r) r]
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[(r #f) r]
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[(r1 r2) (walk r1 r2)]))))
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(define rand
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(let ()
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(define (walk re1 re2)
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(match* (re1 re2)
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[((wildcard-sequence r1) (wildcard-sequence r2)) (rwildseq (walk r1 r2))]
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[((wildcard-sequence r1) r2) (walk (expand-wildseq r1) r2)]
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[(r1 (wildcard-sequence r2)) (walk (expand-wildseq r2) r1)]
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[((? set? v1) (? set? v2)) (set-union v1 v2)]
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[((? hash? h1) (? hash? h2))
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(define w1 (rlookup h1 ?))
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(define w2 (rlookup h2 ?))
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(define w (and w1 w2 (walk w1 w2)))
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;; TODO: if, say, w1 is #f, then we don't need to examine
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;; every key in h2. So there are four cases:
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;; - both false -> examine the intersection of the key sets
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;; (done by enumerating keys in the smaller hash)
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;; - one nonfalse -> examine only the keys in the other
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;; - both nonfalse -> examine the union of the key sets
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;; This is important for avoiding examination of the whole
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;; structure when wildcards aren't being used.
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(for/fold [(acc (rwild w))]
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[(key (set-remove (set-union (hash-keys h1) (hash-keys h2)) ?))]
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(rupdate acc
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key
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(match* ((rlookup h1 key) (rlookup h2 key))
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[(#f #f) #f]
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[(#f k2) (walk-wild w1 key k2)]
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[(k1 #f) (walk-wild w2 key k1)]
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[(k1 k2) (walk k1 k2)])))]))
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(define (walk-wild w key k)
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(and w (cond
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[(key-open? key) (walk (rwildseq w) k)]
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[(key-close? key) (if (wildcard-sequence? w)
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(walk (wildcard-sequence-matcher w) k)
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#f)]
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[else (walk w k)])))
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(lambda (re1 re2)
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(match* (re1 re2)
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[(#f r) #f]
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[(r #f) #f]
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[(r1 r2) (walk r1 r2)]))))
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(define erase-path
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(let ()
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(define (cofinite-pattern)
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(error 'erase-path "Cofinite pattern required"))
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(define (walk path aggregate)
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(match* (path aggregate)
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[((wildcard-sequence r1) (wildcard-sequence r2)) (rwildseq (walk r1 r2))]
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[((wildcard-sequence r1) r2) (walk (expand-wildseq r1) r2)]
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[(r1 (wildcard-sequence r2)) (cofinite-pattern)]
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[((? set? v1) (? set? v2))
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(define v (set-subtract v2 v1))
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(if (set-empty? v) #f v)]
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[((? hash? h1) (? hash? h2))
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(define w1 (rlookup h1 ?))
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(define w2 (rlookup h2 ?))
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(define w (match* (w1 w2)
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[(#f #f) #f]
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[(#f r) r]
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[(r #f) (cofinite-pattern)]
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[(r1 r2) (walk r1 r2)]))
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;; TODO: only need to examine all keys of h2 if w1 nonfalse.
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;; TODO: need to ensure "minimal" remainder in cases where
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;; after an erasure, a particular key's continuation is the
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;; same as the wildcard's continuation. See tests/examples
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;; below.
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(for/fold [(acc (rwild w))]
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[(key (set-remove (set-union (hash-keys h1) (hash-keys h2)) ?))]
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(rupdate acc
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key
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(match* ((rlookup h1 key) (rlookup h2 key))
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[(#f #f) #f]
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[(#f k2) (walk-wild w1 key k2)]
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[(k1 #f) (cofinite-pattern)]
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[(k1 k2) (walk k1 k2)])))]))
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(define (walk-wild w key k)
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(if w
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(cond
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[(key-open? key) (walk (rwildseq w) k)]
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[(key-close? key) (if (wildcard-sequence? w)
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(walk (wildcard-sequence-matcher w) k)
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k)]
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[else (walk w k)])
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k))
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(lambda (re1 re2)
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(match* (re1 re2)
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[(#f r) r]
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[(r #f) (cofinite-pattern)]
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[(r1 r2) (walk r1 r2)]))))
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(define (match-value r v)
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(let walk ((vs (list v)) (stack '(())) (r r))
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(define (walk-wild vs stack)
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(match (rlookup r ?)
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[#f (set)]
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[k (walk vs stack k)]))
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(match r
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[(wildcard-sequence k)
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(match stack
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['() (set)]
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[(cons rest stack1) (walk rest stack1 k)])]
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[(? set?)
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(if (and (null? vs)
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(null? stack))
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r
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(set))]
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[(? hash?)
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(match vs
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['()
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(match stack
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['() (set)]
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[(cons rest stack1)
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(match (rlookup r EOS)
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[#f (set)]
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[k (walk rest stack1 k)])])]
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[(cons (== ?) rest)
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(error 'match-value "Cannot match wildcard as a value")]
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[(cons (cons v1 v2) rest)
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(match (rlookup r SOP)
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[#f (walk-wild rest stack)]
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[k (walk (list v1 v2) (cons rest stack) k)])]
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[(cons (vector vv ...) rest)
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(match (rlookup r SOV)
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[#f (walk-wild rest stack)]
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[k (walk vv (cons rest stack) k)])]
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[(cons (? non-object-struct? s) rest)
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(define-values (t skipped?) (struct-info s))
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(when skipped? (error 'match-value "Cannot reflect on struct instance ~v" s))
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(define fs (cdr (vector->list (struct->vector s))))
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(match (rlookup r t)
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[#f (walk-wild rest stack)]
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[k (walk fs (cons rest stack) k)])]
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[(cons v rest)
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(match (rlookup r v)
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[#f (walk-wild rest stack)]
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[k (walk rest stack k)])])])))
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(module+ test
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(define (pretty-print-matcher m [port (current-output-port)])
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(define (d x) (display x port))
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(define (walk i m)
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(match m
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[#f
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(d "::: no further matches possible")]
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[(wildcard-sequence k)
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(d "...>")
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(walk (+ i 4) k)]
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[(? set? vs)
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(d "{")
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(for ((v vs)) (d v))
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(d "}")]
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[(? hash? h)
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(if (zero? (hash-count h))
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(d " ::: empty hash!")
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(for/fold [(need-sep? #f)] [((key k) (in-hash h))]
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(when need-sep?
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(newline port)
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(d (make-string i #\space)))
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(d " ")
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(define keystr (call-with-output-string (lambda (p) (display key p))))
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(d keystr)
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(walk (+ i 1 (string-length keystr)) k)
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#t))]))
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(newline port)
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(walk 0 m)
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(newline port)
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(flush-output port)
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m)
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(define (check-matches matcher . tests)
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(let walk ((tests tests))
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(match tests
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['() (void)]
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[(list* message expectedstr rest)
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(define actualset (match-value matcher message))
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(printf "~v ==> ~v\n" message actualset)
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(check-equal? actualset
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(apply set (map (lambda (c) (string->symbol (string c)))
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(string->list expectedstr))))
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(walk rest)])))
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(void (pretty-print-matcher
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(ror (pattern->matcher 'A (list (list ?) 'x))
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(pattern->matcher 'B (list (list ?) 'y)))))
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(void (pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B (list (list 'c 'd) 'y)))))
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(void (pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B (list (list ? ?) 'y)))))
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B (list (list ? ?) 'x))))
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(list 'z 'x) ""
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(list (list 'z 'z) 'x) "B"
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(list (list 'z (list 'z)) 'x) "B"
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(list (list 'a 'b) 'x) "AB")
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B (list (list ?) 'y))))
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(list 'z 'y) ""
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(list (list 'z 'z) 'y) ""
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(list (list 'z 'z) 'x) ""
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(list (list 'a 'b) 'x) "A")
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B (list ? 'y))))
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(list 'z 'y) "B"
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(list (list 'z 'z) 'y) "B"
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(list (list 'a 'b) 'x) "A")
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list 'a 'b))
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(pattern->matcher 'B (list 'c 'd))))
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(list 'a 'b) "A"
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(list 'c 'd) "B"
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(list 'a 'd) ""
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(list 'c 'b) "")
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(void (pretty-print-matcher (ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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;; Note: this is a largely nonsense matcher,
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;; since it expects no input at all
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(rseq EOS (rvalue 'B)))))
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list (list 'a 'b) 'x))
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(pattern->matcher 'B ?)))
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(list (list 'a 'b) 'x) "AB"
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'p "B"
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(list 'p) "B")
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(check-matches
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(pretty-print-matcher
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(ror (pattern->matcher 'A (list 'a ?))
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(pattern->matcher 'B (list 'a (list 'b)))))
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(list 'a (list 'b)) "AB"
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(list 'a (list 'b 'b)) "A"
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(list 'a (list 'c 'c)) "A"
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(list 'a (list 'c)) "A"
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(list 'a (list (list))) "A"
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(list 'a (list)) "A"
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(list 'a 'x) "A")
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(check-matches
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(pretty-print-matcher
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(ror (ror (pattern->matcher 'A (list 'a ?))
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(pattern->matcher 'A (list 'q ?)))
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(pattern->matcher 'B (list 'a (list 'b)))))
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(list 'a (list 'b)) "AB"
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(list 'q (list 'b)) "A"
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(list 'a 'x) "A"
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(list 'q 'x) "A"
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(list 'a (list)) "A"
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(list 'q (list)) "A"
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(list 'z (list)) "")
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(define (bigdemo)
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(define ps
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(for/list ((c (in-string "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ")))
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(define csym (string->symbol (string c)))
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(pattern->matcher csym (list csym ?))))
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(ror (foldr ror (rnull) ps)
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(pattern->matcher '+ (list 'Z (list ? '- ?)))))
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(void (pretty-print-matcher (bigdemo)))
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(check-matches
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(bigdemo)
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(list 'a '-) "a"
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(list 'Z '-) "Z"
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(list '? '-) ""
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(list 'a (list '- '- '-)) "a"
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(list 'a (list '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '-)) "a"
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(list 'Z) ""
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(list 'Z 'x) "Z"
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(list 'Z (list)) "Z"
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(list 'Z (list '-)) "Z"
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(list 'Z (list '-)) "Z"
|
|
(list 'Z (list '- '-)) "Z"
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|
(list 'Z (list '- '- '-)) "Z+"
|
|
(list 'Z (list '- '- '- '-)) "Z"
|
|
(list 'Z (list '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '-)) "Z"
|
|
(list 'Z '((()) - -)) "Z+"
|
|
(list '? (list '- '- '-)) "")
|
|
|
|
(check-matches (pretty-print-matcher (pattern->matcher 'A (list* 'a 'b ?)))
|
|
(list 'a 'b 'c 'd 'e 'f) "A"
|
|
(list 'b 'c 'd 'e 'f 'a) ""
|
|
3 "")
|
|
|
|
(void (pretty-print-matcher (rand (pattern->matcher 'A (list 'a))
|
|
(pattern->matcher 'B (list 'b)))))
|
|
|
|
(let ((r1 (ror (pattern->matcher 'A (list ? 'b))
|
|
(pattern->matcher 'A (list ? 'c))))
|
|
(r2 (ror (pattern->matcher 'B (list 'a ?))
|
|
(pattern->matcher 'B (list 'b ?)))))
|
|
(pretty-print-matcher (ror r1 r2))
|
|
(pretty-print-matcher (ror r1 r1))
|
|
(pretty-print-matcher (ror r2 r2))
|
|
(pretty-print-matcher (rand r1 r2))
|
|
(pretty-print-matcher (rand r1 r1))
|
|
(pretty-print-matcher (rand r2 r2))
|
|
(void))
|
|
|
|
(void (pretty-print-matcher (rand (bigdemo) (pattern->matcher 'X (list 'm 'n)))))
|
|
|
|
(check-matches
|
|
(pretty-print-matcher (rand (bigdemo) (pattern->matcher 'X (list 'Z ?))))
|
|
(list 'a '-) ""
|
|
(list 'Z '-) "XZ"
|
|
(list '? '-) ""
|
|
(list 'a (list '- '- '-)) ""
|
|
(list 'a (list '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '-)) ""
|
|
(list 'Z) ""
|
|
(list 'Z 'x) "XZ"
|
|
(list 'Z (list)) "XZ"
|
|
(list 'Z (list '-)) "XZ"
|
|
(list 'Z (list '-)) "XZ"
|
|
(list 'Z (list '- '-)) "XZ"
|
|
(list 'Z (list '- '- '-)) "XZ+"
|
|
(list 'Z (list '- '- '- '-)) "XZ"
|
|
(list 'Z (list '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '- '-)) "XZ"
|
|
(list 'Z '((()) - -)) "XZ+"
|
|
(list '? (list '- '- '-)) "")
|
|
|
|
(let* ((r1 (pattern->matcher 'A (list ? 'b)))
|
|
(r2 (pattern->matcher 'B (list 'a ?)))
|
|
(r12 (ror r1 r2)))
|
|
(printf "\n-=-=-=-=-=-=-=-=- erase1\n")
|
|
(pretty-print-matcher r1)
|
|
(pretty-print-matcher r2)
|
|
(pretty-print-matcher r12)
|
|
;; TODO: these next two are not currently "minimal"
|
|
(pretty-print-matcher (erase-path r1 r12))
|
|
(pretty-print-matcher (erase-path r2 r12))
|
|
(void))
|
|
|
|
(let* ((r1 (ror (pattern->matcher 'A (list 'a ?))
|
|
(pattern->matcher 'A (list 'b ?))))
|
|
(r2 (pattern->matcher 'B (list 'b ?)))
|
|
(r12 (ror r1 r2)))
|
|
(printf "\n-=-=-=-=-=-=-=-=- erase2\n")
|
|
(pretty-print-matcher r12)
|
|
(pretty-print-matcher (erase-path r1 r12))
|
|
(pretty-print-matcher (erase-path r2 r12))
|
|
(void))
|
|
|
|
)
|
|
|
|
(module+ test
|
|
(struct a (x) #:prefab)
|
|
(struct b (x) #:transparent)
|
|
|
|
(define (intersect a b)
|
|
(rand (pattern->matcher 'A a)
|
|
(pattern->matcher 'B b)))
|
|
|
|
(define EAB (E 'A 'B))
|
|
|
|
(check-equal? (intersect ? ?) (rwild EAB))
|
|
(check-equal? (intersect 'a ?) (rseq 'a EAB))
|
|
(check-equal? (intersect 123 ?) (rseq 123 EAB))
|
|
(check-equal? (intersect (cons ? 2) (cons 1 ?)) (rseq* SOP 1 2 EOS EAB))
|
|
(check-equal? (intersect (cons 1 2) ?) (rseq* SOP 1 2 EOS EAB))
|
|
(check-equal? (intersect 1 2) #f)
|
|
(check-equal? (intersect (cons 1 2) (cons ? 2)) (rseq* SOP 1 2 EOS EAB))
|
|
(check-equal? (intersect (cons 1 2) (cons 3 2)) #f)
|
|
(check-equal? (intersect (cons 1 2) (cons 1 3)) #f)
|
|
(check-equal? (intersect (vector 1 2) (vector 1 2)) (rseq* SOV 1 2 EOS EAB))
|
|
(check-equal? (intersect (vector 1 2) (vector 1 2 3)) #f)
|
|
|
|
(check-equal? (intersect (a 'a) (a 'b)) #f)
|
|
(check-equal? (intersect (a 'a) (a 'a)) (rseq* struct:a 'a EOS EAB))
|
|
(check-equal? (intersect (a 'a) (a ?)) (rseq* struct:a 'a EOS EAB))
|
|
(check-equal? (intersect (a 'a) ?) (rseq* struct:a 'a EOS EAB))
|
|
(check-equal? (intersect (b 'a) (b 'b)) #f)
|
|
(check-equal? (intersect (b 'a) (b 'a)) (rseq* struct:b 'a EOS EAB))
|
|
(check-equal? (intersect (b 'a) (b ?)) (rseq* struct:b 'a EOS EAB))
|
|
(check-equal? (intersect (b 'a) ?) (rseq* struct:b 'a EOS EAB))
|
|
|
|
(check-equal? (intersect (a 'a) (b 'a)) #f)
|
|
|
|
(check-exn #px"Cannot match on hash tables at present"
|
|
(lambda ()
|
|
(intersect (hash 'a 1 'b ?) (hash 'a ? 'b 2))))
|
|
;; (check-equal? (intersect (hash 'a 1 'b ?) (hash 'a ? 'b 2)) (hash 'a 1 'b 2))
|
|
;; (check-equal? (intersect (hash 'a 1 'b ?) (hash 'a ?)) (void))
|
|
;; (check-equal? (intersect (hash 'a 1 'b ?) (hash 'a 1 'b ?)) (hash 'a 1 'b ?))
|
|
;; (check-equal? (intersect (hash 'a 1 'b ?) (hash 'a ? 'c ?)) (void))
|
|
|
|
;; (check-equal? (intersect (hash 'a 1 'b ?) (hash 'a 1 'b (list 2 ?)))
|
|
;; (hash 'a 1 'b (list 2 ?)))
|
|
;; (check-equal? (intersect (hash 'a 1 'b (list ? 3)) (hash 'a 1 'b (list 2 ?)))
|
|
;; (hash 'a 1 'b (list 2 3)))
|
|
|
|
)
|