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|
#|
(include-book "m1")
(certify-book "m1-fast" 1)
|#
(in-package "M1")
(include-book "fast")
(defconst *m1-boyer-moore-program*
; Allocation of locals
; pat 0
; j 1
; txt 2
; i 3
; pmax 4 = (length pat)
; tmax 5 = (length txt)
; array 6 = (preprocess pat)
; c 7 = temp - last char read from txt
'(
(load 0) ; 0 (load pat)
(push "") ; 1 (push "")
(ifane 5) ; 2 (ifane loop) ; if pat/="", goto loop
(load 2) ; 3 (load txt)
(push "") ; 4 (push "")
(ifane 40) ; 5 (ifane win) ; if txt/="", goto win
(goto 43) ; 6 (goto lose)
; loop:
(load 1) ; 7 (load j)
(iflt 37) ; 8 (iflt win)) ; if j<0, goto win
(load 5) ; 9 (load tmax)
(load 3) ; 10 (load i)
(sub) ; 11 (sub)
(ifle 37) ; 12 (ifle lose) ; if (length txt)-i <= 0, goto lose
(load 0) ; 13 (load pat)
(load 1) ; 14 (load j)
(aload) ; 15 (aload) ; pat[j]
(load 2) ; 16 (load txt)
(load 3) ; 17 (load i)
(aload) ; 18 (aload) ; txt[i]
(store 7) ; 19 (store v) ; (store into v)
(load 7) ; 20 (load v)
(sub) ; 21 (sub)
(ifne 10) ; 22 (ifne skip) ; if pat[j] /= txt[i], goto skip
(load 1) ; 23 (load j)
(push 1) ; 24 (push 1)
(sub) ; 25 (sub)
(store 1) ; 26 (store j) ; j=j-1
(load 3) ; 27 (load i)
(push 1) ; 28 (push 1)
(sub) ; 29 (sub)
(store 3) ; 30 (store i) ; i=i-1
(goto -24) ; 31 (goto loop) ; goto loop
; skip:
(load 3) ; 32 (load i)
(load 6) ; 33 (load array)
(load 7) ; 34 (load v)
(aload) ; 35 (aload)
(load 1) ; 36 (load j)
(aload) ; 37 (aload)
(add) ; 38 (add)
(store 3) ; 39 (store i) ; i := i+array[c][j]
(load 4) ; 40 (load pmax)
(push 1) ; 41 (push 1)
(sub) ; 42 (sub)
(store 1) ; 43 (store j) ; j := (length pat)-1
(goto -37) ; 44 (goto loop)
; win:
(load 3) ; 45 (load i)
(push 1) ; 46 (push 1)
(add) ; 47 (add)
(return) ; 48 (return)
; lose:
(push nil) ; 49 (push nil)
(return) ) ; 50 (return))
)
; We use the recurrence scheme in fast-loop repeatedly. But when it was
; justified, char and length were enabled so we re-enable them so the
; termination proofs below are just like those for fast-loop. We could have
; (should have) packaged the measure lemma differently.
(in-theory (enable char length))
(defun m1-boyer-moore-loop-sched (pat j txt i)
(declare (xargs :measure (measure pat j txt i)
:well-founded-relation l<))
(cond
((not (and (stringp pat) (integerp j)
(stringp txt) (integerp i)
(<= -1 j) (< j (length pat))
(<= j i)))
nil)
((< j 0)
(repeat 0 6))
((<= (length txt) i)
(repeat 0 8))
((equal (char-code (char pat j)) (char-code (char txt i)))
(append (repeat 0 25)
(m1-boyer-moore-loop-sched pat (- j 1) txt (- i 1))))
(t (append (repeat 0 29)
(m1-boyer-moore-loop-sched pat
(- (length pat) 1)
txt
(+ i (delta (char txt i)
j
pat)))))))
(defun m1-boyer-moore-sched (pat txt)
(if (equal pat "")
(if (equal txt "")
(repeat 0 9)
(repeat 0 10))
(append (repeat 0 3)
(m1-boyer-moore-loop-sched pat
(- (length pat) 1)
txt
(- (length pat) 1)))))
(defun m1-boyer-moore-loop-vars (pat j txt i v)
(declare (xargs :measure (measure pat j txt i)
:well-founded-relation l<))
(cond
((not (and (stringp pat) (integerp j)
(stringp txt) (integerp i)
(<= -1 j) (< j (length pat))
(<= j i)))
(list j i v))
((< j 0)
(list j i v))
((<= (length txt) i)
(list j i v))
((equal (char-code (char pat j)) (char-code (char txt i)))
(m1-boyer-moore-loop-vars
pat
(- j 1)
txt
(- i 1)
(char-code (char txt i))))
(t (m1-boyer-moore-loop-vars
pat
(- (length pat) 1)
txt
(+ i (delta (char txt i)
j
pat))
(char-code (char txt i))))))
(defthm m1-boyer-moore-loop-is-fast-loop
(implies (and (stringp pat)
(stringp txt)
(integerp j)
(<= -1 j)
(< j (length pat))
(integerp i)
(<= j i))
(equal (run (m1-boyer-moore-loop-sched pat j txt i)
(make-state 7
(list pat
j
txt
i
(length pat)
(length txt)
(preprocess pat)
v)
nil
*m1-boyer-moore-program*))
(if (fast-loop pat j txt i)
(make-state 48
(list pat
(nth 0 (m1-boyer-moore-loop-vars pat j txt i v))
txt
(nth 1 (m1-boyer-moore-loop-vars pat j txt i v))
(length pat)
(length txt)
(preprocess pat)
(nth 2 (m1-boyer-moore-loop-vars pat j txt i v)))
(push (fast-loop pat j txt i) nil)
*m1-boyer-moore-program*)
(make-state 50
(list pat
(nth 0 (m1-boyer-moore-loop-vars pat j txt i v))
txt
(nth 1 (m1-boyer-moore-loop-vars pat j txt i v))
(length pat)
(length txt)
(preprocess pat)
(nth 2 (m1-boyer-moore-loop-vars pat j txt i v)))
(push nil nil)
*m1-boyer-moore-program*))))
:hints (("Goal" :in-theory (enable preprocess))))
(in-theory (disable length))
(defthm m1-boyer-moore-is-fast
(implies (and (stringp pat)
(stringp txt))
(equal (top
(stack
(run (m1-boyer-moore-sched pat txt)
(make-state 0
(list pat
(- (length pat) 1)
txt
(- (length pat) 1)
(length pat)
(length txt)
(preprocess pat)
0)
nil
*m1-boyer-moore-program*))))
(fast pat txt))))
(defthm m1-boyer-moore-halts
(implies (and (stringp pat)
(stringp txt))
(haltedp
(run (m1-boyer-moore-sched pat txt)
(make-state 0
(list pat
(- (length pat) 1)
txt
(- (length pat) 1)
(length pat)
(length txt)
(preprocess pat)
0)
nil
*m1-boyer-moore-program*)))))
(defthm m1-boyer-moore-is-correct
(implies (and (stringp pat)
(stringp txt))
(equal (top
(stack
(run (m1-boyer-moore-sched pat txt)
(make-state 0
(list pat
(- (length pat) 1)
txt
(- (length pat) 1)
(length pat)
(length txt)
(preprocess pat)
0)
nil
*m1-boyer-moore-program*))))
(correct pat txt))))
|
