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; Copyright (C) 2017, Regents of the University of Texas
; Marijn Heule, Warren A. Hunt, Jr., and Matt Kaufmann
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; See README. Here we complete the proof for (1).
(in-package "LRAT")
(include-book "cube")
(include-book "clean-formula")
(defun sp-valid-proofp$-top-rec (formula clrat-file posn chunk-size
clrat-file-length old-suffix debug
old-max-var a$ ctx state)
; This version of incl-valid-proofp$-top-rec additionally returns the current
; formula, and for the flag, instead of :complete or :incomplete or nil it
; returns a Boolean flag.
(declare (xargs :guard (and (a$p a$)
(eql (a$ptr a$) 0)
(formula-p formula)
(stringp clrat-file)
(natp posn)
(< posn *2^56*)
(posp chunk-size)
(posp clrat-file-length)
(stringp old-suffix)
(natp old-max-var)
(<= (formula-max-var formula 0)
old-max-var))
:guard-hints
(("Goal"
:in-theory
(disable incl-valid-proofp$ a$ptr clrat-read-next)))
:ruler-extenders
(:lambdas mv-list return-last) ; ugly bug work-around
:measure (nfix (- clrat-file-length posn))
:stobjs (state a$)))
(cond
((and (mbt (natp posn))
(mbt (posp clrat-file-length))
(mbt (posp chunk-size))
(<= posn clrat-file-length))
(prog2$
(and debug
(cw "; Note: Reading from position ~x0~|" posn))
(mv-let (proof suffix new-posn)
(clrat-read-next clrat-file posn chunk-size old-suffix
clrat-file-length state)
(cond
((null suffix) ; error (normally a string, possibly even "")
(mv (er hard? ctx "Implementation error: Null suffix!")
formula
a$))
((null proof)
(mv t formula a$))
((stringp proof) ; impossible
(mv (er hard? ctx
"Implementation error: ~x0 returned a string for its proof, ~
which we thought was impossible!"
'clrat-read-next)
formula
a$))
(t
(mv-let (v new-formula new-max-var a$)
(prog2$
(cw "; Note: Checking next proof segment.~|")
(incl-valid-proofp$ formula proof old-max-var a$))
(cond
; !! Move this up if possible.
((>= new-posn *2^56*)
(mv (er hard? ctx
"Attempted to read at position ~x0, but the maximum ~
legal such position is 2^56 = ~x1."
new-posn *2^56*)
formula
a$))
((not v) (mv nil formula a$))
((eq v :complete)
(mv t new-formula a$))
((> new-posn clrat-file-length)
; If new-posn is exactly clrat-file-length, then as per the discussion of the
; "truncation case" in :doc read-file-into-string, we iterate. But if
; new-posn exceeds clrat-file-length, then we have a valid proof that does not
; include the empty clause.
(mv t new-formula a$))
(t
(sp-valid-proofp$-top-rec new-formula clrat-file new-posn
chunk-size clrat-file-length suffix
debug new-max-var a$ ctx
state)))))))))
(t ; impossible
(mv nil formula a$))))
(defun sp-valid-proofp$-top-aux (formula clrat-file chunk-size
clrat-file-length debug a$ ctx state)
; This is a variant of incl-valid-proofp$-top-aux.
(declare (xargs :stobjs (a$ state)
:guard (and (a$p a$)
(eql (a$ptr a$) 0)
(formula-p formula)
(stringp clrat-file)
(posp chunk-size)
(posp clrat-file-length))))
(sp-valid-proofp$-top-rec formula clrat-file 0 chunk-size
clrat-file-length "" debug
(formula-max-var formula 0)
a$ ctx state))
(defthm sp-valid-proofp$-top-rec-preserves-formula-p
(implies (and (a$p a$)
(eql (a$ptr a$) 0)
(formula-p formula)
(stringp clrat-file)
(natp posn)
(< posn *2^56*)
(posp chunk-size)
(posp clrat-file-length)
(stringp old-suffix)
(natp old-max-var)
(<= (formula-max-var formula 0)
old-max-var))
(formula-p
(mv-nth 1
(sp-valid-proofp$-top-rec formula clrat-file posn chunk-size
clrat-file-length old-suffix debug
old-max-var a$ ctx state))))
:hints (("Goal"
:in-theory
(e/d (sp-valid-proofp$-top-rec)
(incl-valid-proofp$ a$ptr clrat-read-next)))))
(defun transform (cnf-file clrat-file chunk-size debug state)
; This is a variant of incl-valid-proofp$-top.
; See sp-valid-proofp$-top-rec.
(declare (xargs :guard t
:stobjs state
:guard-hints
(("Goal" :in-theory (disable sp-valid-proofp$-top-rec)))))
(let* ((formula (ec-call (cnf-read-file cnf-file state)))
(state (increment-file-clock state))
(ctx 'transform))
(cond
((not (stringp clrat-file))
(er-soft-logic
ctx
"The filename argument is not a string:~|~x0"
clrat-file))
((not (posp chunk-size))
(er-soft-logic
ctx
"The supplied :chunk-size must be a positive integer, but ~x0 is ~
not.~|~x0"
clrat-file))
((not (ordered-formula-p formula))
(er-soft-logic ctx "An invalid formula was supplied by the parser!"))
(t
(mv-let (clrat-file-length state)
(file-length$ clrat-file state)
(cond
((posp clrat-file-length)
(mv-let (val new-formula)
(prog2$
(and debug
(cw "Length of file ~x0: ~x1~|" clrat-file clrat-file-length))
(with-fast-alist
formula
(with-local-stobj a$
(mv-let
(val new-formula a$)
(let ((a$ (resize-a$arr 2 a$))) ; to get a$p to hold
(sp-valid-proofp$-top-aux formula clrat-file chunk-size
clrat-file-length debug a$
ctx state))
(mv val (clean-formula new-formula))))))
(cond (val (value (cons formula new-formula)))
(t (er-soft-logic
ctx
"Invalid proof (check failed)."
clrat-file)))))
((eql clrat-file-length 0)
(er-soft-logic
ctx
"Zero-length file: ~x0."
clrat-file))
(t (er-soft-logic
ctx
"Sorry, Lisp cannot determine the file-length of file ~x0."
clrat-file))))))))
; Start proof of transform-preserves-sat-main
(include-book "../incremental/soundness-main")
(defthm transform-preserves-sat-main
(implies
(and (car (sp-valid-proofp$-top-rec formula
clrat-file posn chunk-size
clrat-file-length
old-suffix debug max-var a$ ctx
state))
(formula-p formula)
(a$p a$)
(equal (a$ptr a$) 0)
(integerp max-var)
(<= (formula-max-var formula 0) max-var)
(satisfiable formula))
(satisfiable
(mv-nth 1 (sp-valid-proofp$-top-rec formula
clrat-file posn chunk-size
clrat-file-length
old-suffix debug max-var a$ ctx
state))))
:hints (("Goal"
:in-theory (e/d (formula-max-var-is-formula-max-var-1)
(incl-valid-proofp$ clrat-read-next a$ptr))
:induct t)))
(defthm transform-preserves-sat
(let* ((result
(mv-nth 1 (transform cnf-file clrat-file chunk-size debug state)))
(formula (car result))
(new-formula (cdr result)))
(implies (and result ; non-error case
(satisfiable formula))
(satisfiable new-formula)))
:hints (("Goal"
:in-theory
(union-theories '(transform
acl2::error1-logic
sp-valid-proofp$-top-aux
transform-preserves-sat-main
(:e a$p)
(:e resize-a$arr)
create-a$
(:e a$ptr)
natp-formula-max-var
ordered-formula-p-implies-formula-p
clean-formula-preserves-satisfiable
sp-valid-proofp$-top-rec-preserves-formula-p)
(theory 'ground-zero)))))
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