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|
; abs-find-file-src.lisp Mihir Mehta
; abs-find-file-src finds the variable, if any, that has a non-enoent value for
; finding the file.
(in-package "ACL2")
(include-book "abs-find-file")
(local (include-book "std/lists/prefixp" :dir :system))
(local
(in-theory
(e/d
(abs-file-p-when-m1-regular-file-p len-when-consp)
((:definition member-equal)
(:definition intersection-equal)
(:definition integer-listp)
(:rewrite true-listp-when-string-list)
(:linear position-equal-ac-when-member)
(:linear position-when-member)
(:rewrite nth-when->=-n-len-l)
(:linear len-of-remove-assoc-1)
(:definition position-equal-ac)
(:definition remove1-assoc-equal)
(:rewrite m1-directory-file-p-correctness-1)
(:rewrite assoc-of-car-when-member)
(:rewrite integerp-of-car-when-integer-listp)
(:linear len-when-hifat-bounded-file-alist-p . 1)
(:rewrite m1-file-p-of-cdar-when-m1-file-alist-p)
(:rewrite natp-of-car-when-nat-listp)
(:rewrite
collapse-1st-index-of-frame-val->src-of-cdr-of-assoc-linear-lemma-2)
(:rewrite when-zp-src-of-1st-collapse-1)
(:rewrite ctx-app-ok-of-abs-fs-fix-1)
(:rewrite abs-fs-fix-of-put-assoc-equal-lemma-2)
(:rewrite hifat-file-alist-fix-guard-lemma-1)
(:rewrite abs-file-alist-p-of-abs-file->contents)
(:rewrite member-of-abs-fs-fix-when-natp)
(:rewrite abs-find-file-helper-of-collapse-lemma-2)
(:rewrite m1-file-alist-p-of-intersection-equal-2)
(:rewrite
abs-separate-of-frame->frame-of-collapse-this-lemma-7)
(:linear 1st-complete-correctness-2)
different-from-own-src-1
(:rewrite m1-file-alist-p-when-subsetp-equal)
(:rewrite stringp-when-nonempty-stringp)
m1-file-alist-p-of-nthcdr
take-of-len-free take-of-too-many
len-of-remove-assoc-2 nth-of-take
no-duplicatesp-of-abs-addrs-of-remove-assoc-lemma-3
hifat-no-dups-p-of-m1-file-contents-of-cdar
(:rewrite abs-complete-when-stringp)
(:rewrite hifat-place-file-correctness-3)
(:rewrite
fat32-filename-list-p-of-cdr-when-fat32-filename-list-p)
(:rewrite
collapse-1st-index-of-frame-val->src-of-cdr-of-assoc-linear-lemma-9)))))
;; This deliberately follows an almost-identical induction scheme to
;; abs-find-file. It was going to be a part of that function, but that just led
;; to too many failures.
(defund
abs-find-file-src (frame path)
(declare
(xargs :guard (and (frame-p frame)
(fat32-filename-list-p path))))
(b*
(((when (atom frame)) 0)
(path (mbe :exec path
:logic (fat32-filename-list-fix path)))
((unless (prefixp (frame-val->path (cdar frame))
path))
(abs-find-file-src (cdr frame) path))
((mv & error-code)
(abs-find-file-helper
(frame-val->dir (cdar frame))
(nthcdr (len (frame-val->path (cdar frame)))
path)))
((when (not (equal error-code *enoent*)))
(mbe :exec (caar frame) :logic (nfix (caar frame)))))
(abs-find-file-src (cdr frame) path)))
(defthmd
abs-find-file-src-correctness-2
(implies
(and (frame-p frame)
(no-duplicatesp-equal (strip-cars frame))
(not (equal (mv-nth 1 (abs-find-file frame path))
*enoent*)))
(and
(consp (assoc-equal (abs-find-file-src frame path)
frame))
(prefixp (frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
(fat32-filename-list-fix path))
(equal
(abs-find-file-helper
(frame-val->dir (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
(nthcdr
(len (frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame))))
path))
(abs-find-file frame path))))
:hints (("goal" :in-theory (enable abs-find-file abs-find-file-src)))
:rule-classes
((:rewrite
:corollary
(implies
(and (frame-p frame)
(no-duplicatesp-equal (strip-cars frame))
(not (equal (mv-nth 1 (abs-find-file frame path))
*enoent*)))
(and
(prefixp
(frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
(fat32-filename-list-fix path))
(fat32-filename-list-prefixp
(frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
path)
(equal
(abs-find-file-helper
(frame-val->dir (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
(nthcdr
(len
(frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame))))
path))
(abs-find-file frame path)))))
(:rewrite
:corollary
(implies
(and (frame-p frame)
(no-duplicatesp-equal (strip-cars frame))
(not (equal (mv-nth 1 (abs-find-file frame path))
*enoent*))
(fat32-filename-list-p path))
(prefixp
(frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame)))
path)))
(:linear
:corollary
(implies
(and (frame-p frame)
(no-duplicatesp-equal (strip-cars frame))
(not (equal (mv-nth 1 (abs-find-file frame path))
*enoent*)))
(< (len (frame-val->path (cdr (assoc-equal (abs-find-file-src frame path)
frame))))
(len path)))
:hints (("goal" :in-theory (enable abs-find-file-helper)
:do-not-induct t)))))
(encapsulate ()
(local
(defthm
lemma
(implies (not (zp (abs-find-file-src frame path)))
(consp (assoc-equal (abs-find-file-src frame path)
frame)))
:hints (("goal" :in-theory (enable abs-find-file abs-find-file-src)))))
(defthm
abs-find-file-src-correctness-1
(implies (consp (assoc-equal 0 frame))
(consp (assoc-equal (abs-find-file-src frame path)
frame)))
:hints (("goal" :in-theory (enable abs-find-file abs-find-file-src)))
:rule-classes
((:rewrite
:corollary
(implies (or (not (zp (abs-find-file-src frame path)))
(consp (assoc-equal 0 frame))
(and (frame-p frame)
(no-duplicatesp-equal (strip-cars frame))
(not (equal (mv-nth 1 (abs-find-file frame path))
*enoent*))))
(consp (assoc-equal (abs-find-file-src frame path)
frame)))
:hints
(("goal"
:use
abs-find-file-src-correctness-2))))))
(defthmd
abs-find-file-src-of-fat32-filename-list-fix
(equal
(abs-find-file-src frame (fat32-filename-list-fix path))
(abs-find-file-src frame path))
:hints (("Goal" :in-theory (enable abs-find-file-src))))
(defcong
fat32-filename-list-equiv
equal (abs-find-file-src frame path)
2
:hints
(("goal"
:use
((:instance abs-find-file-src-of-fat32-filename-list-fix
(path path-equiv))
abs-find-file-src-of-fat32-filename-list-fix))))
(defthm
abs-find-file-src-of-frame-with-root
(equal (abs-find-file-src (frame-with-root root frame)
path)
(if (equal (mv-nth 1 (abs-find-file-helper root path))
2)
(abs-find-file-src frame path)
0))
:hints (("goal" :do-not-induct t
:in-theory (enable abs-find-file-src frame-with-root))))
(defthm
abs-find-file-src-of-remove-assoc-1
(implies
(and
(not (null x))
(no-duplicatesp-equal (strip-cars frame))
(or
(not (prefixp (frame-val->path (cdr (assoc-equal x frame)))
(fat32-filename-list-fix path)))
(equal
(mv-nth 1
(abs-find-file-helper
(frame-val->dir (cdr (assoc-equal x frame)))
(nthcdr (len (frame-val->path (cdr (assoc-equal x frame))))
path)))
*enoent*)))
(equal (abs-find-file-src (remove-assoc-equal x frame)
path)
(abs-find-file-src frame path)))
:hints (("goal" :in-theory (enable abs-find-file-src remove-assoc-equal
no-duplicatesp-equal strip-cars)))
:rule-classes
((:rewrite
:corollary
(implies
(and
(not (null x))
(no-duplicatesp-equal (strip-cars frame))
(or
(not (fat32-filename-list-prefixp
(frame-val->path (cdr (assoc-equal x frame)))
path))
(equal
(mv-nth
1
(abs-find-file-helper
(frame-val->dir (cdr (assoc-equal x frame)))
(nthcdr (len (frame-val->path (cdr (assoc-equal x frame))))
path)))
*enoent*)))
(equal (abs-find-file-src (remove-assoc-equal x frame)
path)
(abs-find-file-src frame path)))
:hints (("goal" :do-not-induct t)))))
|
