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|
; abs-alloc.lisp Mihir Mehta
; abs-alloc allocates a new variable from the contents of an existing variable.
(in-package "ACL2")
(include-book "../abs-separate")
(local (include-book "std/lists/intersectp" :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)
(:definition string-listp)
(: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 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
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))))
(defund abs-alloc (fs path new-index)
(declare (xargs :guard
(and (fat32-filename-list-p path)
(abs-fs-p fs)
(natp new-index))
:verify-guards nil
:measure (len path)))
(b*
((fs (mbe :exec fs :logic (abs-fs-fix fs)))
(new-index
(mbe :exec new-index :logic (nfix new-index)))
((when (atom path))
(mv fs (list new-index)))
(alist-elem (abs-assoc
(mbe :exec (car path) :logic (fat32-filename-fix (car path)))
fs))
((when (or (atom alist-elem)
(not (abs-directory-file-p (cdr alist-elem)))))
(mv nil fs))
((mv x y)
(abs-alloc
(abs-file->contents (cdr alist-elem))
(cdr path)
new-index)))
(mv x
(abs-put-assoc
(mbe :exec (car path) :logic (fat32-filename-fix (car path)))
(change-abs-file
(cdr alist-elem)
:contents
y)
fs))))
(defthm
abs-fs-p-of-abs-alloc-1
(abs-fs-p (mv-nth 1 (abs-alloc fs path new-index)))
:hints (("Goal" :in-theory (enable abs-alloc abs-file-alist-p abs-no-dups-p abs-fs-p)
:induct (abs-alloc fs path new-index))))
(defthm abs-fs-p-of-abs-alloc-2
(abs-fs-p (mv-nth 0 (abs-alloc fs path new-index)))
:hints (("goal" :in-theory (enable abs-alloc)
:induct (abs-alloc fs path new-index))))
(verify-guards abs-alloc)
(defthmd abs-alloc-of-fat32-filename-list-fix
(equal (abs-alloc fs (fat32-filename-list-fix path)
new-index)
(abs-alloc fs path new-index))
:hints (("goal" :in-theory (enable abs-alloc))))
(defthm abs-alloc-when-not-natp
(implies (not (natp new-index))
(equal (abs-alloc fs path new-index)
(abs-alloc fs path 0)))
:hints (("Goal" :in-theory (enable abs-alloc))))
(defcong
fat32-filename-list-equiv equal
(abs-alloc fs path new-index)
2
:hints
(("goal"
:use (abs-alloc-of-fat32-filename-list-fix
(:instance abs-alloc-of-fat32-filename-list-fix
(path path-equiv))))))
(defcong nat-equiv equal
(abs-alloc fs path new-index)
3
:hints (("goal" :in-theory (enable abs-alloc))))
(defthm abs-alloc-correctness-1
(implies (and (not (member-equal (nfix new-index)
(abs-addrs (abs-fs-fix fs))))
(equal (mv-nth 1 (abs-alloc fs path new-index))
(abs-fs-fix fs)))
(equal (mv-nth 0 (abs-alloc fs path new-index))
nil))
:hints (("goal" :in-theory (enable abs-alloc))))
(defthm ctx-app-of-abs-alloc
(equal (ctx-app (mv-nth 1 (abs-alloc fs path new-index))
(mv-nth 0 (abs-alloc fs path new-index))
new-index path)
(abs-fs-fix fs))
:hints (("goal" :in-theory (enable ctx-app abs-alloc abs-fs-fix)
:expand (ctx-app fs nil new-index path))))
(defthm abs-alloc-of-abs-fs-fix
(equal (abs-alloc (abs-fs-fix fs) path new-index)
(abs-alloc fs path new-index))
:hints (("Goal" :in-theory (enable abs-alloc))))
(encapsulate
()
(local
(defthmd
lemma
(implies
(and (abs-fs-p fs) (natp new-index))
(equal
(names-at (mv-nth 1 (abs-alloc fs path new-index))
relpath)
(cond
((or
(equal (mv-nth 1 (abs-alloc fs path new-index))
fs)
(not (fat32-filename-list-prefixp path relpath)))
(names-at fs relpath))
(t nil))))
:hints
(("goal"
:in-theory
(e/d
(abs-top-addrs names-at
abs-alloc fat32-filename-list-fix
abs-fs-p abs-file-alist-p abs-no-dups-p)
((:rewrite abs-fs-p-correctness-1)
(:rewrite abs-no-dups-p-of-put-assoc-equal)
(:rewrite subsetp-of-abs-addrs-of-put-assoc-lemma-1)
(:rewrite abs-fs-p-when-hifat-no-dups-p)
(:rewrite hifat-find-file-correctness-1-lemma-1)
(:rewrite consp-of-assoc-of-abs-fs-fix)
(:rewrite abs-file->contents-when-m1-file-p)
(:rewrite remove-when-absent)
(:definition remove-equal)
(:rewrite m1-file-alist-p-of-cdr-when-m1-file-alist-p)
(:rewrite abs-file-alist-p-when-m1-file-alist-p)
(:rewrite abs-file-alist-p-correctness-1)
(:rewrite abs-no-dups-p-when-m1-file-alist-p)
(:rewrite abs-addrs-when-m1-file-alist-p)
(:rewrite member-of-abs-addrs-when-natp . 2)
(:rewrite member-of-abs-fs-fix-when-natp)
(:rewrite abs-file-contents-p-when-m1-file-contents-p)
(:rewrite fat32-filename-fix-when-fat32-filename-p)))
:induct (mv (fat32-filename-list-prefixp path relpath)
(names-at fs relpath))
:expand
((:free (fs) (names-at fs relpath))
(abs-alloc fs path new-index)
(:with
abs-file-contents-fix-when-abs-file-contents-p
(abs-file-contents-fix
(mv-nth
1
(abs-alloc
(abs-file->contents
(cdr
(assoc-equal (fat32-filename-fix (car path))
fs)))
(cdr path)
new-index)))))))))
(defthm
names-at-of-abs-alloc-1
(equal
(names-at (mv-nth 1 (abs-alloc fs path new-index))
relpath)
(if
(or (equal (mv-nth 1 (abs-alloc fs path new-index))
(abs-fs-fix fs))
(not (fat32-filename-list-prefixp path relpath)))
(names-at fs relpath)
nil))
:hints
(("goal" :use (:instance lemma (fs (abs-fs-fix fs))
(new-index (nfix new-index)))))))
(defthm dist-names-of-abs-alloc-1
(implies (dist-names fs relpath frame)
(dist-names (mv-nth 1 (abs-alloc fs path new-index))
relpath frame))
:hints (("goal" :in-theory (enable dist-names))))
(defthm
subsetp-of-abs-addrs-of-abs-alloc-1
(implies
(and (member-equal (nfix new-index) y)
(subsetp-equal (abs-addrs (abs-fs-fix fs))
y))
(subsetp-equal (abs-addrs (mv-nth 1 (abs-alloc fs path new-index)))
y))
:hints (("goal" :in-theory (enable abs-alloc)
:expand (abs-addrs (list new-index)))))
(defthm
names-at-of-abs-alloc-lemma-1
(implies
(not
(equal
(mv-nth
1
(abs-alloc (abs-file->contents
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(cdr path)
new-index))
(abs-file->contents (cdr (assoc-equal (fat32-filename-fix (car path))
fs)))))
(not
(equal
(put-assoc-equal
(fat32-filename-fix (car path))
(abs-file
(abs-file->d-e
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(mv-nth 1
(abs-alloc
(abs-file->contents
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(cdr path)
new-index)))
fs)
fs)))
:hints
(("goal"
:in-theory (disable (:rewrite put-assoc-equal-without-change . 1))
:use
(:instance
(:rewrite put-assoc-equal-without-change . 1)
(alist fs)
(val
(abs-file
(abs-file->d-e
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(mv-nth 1
(abs-alloc
(abs-file->contents
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(cdr path)
new-index))))
(name (fat32-filename-fix (car path)))))))
(encapsulate
()
(local
(defthmd
lemma
(implies (abs-fs-p fs)
(equal (names-at (mv-nth 0 (abs-alloc fs path new-index))
relpath)
(if (equal (mv-nth 1 (abs-alloc fs path new-index))
(abs-fs-fix fs))
nil
(names-at fs (append path relpath)))))
:hints
(("goal"
:in-theory
(e/d (abs-top-addrs names-at
abs-alloc fat32-filename-list-fix
abs-fs-p abs-file-alist-p abs-no-dups-p)
((:rewrite abs-fs-p-correctness-1)
(:rewrite abs-no-dups-p-of-put-assoc-equal)
(:rewrite subsetp-of-abs-addrs-of-put-assoc-lemma-1)
(:rewrite abs-fs-p-when-hifat-no-dups-p)
(:rewrite hifat-find-file-correctness-1-lemma-1)
(:rewrite consp-of-assoc-of-abs-fs-fix)
(:rewrite abs-file->contents-when-m1-file-p)
(:rewrite remove-when-absent)
(:definition remove-equal)
(:rewrite m1-file-alist-p-of-cdr-when-m1-file-alist-p)
(:rewrite abs-file-alist-p-when-m1-file-alist-p)
(:rewrite abs-file-alist-p-correctness-1)
(:rewrite abs-no-dups-p-when-m1-file-alist-p)
(:rewrite abs-addrs-when-m1-file-alist-p)
(:rewrite member-of-abs-addrs-when-natp . 2)
(:rewrite member-of-abs-fs-fix-when-natp)
(:rewrite abs-file-contents-p-when-m1-file-contents-p)
(:rewrite fat32-filename-fix-when-fat32-filename-p)))
:induct (abs-alloc fs path new-index)
:expand
(:with
(:rewrite put-assoc-equal-without-change . 1)
(equal
(put-assoc-equal
(fat32-filename-fix (car path))
(abs-file
(abs-file->d-e
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(mv-nth
1
(abs-alloc
(abs-file->contents
(cdr (assoc-equal (fat32-filename-fix (car path))
fs)))
(cdr path)
new-index)))
fs)
fs))))))
(defthm
names-at-of-abs-alloc-2
(equal (names-at (mv-nth 0 (abs-alloc fs path new-index)) relpath)
(if (equal (mv-nth 1 (abs-alloc fs path new-index)) (abs-fs-fix fs))
nil
(names-at fs (append path relpath))))
:hints
(("goal"
:use
(:instance
lemma
(fs (abs-fs-fix fs)))))))
(defthm
no-duplicatesp-of-abs-addrs-of-abs-alloc-1
(implies (no-duplicatesp-equal (abs-addrs (abs-fs-fix fs)))
(no-duplicatesp-equal
(abs-addrs (mv-nth 0 (abs-alloc fs path new-index)))))
:hints (("goal" :in-theory (enable abs-alloc abs-fs-fix abs-addrs))))
(defthm
addrs-at-of-abs-alloc-1
(equal (addrs-at (mv-nth 1 (abs-alloc fs path new-index))
relpath)
(cond ((or (equal (mv-nth 1 (abs-alloc fs path new-index))
(abs-fs-fix fs))
(not (fat32-filename-list-prefixp path relpath)))
(addrs-at (abs-fs-fix fs) relpath))
((fat32-filename-list-equiv relpath path)
(list (nfix new-index)))
(t nil)))
:hints
(("goal"
:in-theory (e/d (abs-top-addrs addrs-at abs-fs-fix
abs-alloc fat32-filename-list-fix
fat32-filename-list-equiv
fat32-filename-equiv
abs-fs-p abs-file-alist-p abs-no-dups-p)
((:rewrite abs-no-dups-p-of-put-assoc-equal)
(:rewrite subsetp-of-abs-addrs-of-put-assoc-lemma-1)
(:rewrite abs-fs-p-when-hifat-no-dups-p)
(:rewrite hifat-find-file-correctness-1-lemma-1)
(:rewrite consp-of-assoc-of-abs-fs-fix)
(:rewrite abs-file->contents-when-m1-file-p)
(:rewrite
m1-file-alist-p-of-cdr-when-m1-file-alist-p)
(:rewrite abs-file-alist-p-correctness-1)
(:rewrite abs-no-dups-p-when-m1-file-alist-p)
(:rewrite
abs-file-alist-p-when-m1-file-alist-p)
(:rewrite abs-alloc-correctness-1)
(:rewrite
abs-addrs-of-remove-assoc-lemma-1)
(:rewrite abs-no-dups-p-of-cdr)
(:rewrite abs-addrs-of-put-assoc-lemma-1)
(:rewrite abs-addrs-when-m1-file-alist-p)
(:rewrite
abs-fs-fix-of-put-assoc-equal-lemma-2)
(:rewrite abs-file-alist-p-of-cdr)))
:induct (mv (fat32-filename-list-prefixp path relpath)
(addrs-at fs relpath))
:expand ((:free (fs) (addrs-at fs relpath))
(abs-alloc fs path new-index)))))
(defthm ctx-app-ok-of-abs-alloc-1
(implies
;; This clause becomes a test for path's existence...
(not (equal (mv-nth 1 (abs-alloc fs path new-index))
(abs-fs-fix fs)))
(ctx-app-ok (mv-nth 1 (abs-alloc fs path new-index))
new-index path))
:hints (("goal" :in-theory (enable ctx-app-ok))))
(defthm
no-duplicatesp-of-abs-addrs-of-abs-alloc-lemma-1
(implies
(not (intersectp-equal y (abs-addrs (abs-fs-fix fs))))
(not
(intersectp-equal
y
(abs-addrs (remove-assoc-equal (fat32-filename-fix (car path))
(abs-fs-fix fs)))))))
(defthm
no-duplicatesp-of-abs-addrs-of-abs-alloc-lemma-2
(implies
(and (not (member-equal (nfix new-index) y))
(not (intersectp-equal y (abs-addrs (abs-fs-fix fs)))))
(not (intersectp-equal
y
(abs-addrs (mv-nth 1
(abs-alloc fs path new-index))))))
:hints (("goal" :in-theory (enable abs-alloc abs-addrs)
:induct (abs-alloc fs path new-index))))
(defthm
no-duplicatesp-of-abs-addrs-of-abs-alloc-lemma-3
(implies
(and (abs-directory-file-p (cdr (assoc-equal name fs)))
(no-duplicatesp-equal (abs-addrs fs)))
(not (intersectp-equal
(abs-addrs (remove-assoc-equal name fs))
(abs-addrs (abs-file->contents (cdr (assoc-equal name fs)))))))
:hints (("goal" :in-theory (enable abs-addrs))))
(defthm
no-duplicatesp-of-abs-addrs-of-abs-alloc-2
(implies (and (no-duplicatesp-equal (abs-addrs (abs-fs-fix fs)))
(not (member-equal (nfix new-index)
(abs-addrs (abs-fs-fix fs)))))
(no-duplicatesp-equal
(abs-addrs (mv-nth 1
(abs-alloc fs path new-index)))))
:hints (("goal" :in-theory (e/d
(abs-alloc abs-addrs)
((:rewrite abs-addrs-of-remove-assoc)
(:rewrite commutativity-of-append-under-set-equiv)
(:rewrite intersect-equal-of-cons-left)
(:rewrite intersect-with-subset . 11)
(:rewrite intersect-with-subset . 12)
(:rewrite intersectp-equal-of-atom-left)
(:rewrite intersectp-equal-of-atom-right)
(:rewrite intersectp-is-commutative)
(:rewrite member-of-cons)
(:rewrite member-when-atom)
(:rewrite set-difference$-when-not-intersectp)
(:rewrite subsetp-car-member)
(:rewrite subsetp-member . 3)
(:rewrite subsetp-of-cdr)
(:rewrite true-list-fix-when-true-listp)
(:type-prescription abs-addrs)
(:type-prescription abs-alloc)
(:type-prescription abs-fs-fix)
(:type-prescription set-difference-equal)))
:induct (abs-alloc fs path new-index))))
(defthmd hifat-no-dups-p-of-abs-alloc
(implies (and (hifat-no-dups-p fs)
(m1-file-alist-p fs))
(hifat-no-dups-p (mv-nth 0 (abs-alloc fs path new-index))))
:hints (("goal" :in-theory (enable hifat-no-dups-p abs-alloc
abs-fs-p-when-hifat-no-dups-p))))
|
