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|
(in-package "ACL2")
; hifat-cluster-count.lisp Mihir Mehta
; hifat-cluster-count is related to the problem of counting the number of
; clusters taken up by a HiFAT instance when stored on the disk.
(include-book "../hifat")
(include-book "../utilities/cluster-listp")
(local (in-theory (disable ceiling)))
;; In the subdirectory case, we need to place all the entries (32 bytes each)
;; and two entries (dot and dotdot). The space taken up for these things is
;; determined by the rule len-of-make-clusters, which expresses the length in
;; terms of the greatest integer function.
(defund
hifat-cluster-count (fs cluster-size)
(declare (xargs :guard (and (m1-file-alist-p fs)
(integerp cluster-size)
(< 0 cluster-size))))
(b*
(((unless (consp fs)) 0)
(head (car fs))
(contents (m1-file->contents (cdr head))))
(+
(hifat-cluster-count (cdr fs)
cluster-size)
(if
(m1-regular-file-p (cdr head))
(len (make-clusters contents cluster-size))
(+ (hifat-cluster-count contents cluster-size)
;; This mbe form is here to help make a good type-prescription rule,
;; which identifies this thing as a natural number - not just an
;; integer. As an aside, I guess the battle over whether 0 is a
;; natural number has been lost for a while, since nobody seems to use
;; the term "whole number" any more.
(mbe :exec (ceiling (* 32 (+ 2 (len contents)))
cluster-size)
:logic (nfix (ceiling (* 32 (+ 2 (len contents)))
cluster-size))))))))
(defthm
hifat-cluster-count-of-put-assoc
(implies
(m1-file-alist-p fs)
(equal
(hifat-cluster-count (put-assoc-equal name file fs)
cluster-size)
(b*
((new-contents (m1-file->contents file))
((when (and (atom (assoc-equal name fs))
(m1-regular-file-p file)))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))))
((when (atom (assoc-equal name fs)))
(+ (hifat-cluster-count fs cluster-size)
(+ (hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size)))))
(old-contents
(m1-file->contents (cdr (assoc-equal name fs))))
((when
(and (m1-directory-file-p (cdr (assoc-equal name fs)))
(m1-regular-file-p file)))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))
((when (m1-directory-file-p (cdr (assoc-equal name fs))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))
((when (m1-regular-file-p file))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (len (make-clusters old-contents cluster-size))))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (len (make-clusters old-contents cluster-size)))))))
:hints (("goal" :in-theory (enable hifat-cluster-count)
:induct (put-assoc-equal name file fs))))
(defthm
hifat-cluster-count-of-hifat-place-file-lemma-2
(implies
(and
(equal (len (cdr path)) 1)
(m1-directory-file-p (cdr (assoc-equal (car path) fs)))
(m1-file-alist-p fs)
(hifat-no-dups-p fs)
(fat32-filename-list-p path)
(consp
(assoc-equal (cadr path)
(m1-file->contents (cdr (assoc-equal (car path) fs))))))
(equal
(mv-nth 1
(hifat-find-file
(m1-file->contents (cdr (assoc-equal (car path) fs)))
(cdr path)))
0))
:hints
(("goal"
:expand ((hifat-find-file
(m1-file->contents (cdr (assoc-equal (car path) fs)))
(cdr path))
(len (cdr path))
(len (cddr path))))))
(defthmd hifat-cluster-count-of-hifat-place-file-lemma-3
(implies (equal (+ 1 (len (cddr path))) 1)
(not (consp (cddr path))))
:hints (("goal" :expand (len (cddr path)))))
(encapsulate
()
(local (include-book "arithmetic-3/top" :dir :system))
(defthm
hifat-cluster-count-of-hifat-place-file-lemma-6
(implies (and (integerp cluster-size)
(<= 512 cluster-size))
(and
(equal (ceiling 64 cluster-size)
1)
(equal (ceiling 96 cluster-size)
1)))))
(encapsulate
()
(local
(defthmd
hifat-cluster-count-of-hifat-place-file-lemma-5
(implies
(and (m1-file-alist-p fs)
(hifat-no-dups-p fs)
(fat32-filename-list-p path)
(m1-file-p file)
(integerp cluster-size)
(<= 512 cluster-size))
(equal
(hifat-cluster-count
(mv-nth 0 (hifat-place-file fs path file))
cluster-size)
(b*
((new-contents (m1-file->contents file))
((when
(not (zp (mv-nth 1
(hifat-place-file fs path file)))))
(hifat-cluster-count fs cluster-size))
;; This may be inaccurate because the parent directory's length
;; will change.
((when
(and (not (zp (mv-nth 1 (hifat-find-file fs path))))
(m1-regular-file-p file)))
(+
(hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(nfix
(ceiling
(*
32
(+
3
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size))
(-
(nfix
(ceiling
(*
32
(+
2
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size)))))
;; This may be inaccurate because the parent directory's length
;; will change.
((when
(not (zp (mv-nth 1 (hifat-find-file fs path)))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(nfix
(ceiling
(*
32
(+
3
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size))
(-
(nfix
(ceiling
(*
32
(+
2
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size)))))
(old-file (mv-nth 0 (hifat-find-file fs path)))
(old-contents (m1-file->contents old-file))
((when (and (m1-regular-file-p file)
(m1-regular-file-p old-file)))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (len (make-clusters old-contents cluster-size)))))
((when (m1-regular-file-p file))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))
((when (m1-regular-file-p old-file))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (len (make-clusters old-contents cluster-size))))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))))
:hints
(("goal" :in-theory
(e/d (nfix hifat-place-file hifat-find-file
hifat-cluster-count-of-hifat-place-file-lemma-3)
((:rewrite nfix-when-natp)))
:induct (hifat-place-file fs path file)))))
(defthm
hifat-cluster-count-of-hifat-place-file
(implies
(and (integerp cluster-size)
(<= 512 cluster-size))
(equal
(hifat-cluster-count
(mv-nth 0 (hifat-place-file fs path file))
cluster-size)
(b*
((new-contents (m1-file->contents file))
(fs (hifat-file-alist-fix fs))
(path (fat32-filename-list-fix path))
(file (m1-file-fix file))
((when
(not (zp (mv-nth 1
(hifat-place-file fs path file)))))
(hifat-cluster-count fs cluster-size))
;; This may be inaccurate because the parent directory's length
;; will change.
((when
(and (not (zp (mv-nth 1 (hifat-find-file fs path))))
(m1-regular-file-p file)))
(+
(hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(nfix
(ceiling
(*
32
(+
3
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size))
(-
(nfix
(ceiling
(*
32
(+
2
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size)))))
;; This may be inaccurate because the parent directory's length
;; will change.
((when
(not (zp (mv-nth 1 (hifat-find-file fs path)))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(nfix
(ceiling
(*
32
(+
3
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size))
(-
(nfix
(ceiling
(*
32
(+
2
(len
(m1-file->contents
(mv-nth
0
(hifat-find-file fs (butlast path 1)))))))
cluster-size)))))
(old-file (mv-nth 0 (hifat-find-file fs path)))
(old-contents (m1-file->contents old-file))
((when (and (m1-regular-file-p file)
(m1-regular-file-p old-file)))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (len (make-clusters old-contents cluster-size)))))
((when (m1-regular-file-p file))
(+ (hifat-cluster-count fs cluster-size)
(len (make-clusters new-contents cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))
((when (m1-regular-file-p old-file))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (len (make-clusters old-contents cluster-size))))))
(+ (hifat-cluster-count fs cluster-size)
(hifat-cluster-count new-contents cluster-size)
(nfix (ceiling (* 32 (+ 2 (len new-contents)))
cluster-size))
(- (hifat-cluster-count old-contents cluster-size))
(- (nfix (ceiling (* 32 (+ 2 (len old-contents)))
cluster-size)))))))
:hints
(("goal"
:use (:instance
hifat-cluster-count-of-hifat-place-file-lemma-5
(fs (hifat-file-alist-fix fs))
(path (fat32-filename-list-fix path))
(file (m1-file-fix file)))))))
|
