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|
(in-package "ACL2")
; update-data-region.lisp Mihir Mehta
; This is optimised code for updating the data region from a string, along with
; necessary basic definitions.
(include-book "fat32-in-memory")
(include-book "../utilities/cluster-listp")
(include-book "../utilities/member-intersectp")
(local (include-book "rtl/rel9/arithmetic/top" :dir :system))
;; These are some rules from other books which are either interacting badly
;; with the theory I've built up so far, or else causing a lot of unnecessary
;; frames and tries.
(local
(in-theory (disable take-of-too-many make-list-ac-removal
revappend-removal)))
(local
(in-theory (disable read-file-into-string1 nth update-nth ceiling floor
mod true-listp)))
(defund
cluster-size (fat32$c)
(declare (xargs :stobjs fat32$c
:guard (fat32$c-p fat32$c)))
(mbe :exec (* (bpb_secperclus fat32$c)
(bpb_bytspersec fat32$c))
:logic (nfix (* (bpb_secperclus fat32$c)
(bpb_bytspersec fat32$c)))))
(defthm natp-of-cluster-size
(implies (fat32$c-p fat32$c)
(natp (cluster-size fat32$c)))
:hints (("goal" :in-theory (enable fat32$c-p cluster-size
bpb_bytspersec bpb_secperclus)))
:rule-classes ((:rewrite
:corollary
(implies (fat32$c-p fat32$c)
(integerp (cluster-size fat32$c))))
(:rewrite
:corollary
(implies (fat32$c-p fat32$c)
(rationalp (cluster-size fat32$c))))
(:linear
:corollary
(implies (fat32$c-p fat32$c)
(<= 0 (cluster-size fat32$c))))
(:rewrite
:corollary
(implies (fat32$c-p fat32$c)
(equal
(nfix (cluster-size fat32$c))
(cluster-size fat32$c))))))
(defthm
cluster-size-of-update-nth
(implies
(not (member-equal key
(list *bpb_secperclus* *bpb_bytspersec*)))
(equal (cluster-size (update-nth key val fat32$c))
(cluster-size fat32$c)))
:hints (("goal" :in-theory (enable cluster-size))))
(defthm
cluster-size-of-resize-data-region
(equal (cluster-size (resize-data-region i fat32$c))
(cluster-size fat32$c))
:hints (("goal" :in-theory (enable resize-data-region))))
(defthm
cluster-size-of-resize-fat
(equal (cluster-size (resize-fat i fat32$c))
(cluster-size fat32$c))
:hints (("goal" :in-theory (enable resize-fat))))
(defund
count-of-clusters (fat32$c)
(declare
(xargs :stobjs fat32$c
:guard (and (fat32$c-p fat32$c)
(>= (bpb_secperclus fat32$c) 1))))
(floor (- (bpb_totsec32 fat32$c)
(+ (bpb_rsvdseccnt fat32$c)
(* (bpb_numfats fat32$c)
(bpb_fatsz32 fat32$c))))
(bpb_secperclus fat32$c)))
(defthm
count-of-clusters-of-resize-fat
(equal (count-of-clusters (resize-fat i fat32$c))
(count-of-clusters fat32$c))
:hints (("goal" :in-theory (enable count-of-clusters))))
(defthm
count-of-clusters-of-update-nth
(implies
(not (member key
(list *bpb_totsec32*
*bpb_rsvdseccnt* *bpb_numfats*
*bpb_fatsz32* *bpb_secperclus*)))
(equal
(count-of-clusters (update-nth key val fat32$c))
(count-of-clusters fat32$c)))
:hints (("goal" :in-theory (enable count-of-clusters))))
(defthm
count-of-clusters-of-update-data-regioni
(equal
(count-of-clusters (update-data-regioni i v fat32$c))
(count-of-clusters fat32$c))
:hints
(("goal"
:in-theory (enable update-data-regioni))))
(defun
stobj-cluster-listp-helper
(fat32$c n)
(declare
(xargs
:stobjs fat32$c
:guard (and (fat32$c-p fat32$c)
(natp n)
(<= n (data-region-length fat32$c)))
:guard-hints
(("goal" :in-theory (disable fat32$c-p)))))
(or
(zp n)
(let
((current-cluster
(data-regioni (- (data-region-length fat32$c)
n)
fat32$c)))
(and
(cluster-p current-cluster
(cluster-size fat32$c))
(stobj-cluster-listp-helper fat32$c (- n 1))))))
(defthm
stobj-cluster-listp-helper-correctness-1
(implies
(and (natp n)
(<= n (data-region-length fat32$c)))
(equal
(stobj-cluster-listp-helper fat32$c n)
(cluster-listp
(nthcdr
(- (data-region-length fat32$c)
n)
(true-list-fix (nth *data-regioni* fat32$c)))
(cluster-size fat32$c))))
:hints
(("goal"
:in-theory (e/d (data-regioni data-region-length
nth)
;; Try disabling rules until the proof works again...
((:rewrite a1)
(:rewrite a2)
(:rewrite a4)
(:rewrite a9)))
:induct (stobj-cluster-listp-helper fat32$c n)
:expand
((true-list-fix (nth *data-regioni* fat32$c))
(cluster-listp
(nthcdr
(+ (- n)
(len (nth *data-regioni* fat32$c)))
(true-list-fix (nth *data-regioni* fat32$c)))
(cluster-size fat32$c))
(cluster-listp
(nthcdr
(+ (- n)
(len (cdr (nth *data-regioni* fat32$c))))
(true-list-fix
(cdr (nth *data-regioni* fat32$c))))
(cluster-size fat32$c)))))
:rule-classes
((:rewrite
:corollary
(implies
(and (natp n)
(<= n (data-region-length fat32$c))
(fat32$c-p fat32$c))
(equal (stobj-cluster-listp-helper fat32$c n)
(cluster-listp
(nthcdr (- (data-region-length fat32$c)
n)
(nth *data-regioni* fat32$c))
(cluster-size fat32$c))))
:hints (("goal" :in-theory (enable fat32$c-p))))))
(defund
fat-entry-count (fat32$c)
(declare (xargs :guard (fat32$c-p fat32$c)
:stobjs fat32$c))
(floor (* (bpb_fatsz32 fat32$c)
(bpb_bytspersec fat32$c))
4))
(defthm
fat-entry-count-of-update-nth
(implies
(not (member-equal key
(list *bpb_fatsz32* *bpb_bytspersec*)))
(equal (fat-entry-count (update-nth key val fat32$c))
(fat-entry-count fat32$c)))
:hints
(("goal" :in-theory (enable fat-entry-count
bpb_bytspersec bpb_fatsz32))))
(defthm
fat-entry-count-of-resize-data-region
(equal (fat-entry-count
(resize-data-region i fat32$c))
(fat-entry-count fat32$c))
:hints (("goal" :in-theory (enable resize-data-region))))
(defthm
fat32-entry-p-of-bpb_rootclus-when-fat32$c-p
(implies (fat32$c-p fat32$c)
(fat32-entry-p (bpb_rootclus fat32$c)))
:hints (("goal" :in-theory (enable fat32-entry-p))))
(defthm
fat-entry-count-of-update-fati
(equal (fat-entry-count (update-fati i v fat32$c))
(fat-entry-count fat32$c))
:hints
(("goal" :in-theory (enable fat-entry-count update-fati))))
(encapsulate
()
;; Trying to remove this is hazardous, even though it doesn't seem to be used
;; anywhere!
(local
(defthm
lemma-1
(implies (and
(fat32$c-p fat32$c)
(>= (bpb_bytspersec fat32$c) *ms-min-bytes-per-sector*)
(>= (bpb_secperclus fat32$c) 1))
(not (equal (cluster-size fat32$c)
0)))
:hints (("goal" :in-theory (enable cluster-size)))))
(defund lofat-fs-p (fat32$c)
(declare (xargs :stobjs fat32$c :guard t))
(and (fat32$c-p fat32$c)
(>= (bpb_bytspersec fat32$c)
*ms-min-bytes-per-sector*)
(>= (bpb_secperclus fat32$c) 1)
(>= (count-of-clusters fat32$c)
*ms-min-count-of-clusters*)
(<= (+ *ms-first-data-cluster*
(count-of-clusters fat32$c))
*ms-bad-cluster*)
(>= (bpb_rsvdseccnt fat32$c) 1)
(>= (bpb_numfats fat32$c) 1)
(>= (bpb_fatsz32 fat32$c) 1)
;; These constraints on bpb_rootclus aren't in the spec, but they are
;; clearly implied
(>= (fat32-entry-mask (bpb_rootclus fat32$c))
*ms-first-data-cluster*)
(< (fat32-entry-mask (bpb_rootclus fat32$c))
(+ *ms-first-data-cluster*
(count-of-clusters fat32$c)))
(<= (+ (count-of-clusters fat32$c)
*ms-first-data-cluster*)
(fat-entry-count fat32$c))
;; The spec (page 9) imposes both hard and soft limits on the legal
;; values of the cluster size, limiting it to being a power of 2 from
;; 512 through 32768. The following two clauses, however, are less
;; stringent - they allow values of cluster size which are powers of 2
;; going up to 2097152, although the lower bound of 512 is retained
;; thanks to the lower bounds on bpb_bytspersec and bpb_secperclus
;; above.
(equal (mod (cluster-size fat32$c)
*ms-d-e-length*)
0)
(equal (mod *ms-max-dir-size*
(cluster-size fat32$c))
0)
;; Some array properties in addition to the scalar properties
(stobj-cluster-listp-helper
fat32$c
(data-region-length fat32$c))
(equal (data-region-length fat32$c)
(count-of-clusters fat32$c))
(equal (* 4 (fat-length fat32$c))
(* (bpb_fatsz32 fat32$c)
(bpb_bytspersec fat32$c)))))
(local
(defthm
lemma-2
(implies (and (fat32$c-p fat32$c)
(< 0 (bpb_bytspersec fat32$c)))
(< (fat-entry-count fat32$c)
(ash 1 48)))
:rule-classes ()
:hints (("goal"
:do-not-induct t
:in-theory
(enable fat32$c-p fat-entry-count
bpb_bytspersec bpb_fatsz32)))))
(defthm
lofat-fs-p-correctness-1
(implies (lofat-fs-p fat32$c)
(and (fat32$c-p fat32$c)
(integerp (cluster-size fat32$c))
(>= (cluster-size fat32$c)
*ms-min-bytes-per-sector*)
(>= (count-of-clusters fat32$c)
*ms-min-count-of-clusters*)
(equal (mod (cluster-size fat32$c)
*ms-d-e-length*)
0)
(equal (mod *ms-max-dir-size*
(cluster-size fat32$c))
0)
(<= (+ *ms-first-data-cluster*
(count-of-clusters fat32$c))
*ms-bad-cluster*)
(>= (bpb_secperclus fat32$c) 1)
(>= (bpb_rsvdseccnt fat32$c) 1)
(>= (bpb_numfats fat32$c) 1)
(>= (bpb_fatsz32 fat32$c) 1)
(>= (fat32-entry-mask (bpb_rootclus fat32$c))
*ms-first-data-cluster*)
;; There was a bug here, which we fixed - previously,
;; bpb_rootclus was only allowed to point at clusters up to
;; but not including (count-of-clusters fat32$c),
;; which causes two clusters (up to but not including
;; (+ 2 (count-of-clusters fat32$c))) to be left out.
(< (fat32-entry-mask (bpb_rootclus fat32$c))
(+ *ms-first-data-cluster*
(count-of-clusters fat32$c)))
(>= (bpb_bytspersec fat32$c)
*ms-min-bytes-per-sector*)
(equal (data-region-length fat32$c)
(count-of-clusters fat32$c))
(<= (+ (count-of-clusters fat32$c)
*ms-first-data-cluster*)
(fat-length fat32$c))
(equal (fat-length fat32$c)
(fat-entry-count fat32$c))
;; This also represents a fixed bug - earlier, we were going
;; to return an error for all filesystems with fat-length
;; greater than *ms-bad-cluster*. The upper limit is actually
;; (ash 1 28) - only slightly greater than *ms-bad-cluster* -
;; derived from bpb_fatsz32 being up to (ash 1 16) and
;; bpb_bytspersec being up to 4096.
(< (fat-entry-count fat32$c)
(ash 1 48))))
:hints
(("goal"
:in-theory
(e/d
(lofat-fs-p cluster-size fat-entry-count)
(fat32$c-p))
:use
lemma-2))
:rule-classes
((:rewrite
:corollary
(implies (lofat-fs-p fat32$c)
(and (fat32$c-p fat32$c)
(integerp (cluster-size fat32$c))
(equal (mod (cluster-size fat32$c)
*ms-d-e-length*)
0)
(equal (mod *ms-max-dir-size*
(cluster-size fat32$c))
0)
(equal (data-region-length fat32$c)
(count-of-clusters fat32$c))
(equal (fat-length fat32$c)
(fat-entry-count fat32$c)))))
(:forward-chaining
:corollary
(implies (lofat-fs-p fat32$c)
(integerp (cluster-size fat32$c))))
(:linear
:corollary
(implies
(lofat-fs-p fat32$c)
(and (>= (cluster-size fat32$c)
*ms-min-bytes-per-sector*)
(>= (count-of-clusters fat32$c)
*ms-min-count-of-clusters*)
(<= (+ *ms-first-data-cluster*
(count-of-clusters fat32$c))
*ms-bad-cluster*)
(>= (bpb_secperclus fat32$c) 1)
(>= (bpb_rsvdseccnt fat32$c) 1)
(>= (bpb_numfats fat32$c) 1)
(>= (bpb_fatsz32 fat32$c) 1)
(>= (fat32-entry-mask (bpb_rootclus fat32$c))
*ms-first-data-cluster*)
(< (fat32-entry-mask (bpb_rootclus fat32$c))
(+ *ms-first-data-cluster*
(count-of-clusters fat32$c)))
(>= (bpb_bytspersec fat32$c)
*ms-min-bytes-per-sector*)
(>= (* (cluster-size fat32$c)
(count-of-clusters fat32$c))
(* *ms-min-bytes-per-sector*
*ms-min-count-of-clusters*))
(<= (+ (count-of-clusters fat32$c)
*ms-first-data-cluster*)
(fat-entry-count fat32$c))
(< (fat-entry-count fat32$c)
(ash 1 48))))))))
(defthm
fati-when-lofat-fs-p
(implies (lofat-fs-p fat32$c)
(equal (fat32-entry-p (fati i fat32$c))
(< (nfix i) (fat-length fat32$c))))
:hints (("goal" :in-theory (enable lofat-fs-p fat32$c-p fati fat-length)))
:rule-classes
(:rewrite
(:rewrite :corollary (implies (lofat-fs-p fat32$c)
(equal (unsigned-byte-p 32 (fati i fat32$c))
(< (nfix i) (fat-length fat32$c))))
:hints (("goal" :do-not-induct t
:in-theory (enable fat32-entry-p))))))
(defthm
cluster-size-of-update-fati
(equal (cluster-size (update-fati i v fat32$c))
(cluster-size fat32$c))
:hints
(("goal" :in-theory (enable cluster-size update-fati))))
(defthm
count-of-clusters-of-update-fati
(equal (count-of-clusters (update-fati i v fat32$c))
(count-of-clusters fat32$c))
:hints
(("goal"
:in-theory (enable count-of-clusters update-fati bpb_totsec32))))
;; After disabling, this function used to cause 9419883 frames and 76526
;; tries. So we went back to leaving it enabled and those numbers are now
;; 9446133 and 82621 respectively.
(defthm
lofat-fs-p-of-update-fati
(implies (and (lofat-fs-p fat32$c)
(case-split (< i (fat-length fat32$c))))
(equal (lofat-fs-p (update-fati i v fat32$c))
(fat32-entry-p v)))
:hints
(("goal"
:in-theory
'((:compound-recognizer natp-compound-recognizer)
(:compound-recognizer true-listp-when-fat32-entry-list-p-compound-recognizer)
(:definition bpb_bkbootsecp)
(:definition bpb_bytspersecp)
(:definition bpb_extflagsp)
(:definition bpb_fatsz16p)
(:definition bpb_fatsz32p)
(:definition bpb_fsinfop)
(:definition bpb_fsver_majorp)
(:definition bpb_fsver_minorp)
(:definition bpb_hiddsecp)
(:definition bpb_mediap)
(:definition bpb_numfatsp)
(:definition bpb_numheadsp)
(:definition bpb_reservedp-alt)
(:definition bpb_rootclusp)
(:definition bpb_rootentcntp)
(:definition bpb_rsvdseccntp)
(:definition bpb_secperclusp)
(:definition bpb_secpertrkp)
(:definition bpb_totsec16p)
(:definition bpb_totsec32p)
(:definition bs_bootsigp)
(:definition bs_drvnump)
(:definition bs_filsystypep-alt)
(:definition bs_jmpbootp-alt)
(:definition bs_oemnamep-alt)
(:definition bs_reserved1p)
(:definition bs_volidp)
(:definition bs_vollabp-alt)
(:definition count-of-clusters)
(:definition data-region-length)
(:definition data-regionp-alt)
(:definition fat-length)
(:definition fat32$c-p)
(:definition fatp-alt)
(:definition force)
(:definition integer-range-p)
(:definition length)
(:definition lofat-fs-p)
(:definition max)
(:definition nfix)
(:definition not)
(:definition nthcdr)
(:definition unsigned-byte-p)
(:definition update-fati)
(:definition update-nth-array)
(:executable-counterpart binary-+)
(:executable-counterpart equal)
(:executable-counterpart expt)
(:executable-counterpart integerp)
(:executable-counterpart max)
(:executable-counterpart member-equal)
(:executable-counterpart nfix)
(:executable-counterpart not)
(:executable-counterpart zp)
(:rewrite bpb_bytspersec-of-update-nth . 23)
(:rewrite bpb_fatsz32-of-update-nth . 23)
(:rewrite bpb_numfats-of-update-nth . 23)
(:rewrite bpb_rootclus-of-update-nth . 23)
(:rewrite bpb_rsvdseccnt-of-update-nth . 23)
(:rewrite bpb_secperclus-of-update-nth . 23)
(:rewrite cluster-size-of-update-nth)
(:rewrite commutativity-2-of-+)
(:rewrite commutativity-of-*)
(:rewrite commutativity-of-+)
(:rewrite count-of-clusters-of-update-nth)
(:rewrite distributivity-of-minus-over-+)
(:rewrite fat-entry-count-of-update-nth)
(:rewrite fat32-entry-list-p-of-update-nth)
(:rewrite inverse-of-+)
(:rewrite len-update-nth)
(:rewrite nth-update-nth)
(:rewrite stobj-cluster-listp-helper-correctness-1)
(:type-prescription cluster-listp)
(:type-prescription count-of-clusters)
(:type-prescription fat-entry-count)
(:type-prescription fat32-entry-mask)
(:type-prescription fat32-entry-p)
(:type-prescription floor)
(:type-prescription len)
(:type-prescription string-listp)
(:type-prescription true-listp-update-nth)
(:type-prescription unsigned-byte-listp)
(:type-prescription update-nth))
:use cluster-size-of-update-fati)))
(defthm
data-regioni-when-lofat-fs-p
(implies (and (lofat-fs-p fat32$c)
(< (nfix i)
(data-region-length fat32$c)))
(cluster-p (data-regioni i fat32$c)
(cluster-size fat32$c)))
:hints
(("goal" :in-theory (e/d (lofat-fs-p
fat32$c-p
data-regioni data-region-length)
(unsigned-byte-p))))
:rule-classes
(:rewrite
(:rewrite
:corollary
(implies
(and (lofat-fs-p fat32$c)
(< (nfix i)
(data-region-length fat32$c)))
(and
(stringp (data-regioni i fat32$c))
(equal (len (explode (data-regioni i fat32$c)))
(cluster-size fat32$c))))
:hints (("goal" :in-theory (enable cluster-p))))))
(defthm
cluster-size-of-update-data-regioni
(equal
(cluster-size (update-data-regioni i v fat32$c))
(cluster-size fat32$c))
:hints
(("goal"
:in-theory (enable cluster-size update-data-regioni))))
(defthm
lofat-fs-p-of-update-data-regioni
(implies
(and (lofat-fs-p fat32$c)
(< i (data-region-length fat32$c)))
(equal (lofat-fs-p (update-data-regioni i v fat32$c))
(cluster-p v (cluster-size fat32$c))))
:hints
(("goal"
:do-not-induct t
:in-theory
'((:compound-recognizer natp-compound-recognizer)
(:compound-recognizer true-listp-when-fat32-entry-list-p-compound-recognizer)
(:definition bpb_bkbootsecp)
(:definition bpb_bytspersecp)
(:definition bpb_extflagsp)
(:definition bpb_fatsz16p)
(:definition bpb_fatsz32p)
(:definition bpb_fsinfop)
(:definition bpb_fsver_majorp)
(:definition bpb_fsver_minorp)
(:definition bpb_hiddsecp)
(:definition bpb_mediap)
(:definition bpb_numfatsp)
(:definition bpb_numheadsp)
(:definition bpb_reservedp-alt)
(:definition bpb_rootclusp)
(:definition bpb_rootentcntp)
(:definition bpb_rsvdseccntp)
(:definition bpb_secperclusp)
(:definition bpb_secpertrkp)
(:definition bpb_totsec16p)
(:definition bpb_totsec32p)
(:definition bs_bootsigp)
(:definition bs_drvnump)
(:definition bs_filsystypep-alt)
(:definition bs_jmpbootp-alt)
(:definition bs_oemnamep-alt)
(:definition bs_reserved1p)
(:definition bs_volidp)
(:definition bs_vollabp-alt)
(:definition count-of-clusters)
(:definition data-region-length)
(:definition data-regionp-alt)
(:definition fat-length)
(:definition fat32$c-p)
(:definition fatp-alt)
(:definition fix)
(:definition integer-range-p)
(:definition length)
(:definition lofat-fs-p)
(:definition max)
(:definition nfix)
(:definition not)
(:definition nthcdr)
(:definition unsigned-byte-p)
(:definition update-data-regioni)
(:definition update-nth-array)
(:executable-counterpart binary-+)
(:executable-counterpart equal)
(:executable-counterpart expt)
(:executable-counterpart integerp)
(:executable-counterpart max)
(:executable-counterpart member-equal)
(:executable-counterpart nfix)
(:executable-counterpart not)
(:executable-counterpart unary--)
(:executable-counterpart zp)
(:rewrite bpb_bytspersec-of-update-nth . 23)
(:rewrite bpb_fatsz32-of-update-nth . 23)
(:rewrite bpb_numfats-of-update-nth . 23)
(:rewrite bpb_rootclus-of-update-nth . 23)
(:rewrite bpb_rsvdseccnt-of-update-nth . 23)
(:rewrite bpb_secperclus-of-update-nth . 23)
(:rewrite cluster-listp-of-update-nth)
(:rewrite cluster-p-correctness-1)
(:rewrite cluster-size-of-update-nth)
(:rewrite commutativity-2-of-+)
(:rewrite commutativity-of-*)
(:rewrite commutativity-of-+)
(:rewrite count-of-clusters-of-update-nth)
(:rewrite distributivity-of-minus-over-+)
(:rewrite fat-entry-count-of-update-nth)
(:rewrite fat-length-of-update-nth)
(:rewrite inverse-of-+)
(:rewrite len-update-nth)
(:rewrite nth-update-nth)
(:rewrite nthcdr-of-update-nth)
(:rewrite stobj-cluster-listp-helper-correctness-1)
(:rewrite string-listp-of-update-nth)
(:rewrite unicity-of-0)
(:type-prescription cluster-listp)
(:type-prescription cluster-p)
(:type-prescription count-of-clusters)
(:type-prescription fat-entry-count)
(:type-prescription fat32-entry-mask)
(:type-prescription floor)
(:type-prescription len)
(:type-prescription max)
(:type-prescription string-listp)
(:type-prescription true-listp-update-nth)
(:type-prescription unsigned-byte-listp)
(:type-prescription update-nth))
:use cluster-size-of-update-data-regioni)))
(defun
update-data-region
(fat32$c str len)
(declare
(xargs
:guard (and (stringp str)
(natp len)
(<= len
(data-region-length fat32$c))
(>= (length str)
(* (- (data-region-length fat32$c)
len)
(cluster-size fat32$c)))
(<= len
(- *ms-bad-cluster*
*ms-first-data-cluster*)))
:stobjs fat32$c
:measure (nfix len)))
(b*
((len (the (unsigned-byte 28) len))
((when (zp len)) (mv fat32$c 0))
(cluster-size (cluster-size fat32$c))
(index (- (data-region-length fat32$c)
len)))
(if
(<= (* (+ index 1) cluster-size)
(length str))
(b*
((current-cluster (subseq str (* index cluster-size)
(* (+ index 1) cluster-size)))
(fat32$c
(update-data-regioni
index current-cluster fat32$c)))
(update-data-region
fat32$c
str (the (unsigned-byte 28) (- len 1))))
(b*
((current-cluster (subseq str (* index cluster-size) nil))
(fat32$c
(update-data-regioni
index current-cluster fat32$c)))
(mv fat32$c *eio*)))))
(defun
update-data-region-from-disk-image
(fat32$c len state tmp_init image-path)
(declare
(xargs
:guard
(and (natp tmp_init)
(stringp image-path)
(stringp (read-file-into-string image-path))
(natp len)
(<= len
(data-region-length fat32$c))
(>= (length (read-file-into-string image-path))
(+ tmp_init
(* (- (data-region-length fat32$c)
len)
(cluster-size fat32$c))))
(<= len
(- *ms-bad-cluster*
*ms-first-data-cluster*)))
:stobjs (fat32$c state)
:measure (nfix len)))
(b*
((len (the (unsigned-byte 28) len))
((when (zp len)) (mv fat32$c 0))
(cluster-size (cluster-size fat32$c))
(index (- (data-region-length fat32$c)
len))
(fat32$c
(update-data-regioni
index
(read-file-into-string
image-path
:start (+ tmp_init (* index cluster-size))
:bytes cluster-size)
fat32$c)))
(if (equal (length (data-regioni index fat32$c))
cluster-size)
(update-data-region-from-disk-image
fat32$c
(the (unsigned-byte 28) (- len 1))
state tmp_init image-path)
(mv fat32$c *eio*))))
(defthm
update-data-region-from-disk-image-correctness-1
(implies
(and (natp tmp_init)
(<= len
(data-region-length fat32$c))
(>= (length (read-file-into-string image-path))
(+ tmp_init
(* (- (data-region-length fat32$c)
len)
(cluster-size fat32$c))))
(not (zp (cluster-size fat32$c))))
(equal (update-data-region-from-disk-image fat32$c
len state tmp_init image-path)
(update-data-region fat32$c
(subseq (read-file-into-string image-path)
tmp_init nil)
len)))
:hints
(("goal"
:induct (update-data-region-from-disk-image fat32$c
len state tmp_init image-path)
:in-theory (enable take-of-nthcdr)
:expand (:free (fat32$c str)
(update-data-region fat32$c str len)))))
(defthm
fat32$c-p-of-update-data-regioni
(implies
(fat32$c-p fat32$c)
(equal
(fat32$c-p (update-data-regioni i v fat32$c))
(and (stringp v)
(<= (nfix i)
(data-region-length fat32$c)))))
:hints
(("goal"
:in-theory (enable fat32$c-p update-data-regioni
data-region-length))))
(defthm
fat32$c-p-of-update-data-region
(implies (and (fat32$c-p fat32$c)
(stringp str))
(fat32$c-p
(mv-nth 0
(update-data-region fat32$c str len)))))
(defthm
bpb_bytspersec-of-update-data-region
(equal
(bpb_bytspersec (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_bytspersec fat32$c)))
(defthm
bpb_secperclus-of-update-data-region
(equal
(bpb_secperclus (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_secperclus fat32$c)))
(defthm
bpb_rsvdseccnt-of-update-data-region
(equal
(bpb_rsvdseccnt (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_rsvdseccnt fat32$c)))
(defthm
bpb_totsec32-of-update-data-region
(equal
(bpb_totsec32 (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_totsec32 fat32$c)))
(defthm
bpb_fatsz32-of-update-data-region
(equal
(bpb_fatsz32 (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_fatsz32 fat32$c)))
(defthm
bpb_numfats-of-update-data-region
(equal
(bpb_numfats (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_numfats fat32$c)))
(defthm
bpb_rootclus-of-update-data-region
(equal
(bpb_rootclus (mv-nth 0 (update-data-region fat32$c str len)))
(bpb_rootclus fat32$c)))
(defthm
fat-length-of-update-data-region
(equal
(fat-length (mv-nth 0 (update-data-region fat32$c str len)))
(fat-length fat32$c)))
(defthm
fat-entry-count-of-update-data-region
(equal (fat-entry-count
(mv-nth 0 (update-data-region fat32$c str len)))
(fat-entry-count fat32$c))
:hints (("goal" :in-theory (enable fat-entry-count))))
(defthm
data-region-length-of-update-data-region
(implies
(<= len
(data-region-length fat32$c))
(equal (data-region-length
(mv-nth 0 (update-data-region fat32$c str len)))
(data-region-length fat32$c)))
:rule-classes
(:rewrite
(:rewrite
:corollary
(implies
(<= len
(data-region-length fat32$c))
(equal
(consp (nth *data-regioni*
(mv-nth 0 (update-data-region fat32$c str len))))
(consp (nth *data-regioni* fat32$c))))
:hints
(("goal"
:in-theory (enable data-region-length)
:do-not-induct t
:expand
((len (nth *data-regioni*
(mv-nth 0 (update-data-region fat32$c str len))))
(len (nth *data-regioni* fat32$c))))))))
(defthmd
update-data-region-correctness-2
(equal
(update-data-region fat32$c str len)
(mv (mv-nth 0
(update-data-region fat32$c str len))
(mv-nth 1
(update-data-region fat32$c str len)))))
(local
(defthm
update-data-region-correctness-1-lemma-1
(implies (and (not (zp len))
(<= (* cluster-size
data-region-length)
(+ length-str
(* len cluster-size)))
(< (+ length-str
(* len cluster-size))
(+ cluster-size
(* cluster-size
data-region-length))))
(< length-str
(* cluster-size
data-region-length)))
:hints (("goal" :in-theory (disable (:rewrite product-less-than-zero))
:use ((:instance (:rewrite product-less-than-zero)
(y cluster-size)
(x (+ -1 len))))))))
;; It would be nice to make this a rule that just rewrites the inner (mv-nth
;; 1 ...) subexpression rather than the (equal (mv-nth 1 ...) ...)
;; expression, but that causes trouble with
;; string-to-lofat-ignore-lemma-14 in another book.
(defthm
update-data-region-correctness-1
(implies (and (natp len)
(<= len
(data-region-length fat32$c))
(>= (length str)
(* (- (data-region-length fat32$c)
len)
(cluster-size fat32$c))))
(iff
(equal (mv-nth 1
(update-data-region fat32$c str len))
0)
(>= (length str)
(* (data-region-length fat32$c)
(cluster-size fat32$c))))))
(encapsulate
()
(local
(defthm
update-data-region-alt-lemma-1
(equal (update-nth *data-regioni* val
(update-data-regioni i v fat32$c))
(update-nth *data-regioni* val fat32$c))
:hints (("goal" :in-theory (enable update-data-regioni)))))
(local
(defthm
update-data-region-alt-lemma-2
(implies (fat32$c-p fat32$c)
(and
(true-listp (nth *data-regioni* fat32$c))
(equal
(update-nth *data-regioni*
(nth *data-regioni* fat32$c)
fat32$c)
fat32$c)))
:hints (("goal" :in-theory (enable fat32$c-p)))))
(local
(defthm
update-data-region-alt-lemma-3
(equal
(nth *data-regioni*
(update-data-regioni i v fat32$c))
(update-nth i v
(nth *data-regioni* fat32$c)))
:hints (("goal" :in-theory (enable update-data-regioni)) )))
(defthm
update-data-region-alt-lemma-4
(implies (and (not (zp len))
(< (len (explode str))
(+ (cluster-size fat32$c)
(* -1 len (cluster-size fat32$c))
(* (cluster-size fat32$c)
(len (nth *data-regioni* fat32$c)))))
(fat32$c-p fat32$c))
(< (len (explode str))
(* (cluster-size fat32$c)
(len (nth *data-regioni* fat32$c)))))
:hints (("goal" :cases ((<= (+ (cluster-size fat32$c)
(* -1 len (cluster-size fat32$c)))
0)))))
(defthmd
update-data-region-alt
(implies
(and (stringp str)
(natp len)
(>= (data-region-length fat32$c)
len)
(fat32$c-p fat32$c)
(< 0 (cluster-size fat32$c))
(>= (length str)
(* (data-region-length fat32$c)
(cluster-size fat32$c))))
(equal
(update-data-region fat32$c str len)
(mv
(update-nth
*data-regioni*
(append
(take (- (data-region-length fat32$c)
len)
(nth *data-regioni* fat32$c))
(make-clusters
(subseq str
(* (- (data-region-length fat32$c)
len)
(cluster-size fat32$c))
(* (data-region-length fat32$c)
(cluster-size fat32$c)))
(cluster-size fat32$c)))
fat32$c)
0)))
:hints
(("goal"
:in-theory
(e/d (data-region-length make-clusters
remember-that-time-with-update-nth
take-of-nthcdr)
(append take))
:induct (update-data-region fat32$c str len)))))
(defthm
cluster-listp-after-update-data-region
(implies
(and
(fat32$c-p fat32$c)
(stringp str)
(natp len)
(>= (len (explode str))
(* (cluster-size fat32$c)
(data-region-length fat32$c)))
(< 0 (cluster-size fat32$c))
(cluster-listp (take (- (data-region-length fat32$c)
len)
(nth *data-regioni* fat32$c))
(cluster-size fat32$c))
(>= (data-region-length fat32$c)
len))
(cluster-listp
(nth *data-regioni*
(mv-nth 0
(update-data-region fat32$c str len)))
(cluster-size fat32$c)))
:hints (("goal" :use update-data-region-alt))
:rule-classes
(:rewrite
(:rewrite
:corollary
(implies
(and (fat32$c-p fat32$c)
(stringp str)
(natp len)
(>= (len (explode str))
(* (cluster-size fat32$c)
(data-region-length fat32$c)))
(< 0 (cluster-size fat32$c))
(cluster-listp
(take (- (data-region-length fat32$c)
len)
(nth *data-regioni* fat32$c))
cluster-size)
(>= (data-region-length fat32$c)
len)
(equal cluster-size
(cluster-size fat32$c)))
(cluster-listp
(nth
*data-regioni*
(mv-nth 0
(update-data-region fat32$c str len)))
cluster-size))
:hints
(("goal"
:in-theory (e/d (fat32$c-p)
(fat32$c-p-of-update-data-region
(:definition update-data-region)
(:rewrite
update-data-region-correctness-1-lemma-1)
(:definition nthcdr)
(:rewrite cancel-common-factors-in-<)
(:rewrite rationalp-prod)
(:rewrite rationalp-sum)
(:rewrite integerp-prod)))
:use fat32$c-p-of-update-data-region
:do-not-induct t)))))
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