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; (value :q)
; (ccl::gc-verbose nil nil)
; (lp)
; (include-book "tmi-reductions")
; (time$ (with-output :off :all (certify-book "implementation" 1)))
; Timings on Whitehart:
; Mon Jul 16 09:26:20 2012
; 86.29 seconds realtime, 77.47 seconds runtime
(in-package "M1")
(include-book "defsys")
(defthm nst-out-bound
(implies (natp w)
(< (nst-out cell w) (expt 2 w)))
:hints (("Goal" :in-theory (enable nst-out)))
:rule-classes :linear)
(defthm current-symn-bound
(< (current-symn tape pos) 2)
:hints (("Goal" :in-theory (enable current-symn)))
:rule-classes :linear)
(defun ninstr1 (st sym tm w nnil)
(if (natp w)
(if (zp tm)
-1
(if (equal tm nnil)
-1
(let ((cell (ncar tm w)))
(if (and (equal st (nst-in cell w))
(equal sym (nsym cell w)))
cell
(ninstr1 st sym (ncdr tm w) w nnil)))))
-1))
(defthm ninstr1-nnil-is-ninstr
(equal (ninstr1 st sym tm w (nnil w))
(ninstr st sym tm w))
:hints (("Goal" :in-theory (enable ninstr))))
(in-theory (enable nst-in nsym nop nst-out ncar ncdr current-symn new-tape2))
(defsys :ld-flg nil
:modules
((lessp :formals (x y)
:input (and (natp x)
(natp y))
:output (if (< x y) 1 0)
:code (ifeq y
0
(ifeq x
1
(lessp (- x 1) (- y 1)))))
(mod :formals (x y)
:input (and (natp x)
(natp y)
(not (equal y 0)))
:output (mod x y)
:code (ifeq (lessp x y)
(mod (- x y) y)
x))
(floor :formals (x y a)
:input (and (natp x)
(natp y)
(not (equal y 0))
(natp a))
:output (+ a (floor x y))
:code (ifeq (lessp x y)
(floor (- x y) y (+ a 1))
a))
(log2 :formals (x a)
:input (and (natp x)
(natp a))
:output (+ a (log2 x))
:code (ifeq x
a
(ifeq (- x 1)
a
(log2 (floor x 2 0) (+ 1 a)))))
(expt :formals (x n a)
:input (and (natp x)
(natp n)
(natp a))
:output (* a (expt x n))
:code (ifeq n
a
(expt x (- n 1) (* x a))))
(nst-in :formals (cell w)
:input (and (natp cell)
(natp w))
:output (nst-in cell w)
:code (mod cell (expt 2 w 1)))
(nsym :formals (cell w)
:input (and (natp cell) (natp w))
:output (nsym cell w)
:code (mod (floor cell (expt 2 w 1) 0) 2))
(nop :formals (cell w)
:input (and (natp cell) (natp w))
:output (nop cell w)
:code (mod (floor cell (expt 2 (+ 1 w) 1) 0)
8))
(nst-out :formals (cell w)
:input (and (natp cell) (natp w))
:output (nst-out cell w)
:code (mod (floor cell (expt 2 (+ 4 w) 1) 0)
(expt 2 w 1)))
(ncar :formals (tm w)
:input (and (natp tm) (natp w))
:output (ncar tm w)
:code (mod tm (expt 2 (+ 4 (* 2 w)) 1)))
(ncdr :formals (tm w)
:input (and (natp tm) (natp w))
:output (ncdr tm w)
:code (floor tm (expt 2 (+ 4 (* 2 w)) 1) 0))
(current-symn :formals (tape pos)
:input (and (natp tape)
(natp pos))
:output (current-symn tape pos)
:code (ifeq (- pos (log2 tape 0))
0
(mod (floor tape (expt 2 pos 1) 0)
2)))
(ninstr1 :formals (st sym tm w nnil)
:input (and (natp st)
(natp sym)
(natp tm)
(natp w)
(equal nnil (nnil w)))
:output (ninstr1 st sym tm w nnil)
:code
(ifeq tm
-1
(ifeq (- tm nnil)
-1
(ifeq (ifeq (- st (nst-in (ncar tm w) w))
(- sym (nsym (ncar tm w) w))
1)
(ncar tm w)
(ninstr1 st sym (ncdr tm w) w nnil)))))
(new-tape2 :formals (op tape pos)
:input (and (natp op)
(natp tape)
(natp pos))
:output (mv (acl2::mv-nth 0 (new-tape2 op tape pos))
(acl2::mv-nth 1 (new-tape2 op tape pos)))
:code
(ifeq (ifeq op
0
(ifeq (- op 1)
0
1))
(ifeq (- pos (log2 tape 0))
(ifeq op
(mv (+ tape (expt 2 pos 1)) pos)
(mv (+ tape (expt 2 (+ pos 1) 1)) pos))
(ifeq (- (current-symn tape pos) op)
(mv tape pos)
(ifeq (current-symn tape pos)
(mv (+ tape (expt 2 pos 1)) pos)
(mv (- tape (expt 2 pos 1)) pos))))
(ifeq (- op 2)
(ifeq pos
(mv (* 2 tape) 0)
(mv tape (- pos 1)))
(ifeq (- pos (log2 tape 0))
(mv (+ (- tape (expt 2 pos 1))
(expt 2 (+ 1 pos) 1))
(+ 1 pos))
(mv tape (+ pos 1)))))
:ghost-base-value (mv tape pos))
(tmi3 :formals (st tape pos tm w nnil)
:dcls ((declare (xargs :measure (acl2-count n))))
:input (and (natp st)
(natp tape)
(natp pos)
(natp tm)
(natp w)
(equal nnil (nnil w))
(< st (expt 2 w)))
:output (tmi3 st tape pos tm w n) ; the logic's tmi3 doesn't take nnil as an arg.
:output-arity 4
:code
(ifeq (- (ninstr1 st (current-symn tape pos) tm w nnil) -1)
(mv 1 st tape pos)
(tmi3 (nst-out (ninstr1 st (current-symn tape pos) tm w nnil)
w)
(new-tape2 (nop (ninstr1 st (current-symn tape pos) tm w nnil)
w)
tape pos)
tm w nnil))
:ghost-formals (n)
:ghost-base-test (zp n)
:ghost-base-value (mv 0 st tape pos)
:ghost-decr ((- n 1)))
(main :formals (st tape pos tm w nnil)
:input (and (natp st)
(natp tape)
(natp pos)
(natp tm)
(natp w)
(equal nnil (nnil w))
(< st (expt 2 w)))
:output (tmi3 st tape pos tm w n)
:output-arity 4
:code (tmi3 st tape pos tm w nnil)
:ghost-formals (n)
:ghost-base-value (mv 0 st tape pos)))
:edit-commands
((defun !ninstr1
:before
((defthm natp-ncar
(implies (natp tm)
(natp (ncar tm w)))
:rule-classes :type-prescription)
(defthm natp-ncdr-x
(implies (natp tm)
(natp (ncdr tm w)))
:rule-classes :type-prescription)
(in-theory (disable ncar ncdr))
(defthm natp-nst-in
(implies (natp cell)
(natp (nst-in cell w)))
:rule-classes :type-prescription)
; The type-prescriptions for nsym, nop, and nst-out specify NATP.
(in-theory (disable nst-in nsym nop nst-out))
; The type-prescription for current-symn specifies NATP.
(in-theory (disable current-symn))
))
(defun !tmi3
:before
((defthm integerp-ninstr1
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w)
(equal nnil (nnil w)))
(and (integerp (ninstr1 st sym tm w nnil))
(<= -1 (ninstr1 st sym tm w nnil))))
:rule-classes
((:type-prescription
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w)
(equal nnil (nnil w)))
(integerp (ninstr1 st sym tm w nnil))))
(:linear
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w)
(equal nnil (nnil w)))
(<= -1 (ninstr1 st sym tm w nnil))))
(:rewrite
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w)
(equal nnil (nnil w))
(not (equal (ninstr1 st sym tm w nnil) -1)))
(and (integerp (ninstr1 st sym tm w nnil))
(<= 0 (ninstr1 st sym tm w nnil)))))))
(defthm integerp-ninstr
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w))
(and (integerp (ninstr st sym tm w))
(<= -1 (ninstr st sym tm w))))
:rule-classes
((:type-prescription
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w))
(integerp (ninstr st sym tm w))))
(:linear
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w))
(<= -1 (ninstr st sym tm w))))
(:rewrite
:corollary
(implies (and (natp st)
(natp sym)
(natp tm)
(natp w)
(not (equal (ninstr st sym tm w) -1)))
(and (integerp (ninstr st sym tm w))
(<= 0 (ninstr st sym tm w)))))))
(defthm natp-mv-nth-0-new-tape2
(implies (and (natp tape)
(natp pos))
(natp (acl2::mv-nth 0 (new-tape2 op tape pos))))
:hints (("Goal" :nonlinearp t :in-theory (enable current-symn)))
:rule-classes :type-prescription)
(defthm natp-mv-nth-1-new-tape2
(implies (and (natp tape)
(natp pos))
(natp (acl2::mv-nth 1 (new-tape2 op tape pos))))
:hints (("Goal" :nonlinearp t :in-theory (enable current-symn)))
:rule-classes :type-prescription)
(in-theory (disable ncar ncdr ninstr1 new-tape2 current-symn
!ncar !ncdr !ninstr1 !new-tape2 !current-symn
nst-in nst-out nop nsym
!nst-in !nst-out !nop !nsym))))
(defthm !tmi3-spec
:hints
(("Subgoal *1/10'" :expand (!TMI3 ST TAPE POS TM W (NNIL W) N))))))
|
