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;; Copyright (C) 2017, Regents of the University of Texas
;; Written by Cuong Chau (derived from the FM9001 work of Brock and Hunt)
;; License: A 3-clause BSD license. See the LICENSE file distributed with
;; ACL2.
;; The ACL2 source code for the FM9001 work is available at
;; https://github.com/acl2/acl2/tree/master/books/projects/fm9001.
;; Cuong Chau <ckcuong@cs.utexas.edu>
;; January 2019
;; The high level specification of the ALU
(in-package "ADE")
(include-book "constants")
(include-book "../../hard-spec")
;; ======================================================================
;; CVZBV is used to construct all of the values returned by the ALU
;; specification V-ALU.
(defun cvzbv (carry overflow vector)
(declare (xargs :guard t))
(cons carry (cons overflow (cons (v-zp vector) vector))))
(defun c (cvzbv)
(declare (xargs :guard (true-listp cvzbv)))
(car cvzbv))
(defun v (cvzbv)
(declare (xargs :guard (true-listp cvzbv)))
(cadr cvzbv))
(defun bv (cvzbv)
(declare (xargs :guard (true-listp cvzbv)))
(cdddr cvzbv))
(defun n (cvzbv)
(declare (xargs :guard (true-listp cvzbv)))
(v-negp (bv cvzbv)))
(defun zb (cvzbv)
(declare (xargs :guard (true-listp cvzbv)))
(caddr cvzbv))
(defthm booleanp-n
(implies (bvp (bv v))
(booleanp (n v)))
:rule-classes :type-prescription)
(defthm booleanp-zp-cvzbv
(booleanp (zb (cvzbv c v bv)))
:rule-classes :type-prescription)
(defthm booleanp-bvp-cvzbv
(and
(equal (booleanp (c (cvzbv c v bv)))
(booleanp c))
(equal (booleanp (v (cvzbv c v bv)))
(booleanp v))
(equal (bvp (bv (cvzbv c v bv)))
(bvp bv))))
(defthmd bvp-cvzbv
(implies (and (true-listp cvzbv)
(booleanp (c cvzbv))
(booleanp (v cvzbv))
(booleanp (zb cvzbv))
(bvp (bv cvzbv)))
(bvp cvzbv))
:hints (("Goal" :in-theory (enable bvp)))
:rule-classes (:rewrite :type-prescription))
(in-theory (disable c v n zb bv))
;; Specification abbreviations for V-ALU.
(defun cvzbv-v-ror (c a)
(declare (xargs :guard (true-listp a)))
(cvzbv (if (atom a) c (nth 0 a))
nil
(v-ror a c)))
(defun cvzbv-v-adder (c a b)
(declare (xargs :guard (and (consp a)
(true-listp a)
(consp b)
(true-listp b))))
(cvzbv (v-adder-carry-out c a b)
(v-adder-overflowp c a b)
(v-adder-output c a b)))
(defun cvzbv-v-lsl (a)
(declare (xargs :guard (and (consp a)
(true-listp a))))
(cvzbv-v-adder nil a a))
(defun cvzbv-v-subtracter (c a b)
(declare (xargs :guard (and (consp a)
(true-listp a)
(consp b)
(true-listp b))))
(cvzbv (v-subtracter-carry-out c a b)
(v-subtracter-overflowp c a b)
(v-subtracter-output c a b)))
(defun cvzbv-inc (a)
(declare (xargs :guard (and (consp a)
(true-listp a))
:guard-hints (("Goal" :in-theory (enable nat-to-v)))))
(cvzbv-v-adder t a (nat-to-v 0 (len a))))
(defun cvzbv-neg (a)
(declare (xargs :guard (and (consp a)
(true-listp a))
:guard-hints (("Goal" :in-theory (enable nat-to-v)))))
(cvzbv-v-subtracter nil a (nat-to-v 0 (len a))))
(defun cvzbv-dec (a)
(declare (xargs :guard (and (consp a)
(true-listp a))
:guard-hints (("Goal" :in-theory (enable nat-to-v)))))
(cvzbv-v-subtracter t (nat-to-v 0 (len a)) a))
(defun cvzbv-v-not (a)
(declare (xargs :guard t))
(cvzbv nil nil (v-not a)))
(defun cvzbv-v-asr (a)
(declare (xargs :guard (true-listp a)))
(cvzbv (if (consp a) (nth 0 a) nil)
nil
(v-asr a)))
(defun cvzbv-v-lsr (a)
(declare (xargs :guard (true-listp a)))
(cvzbv (if (listp a) (nth 0 a) nil)
nil
(v-lsr a)))
;; V-ALU c a b op
;; The programmer's view of the ALU
(defun v-alu (c a b op)
(declare (xargs :guard (and (consp a)
(true-listp a)
(consp b)
(true-listp b))))
(cond ((equal op *v0000*) (cvzbv nil nil (v-buf a)))
((equal op *v0001*) (cvzbv-inc a))
((equal op *v0010*) (cvzbv-v-adder c a b))
((equal op *v0011*) (cvzbv-v-adder nil a b))
((equal op *v0100*) (cvzbv-neg a))
((equal op *v0101*) (cvzbv-dec a))
((equal op *v0110*) (cvzbv-v-subtracter c a b))
((equal op *v0111*) (cvzbv-v-subtracter nil a b))
((equal op *v1000*) (cvzbv-v-ror c a))
((equal op *v1001*) (cvzbv-v-asr a))
((equal op *v1010*) (cvzbv-v-lsr a))
((equal op *v1011*) (cvzbv nil nil (v-xor a b)))
((equal op *v1100*) (cvzbv nil nil (v-or a b)))
((equal op *v1101*) (cvzbv nil nil (v-and a b)))
((equal op *v1110*) (cvzbv-v-not a))
(t (cvzbv nil nil (v-buf a)))))
(defthm true-listp-v-alu
(true-listp (v-alu c a b op))
:rule-classes :type-prescription)
(defthm booleanp-c-v-alu
(implies (and (booleanp c)
(bvp a)
(not (equal (len a) 0)))
(booleanp (c (v-alu c a b op))))
:hints (("Goal" :in-theory (enable c bvp)))
:rule-classes :type-prescription)
(defthm booleanp-v-v-alu
(implies (and (booleanp c)
(bvp a)
(not (equal (len a) 0)))
(booleanp (v (v-alu c a b op))))
:hints (("Goal" :in-theory (enable v)))
:rule-classes :type-prescription)
(defthm booleanp-zb-v-alu
(booleanp (zb (v-alu c a b op)))
:hints (("Goal" :in-theory (enable zb)))
:rule-classes :type-prescription)
(defthm bvp-bv-v-alu
(implies (bvp a)
(bvp (bv (v-alu c a b op))))
:hints (("Goal" :in-theory (enable bv)))
:rule-classes (:rewrite :type-prescription))
(defthm bvp-v-alu
(implies (and (bvp a)
(booleanp c)
(not (equal (len a) 0)))
(bvp (v-alu c a b op)))
:hints (("Goal" :in-theory (enable bvp)))
:rule-classes (:rewrite :type-prescription))
(defthm len-cvzbv-adder
(equal (len (cvzbv-v-adder c a b))
(+ 3 (len a))))
(defthm len-cvzbv-subtracter
(equal (len (cvzbv-v-subtracter c a b))
(+ 3 (len a))))
(defthm len-v-alu
(implies (equal (len b) (len a))
(equal (len (v-alu c a b op))
(+ 3 (len a)))))
(defthm len-bv
(implies (<= 3 (len x))
(equal (len (bv x))
(- (len x) 3)))
:hints (("Goal" :in-theory (enable bv))))
(defthm bvp-bv
(implies (bvp x)
(bvp (bv x)))
:hints (("Goal" :in-theory (enable bv bvp)))
:rule-classes (:rewrite :type-prescription))
(in-theory (disable v-alu))
;; UNARY-OP-CODE-P op-code
;; Recognizes ALU op-codes which are unary operations on the A operand. For
;; unary ALU op-codes, the B operand is arbitrary. We also define a
;; "1-argument" version of V-ALU which is equivalent to V-ALU when the ALU
;; op-code is unary.
(defun unary-op-code-p (op-code)
(declare (xargs :guard t))
(or (equal op-code *v0000*) ;Move
(equal op-code *v0001*) ;Inc
(equal op-code *v0100*) ;Neg
(equal op-code *v0101*) ;Dec
(equal op-code *v1000*) ;ROR
(equal op-code *v1001*) ;ASR
(equal op-code *v1010*) ;LSR
(equal op-code *v1110*) ;Not
(equal op-code *v1111*) ;Move-15
))
(defthm booleanp-unary-op-code-p
(booleanp (unary-op-code-p op-code))
:rule-classes :type-prescription)
(in-theory (disable unary-op-code-p))
;; V-ALU-1 op-code
;; The 1-arg ALU
(defun v-alu-1 (c a op-code)
(declare (xargs :guard (and (consp a)
(true-listp a))))
(v-alu c a a op-code))
(defthm bvp-v-alu-1
(implies (and (bvp a)
(booleanp c)
(not (equal (len a) 0)))
(bvp (v-alu-1 c a op)))
:rule-classes (:rewrite :type-prescription))
(defthm len-v-alu-1
(equal (len (v-alu-1 c a op))
(+ 3 (len a))))
(defthmd unary-op-code-p->v-alu=v-alu-1
(implies (unary-op-code-p op-code)
(equal (v-alu c a b op-code)
(v-alu-1 c a op-code)))
:hints (("Goal" :in-theory (enable unary-op-code-p v-alu))))
(in-theory (disable v-alu-1))
;; ALU-INC-OP
;; ALU-DEC-OP
;; These abbreviations are used for those cases where the processor ALU is used
;; for register pre-decrement and post-increment operations.
(defun alu-inc-op ()
(declare (xargs :guard t))
*v0001*)
(defthm bvp-alu-inc-op
(bvp (alu-inc-op))
:rule-classes (:rewrite :type-prescription))
(defthm len-alu-inc-op
(equal (len (alu-inc-op)) 4))
(defthm bv-v-alu-alu-inc-op
(equal (bv (v-alu c a b (alu-inc-op)))
(v-inc a))
:hints (("Goal" :in-theory (enable bv v-alu v-inc))))
(in-theory (disable alu-inc-op))
(defun alu-dec-op ()
(declare (xargs :guard t))
*v0101*)
(defthm bvp-alu-dec-op
(bvp (alu-dec-op))
:rule-classes (:rewrite :type-prescription))
(defthm len-alu-dec-op
(equal (len (alu-dec-op)) 4))
(defthm bv-v-alu-alu-dec-op
(equal (bv (v-alu c a b (alu-dec-op)))
(v-dec a))
:hints (("Goal" :in-theory (enable bv v-alu v-dec))))
(in-theory (disable alu-dec-op))
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