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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
;; A tree based, reducing OR-NOR
(in-package "ADE")
(include-book "../de")
(include-book "../tree-number")
;; ======================================================================
(defun t-or-nor-body (tree parity)
(declare (xargs :guard (listp tree)))
(let ((a-names (sis 'a 0 (tree-size tree))))
(let ((left-a-names (tfirstn a-names tree))
(right-a-names (trestn a-names tree)))
(if (atom tree)
(list (list 'leaf
(list 'out)
(if parity 'b-not 'b-buf)
(list (si 'a 0))))
(if (and (atom (car tree))
(atom (cdr tree)))
(list (list 'leaf
(list 'out)
(if parity 'b-nor 'b-or)
(list (si 'a 0) (si 'a 1))))
(list
;; The LHS tree.
(list 'left
(list 'left-out)
(si (if parity 't-or 't-nor) (tree-number (car tree)))
left-a-names)
;; The RHS tree.
(list 'right
(list 'right-out)
(si (if parity 't-or 't-nor) (tree-number (cdr tree)))
right-a-names)
(list 'output
(list 'out)
(if parity 'b-nor 'b-nand)
(list 'left-out 'right-out))))))))
(module-generator
t-or-nor* (tree parity)
;; Name
(si (if parity 't-nor 't-or) (tree-number tree))
;; Inputs
(sis 'a 0 (tree-size tree))
;; Outputs
(list 'out)
;; States
nil
;; Occurrences
(t-or-nor-body tree parity)
(declare (xargs :guard (listp tree))))
(defund t-or-nor$netlist (tree parity)
(declare (xargs :guard (tv-guard tree)))
(if (or (atom tree)
(and (atom (car tree))
(atom (cdr tree))))
(list (t-or-nor* tree parity))
(cons (t-or-nor* tree parity)
(union$ (t-or-nor$netlist (car tree) (not parity))
(t-or-nor$netlist (cdr tree) (not parity))
:test 'equal))))
(defund t-or-nor& (netlist tree parity)
(declare (xargs :guard (and (alistp netlist)
(tv-guard tree))))
(let ((delete-result (delete-to-eq (si (if parity 't-nor 't-or)
(tree-number tree))
netlist))
(lookup-okp (equal (assoc (si (if parity 't-nor 't-or)
(tree-number tree))
netlist)
(t-or-nor* tree parity))))
(if (or (atom tree)
(and (atom (car tree))
(atom (cdr tree))))
lookup-okp
(and lookup-okp
(t-or-nor& delete-result (car tree) (not parity))
(t-or-nor& delete-result (cdr tree) (not parity))))))
(defun t-or-nor-induction (tree parity call-name a st netlist)
(if (or (atom tree)
(and (atom (car tree))
(atom (cdr tree))))
(list call-name a st netlist)
(and (t-or-nor-induction (car tree)
(not parity)
(if (not parity) 't-nor 't-or)
(tfirstn a tree)
nil
(delete-to-eq (si (if parity 't-nor 't-or)
(tree-number tree))
netlist))
(t-or-nor-induction (cdr tree)
(not parity)
(if (not parity) 't-nor 't-or)
(trestn a tree)
nil
(delete-to-eq (si (if parity 't-nor 't-or)
(tree-number tree))
netlist)))))
(defund tr-or-nor (a parity tree)
(declare (xargs :measure (acl2-count tree)
:guard (and (true-listp a)
(tv-guard tree))))
(if (atom tree)
(if parity (f-not (car a)) (f-buf (car a)))
(if (and (atom (car tree))
(atom (cdr tree)))
(if parity
(f-nor (car a) (cadr a))
(f-or (car a) (cadr a)))
(if parity
(f-nor (tr-or-nor (tfirstn a tree) (not parity) (car tree))
(tr-or-nor (trestn a tree) (not parity) (cdr tree)))
(f-nand (tr-or-nor (tfirstn a tree) (not parity) (car tree))
(tr-or-nor (trestn a tree) (not parity) (cdr tree)))))))
(local
(defthm tr-or-nor-of-v-threefix-canceled-aux
(implies (not (booleanp (car (v-threefix x))))
(not (booleanp (car x))))))
(defthm tr-or-nor-of-v-threefix-canceled
(equal (tr-or-nor (v-threefix a) parity tree)
(tr-or-nor a parity tree))
:hints (("Goal" :in-theory (enable f-or
f-nor
f-not
tr-or-nor))))
(not-primp-lemma t-or)
(not-primp-lemma t-nor)
(defthm t-or-nor$value
(implies (and (t-or-nor& netlist tree parity)
(equal call-name (if parity 't-nor 't-or))
(true-listp a)
(equal (len a) (tree-size tree)))
(equal (se (si call-name (tree-number tree))
a st netlist)
(list (tr-or-nor a parity tree))))
:hints (("Goal"
:induct (t-or-nor-induction tree parity call-name a st netlist)
:in-theory (e/d (de-rules
open-se
t-or-nor&
t-or-nor*$destructure
tr-or-nor
tree-size)
(de-module-disabled-rules)))))
(defund btr-or-nor (a parity tree)
(declare (xargs :measure (acl2-count tree)
:guard (and (true-listp a)
(tv-guard tree))))
(if (atom tree)
(if parity (b-not (car a)) (b-buf (car a)))
(if (and (atom (car tree))
(atom (cdr tree)))
(if parity
(b-nor (car a) (cadr a))
(b-or (car a) (cadr a)))
(if parity
(b-nor (btr-or-nor (tfirstn a tree) (not parity) (car tree))
(btr-or-nor (trestn a tree) (not parity) (cdr tree)))
(b-nand (btr-or-nor (tfirstn a tree) (not parity) (car tree))
(btr-or-nor (trestn a tree) (not parity) (cdr tree)))))))
(defthm tr-or-nor=btr-or-nor
(implies (bvp a)
(equal (tr-or-nor a parity tree)
(btr-or-nor a parity tree)))
:hints (("Goal"
:in-theory (enable bvp tr-or-nor btr-or-nor))))
(defthm btr-or-nor-is-v-zp-nzp
(implies (and (bvp a)
(equal (len a) (tree-size tree)))
(equal (btr-or-nor a parity tree)
(if parity
(v-zp a)
(v-nzp a))))
:hints (("Goal"
:in-theory (enable btr-or-nor
tree-size
bvp
v-zp
v-nzp))))
;; ======================================================================
;; TV-ZP* tree
;; A zero-detector module built from T-OR-NOR*. The choice of implementation
;; is optimized for balanced trees.
(module-generator
tv-zp* (tree)
;; Name
(si 'tv-zp (tree-number tree))
;; Inputs
(sis 'in 0 (tree-size tree))
;; Output
'(out)
;; States
nil
;; Body
(if (equal (mod (tree-height tree) 2) 1)
(list
(list 'g0
'(out-)
(si 't-or (tree-number tree))
(sis 'in 0 (tree-size tree)))
(list 'g1 '(out) 'b-not '(out-)))
(list
(list 'g0
'(out)
(si 't-nor (tree-number tree))
(sis 'in 0 (tree-size tree)))))
(declare (xargs :guard t)))
(defund tv-zp$netlist (tree)
(declare (xargs :guard (tv-guard tree)))
(let ((odd-height (equal (mod (tree-height tree) 2) 1)))
(cons (tv-zp* tree)
(t-or-nor$netlist tree (not odd-height)))))
(defund tv-zp& (netlist tree)
(declare (xargs :guard (and (alistp netlist)
(tv-guard tree))))
(b* ((odd-height (equal (mod (tree-height tree) 2) 1))
(subnetlist (delete-to-eq (si 'tv-zp (tree-number tree)) netlist)))
(and (equal (assoc (si 'tv-zp (tree-number tree)) netlist)
(tv-zp* tree))
(t-or-nor& subnetlist tree (not odd-height)))))
(defund f$tv-zp (a tree)
(declare (xargs :guard (and (true-listp a)
(tv-guard tree))))
(let ((odd-height (equal (mod (tree-height tree) 2) 1)))
(if odd-height
(f-not (tr-or-nor a nil tree))
(tr-or-nor a t tree))))
(defthm tv-zp$value
(implies (and (tv-zp& netlist tree)
(equal (len a) (tree-size tree))
(true-listp a))
(equal (se (si 'tv-zp (tree-number tree)) a st netlist)
(list (f$tv-zp a tree))))
:hints (("Goal"
:expand (:free (n)
(se (si 'tv-zp n)
a
st
netlist))
:in-theory (e/d (de-rules
tv-zp&
tv-zp*$destructure
f$tv-zp)
(de-module-disabled-rules)))))
(defthm f$tv-zp=v-zp
(implies (and (bvp a)
(equal (len a) (tree-size tree)))
(equal (f$tv-zp a tree)
(v-zp a)))
:hints (("Goal" :in-theory (enable f$tv-zp v-zp))))
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