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• Aignet-construction

Aignet-hash-xor

Add an XOR node to an AIGNET, or find a node already representing the required logical expression.

Signature

(aignet-hash-xor lit1 lit2 gatesimp strash aignet) 
  → 
(mv xor-lit new-strash new-aignet)

Arguments

lit1 — Literal to XOR with lit2.
    Guard (litp lit1).

lit2 — Guard (litp lit2).

gatesimp — Configuration for how much simplification to try and whether to use hashing.
    Guard (gatesimp-p gatesimp).

strash — Stobj containing the aignet's structural hash table.

Returns

xor-lit — Type (litp xor-lit).

See aignet-construction.

Definitions and Theorems

Function: aignet-hash-xor

(defun
 aignet-hash-xor
 (lit1 lit2 gatesimp strash aignet)
 (declare (xargs :stobjs (strash aignet)))
 (declare (type (unsigned-byte 30) lit1)
          (type (unsigned-byte 30) lit2)
          (type (unsigned-byte 6) gatesimp))
 (declare (xargs :guard (and (litp lit1)
                             (litp lit2)
                             (gatesimp-p gatesimp))))
 (declare (xargs :guard (and (fanin-litp lit1 aignet)
                             (fanin-litp lit2 aignet))
                 :split-types t))
 (let
   ((__function__ 'aignet-hash-xor))
   (declare (ignorable __function__))
   (b* ((lit1 (mbe :logic (non-exec (aignet-lit-fix lit1 aignet))
                   :exec lit1))
        (lit2 (mbe :logic (non-exec (aignet-lit-fix lit2 aignet))
                   :exec lit2))
        ((when (eql 0 (gatesimp->xor-mode gatesimp)))
         (aignet-build (and (not (and lit1 lit2))
                            (not (and (not lit1) (not lit2))))
                       gatesimp strash aignet))
        ((mv code key lit1 lit2)
         (aignet-xor-gate-simp/strash
              lit1 lit2 gatesimp strash aignet)))
       (aignet-install-gate code
                            key lit1 lit2 gatesimp strash aignet))))

Theorem: litp-of-aignet-hash-xor.xor-lit

(defthm acl2::litp-of-aignet-hash-xor.xor-lit
        (b* (((mv ?xor-lit ?new-strash ?new-aignet)
              (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
            (litp xor-lit))
        :rule-classes (:rewrite :type-prescription))

Theorem: aignet-extension-p-of-aignet-hash-xor

(defthm
    acl2::aignet-extension-p-of-aignet-hash-xor
    (aignet-extension-p
         (mv-nth 2
                 (aignet-hash-xor lit1 lit2 gatesimp strash aignet))
         aignet)
    :rule-classes :rewrite)

Theorem: aignet-litp-of-aignet-hash-xor

(defthm aignet-litp-of-aignet-hash-xor
        (b* (((mv ?xor-lit ?new-strash ?new-aignet)
              (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
            (aignet-litp xor-lit new-aignet)))

Theorem: deps-of-aignet-hash-xor

(defthm deps-of-aignet-hash-xor
        (b* (((mv ?xor-lit ?new-strash ?new-aignet)
              (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
            (implies (and (not (depends-on (lit->var lit1)
                                           ci-id aignet))
                          (not (depends-on (lit->var lit2)
                                           ci-id aignet)))
                     (not (depends-on (lit->var xor-lit)
                                      ci-id new-aignet)))))

Theorem: lit-eval-of-aignet-hash-xor

(defthm lit-eval-of-aignet-hash-xor
        (b* (((mv ?xor-lit ?new-strash ?new-aignet)
              (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
            (equal (lit-eval xor-lit invals regvals new-aignet)
                   (b-xor (lit-eval lit1 invals regvals aignet)
                          (lit-eval lit2 invals regvals aignet)))))

Theorem: stype-counts-preserved-of-aignet-hash-xor

(defthm
     stype-counts-preserved-of-aignet-hash-xor
     (b* (((mv ?xor-lit ?new-strash ?new-aignet)
           (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
         (implies (and (not (equal (stype-fix stype) (and-stype)))
                       (not (equal (stype-fix stype) (xor-stype))))
                  (equal (stype-count stype new-aignet)
                         (stype-count stype aignet)))))

Theorem: unsigned-byte-p-of-aignet-hash-xor

(defthm unsigned-byte-p-of-aignet-hash-xor
        (b* (((mv ?xor-lit ?new-strash ?new-aignet)
              (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
            (implies (and (< (fanin-count aignet) 536870909)
                          (natp n)
                          (<= 30 n))
                     (unsigned-byte-p n xor-lit))))

Theorem: aignet-hash-xor-of-lit-fix-lit1

(defthm acl2::aignet-hash-xor-of-lit-fix-lit1
        (equal (aignet-hash-xor (lit-fix lit1)
                                lit2 gatesimp strash aignet)
               (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))

Theorem: aignet-hash-xor-lit-equiv-congruence-on-lit1

(defthm
  acl2::aignet-hash-xor-lit-equiv-congruence-on-lit1
  (implies (lit-equiv lit1 acl2::lit1-equiv)
           (equal (aignet-hash-xor lit1 lit2 gatesimp strash aignet)
                  (aignet-hash-xor acl2::lit1-equiv
                                   lit2 gatesimp strash aignet)))
  :rule-classes :congruence)

Theorem: aignet-hash-xor-of-lit-fix-lit2

(defthm acl2::aignet-hash-xor-of-lit-fix-lit2
        (equal (aignet-hash-xor lit1 (lit-fix lit2)
                                gatesimp strash aignet)
               (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))

Theorem: aignet-hash-xor-lit-equiv-congruence-on-lit2

(defthm
  acl2::aignet-hash-xor-lit-equiv-congruence-on-lit2
  (implies (lit-equiv lit2 acl2::lit2-equiv)
           (equal (aignet-hash-xor lit1 lit2 gatesimp strash aignet)
                  (aignet-hash-xor lit1 acl2::lit2-equiv
                                   gatesimp strash aignet)))
  :rule-classes :congruence)

Theorem: aignet-hash-xor-of-gatesimp-fix-gatesimp

(defthm acl2::aignet-hash-xor-of-gatesimp-fix-gatesimp
        (equal (aignet-hash-xor lit1 lit2 (gatesimp-fix gatesimp)
                                strash aignet)
               (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))

Theorem: aignet-hash-xor-gatesimp-equiv-congruence-on-gatesimp

(defthm
  acl2::aignet-hash-xor-gatesimp-equiv-congruence-on-gatesimp
  (implies
       (gatesimp-equiv gatesimp acl2::gatesimp-equiv)
       (equal (aignet-hash-xor lit1 lit2 gatesimp strash aignet)
              (aignet-hash-xor lit1 lit2
                               acl2::gatesimp-equiv strash aignet)))
  :rule-classes :congruence)

Theorem: aignet-hash-xor-of-node-list-fix-aignet

(defthm
     acl2::aignet-hash-xor-of-node-list-fix-aignet
     (equal (aignet-hash-xor lit1 lit2
                             gatesimp strash (node-list-fix aignet))
            (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))

Theorem: aignet-hash-xor-node-list-equiv-congruence-on-aignet

(defthm
  acl2::aignet-hash-xor-node-list-equiv-congruence-on-aignet
  (implies
       (node-list-equiv aignet acl2::aignet-equiv)
       (equal (aignet-hash-xor lit1 lit2 gatesimp strash aignet)
              (aignet-hash-xor lit1 lit2
                               gatesimp strash acl2::aignet-equiv)))
  :rule-classes :congruence)