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• Aignet-construction

Aignet-hash-iff

Implement an IFF of two literals node in an AIGNET, or find a node already representing the required logical expression.

Signature

(aignet-hash-iff lit1 lit2 gatesimp strash aignet) 
  → 
(mv result new-strash new-aignet)

Arguments

lit1 — Literal to AND 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

result — Type (litp result).

See aignet-construction.

Definitions and Theorems

Function: aignet-hash-iff

(defun aignet-hash-iff (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-iff))
    (declare (ignorable __function__))
    (b* (((mv lit strash aignet)
          (aignet-hash-xor lit1 lit2 gatesimp strash aignet)))
      (mv (lit-negate lit) strash aignet))))

Theorem: litp-of-aignet-hash-iff.result

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

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

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

Theorem: aignet-litp-of-aignet-hash-iff

(defthm aignet-litp-of-aignet-hash-iff
  (b* (((mv ?result ?new-strash ?new-aignet)
        (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))
    (implies (and (aignet-litp lit1 aignet)
                  (aignet-litp lit2 aignet))
             (aignet-litp result new-aignet))))

Theorem: deps-of-aignet-hash-iff

(defthm deps-of-aignet-hash-iff
  (b* (((mv ?result ?new-strash ?new-aignet)
        (aignet-hash-iff 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 result)
                              ci-id new-aignet)))))

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

(defthm lit-eval-of-aignet-hash-iff
  (b* (((mv ?result ?new-strash ?new-aignet)
        (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))
    (equal (lit-eval result invals regvals new-aignet)
           (b-not (b-xor (lit-eval lit1 invals regvals aignet)
                         (lit-eval lit2 invals regvals aignet))))))

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

(defthm stype-counts-preserved-of-aignet-hash-iff
  (b* (((mv ?result ?new-strash ?new-aignet)
        (aignet-hash-iff 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-iff

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

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

(defthm aignet-hash-iff-of-lit-fix-lit1
  (equal (aignet-hash-iff (lit-fix lit1)
                          lit2 gatesimp strash aignet)
         (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))

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

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

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

(defthm aignet-hash-iff-of-lit-fix-lit2
  (equal (aignet-hash-iff lit1 (lit-fix lit2)
                          gatesimp strash aignet)
         (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))

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

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

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

(defthm aignet-hash-iff-of-gatesimp-fix-gatesimp
  (equal (aignet-hash-iff lit1 lit2 (gatesimp-fix gatesimp)
                          strash aignet)
         (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))

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

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

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

(defthm aignet-hash-iff-of-node-list-fix-aignet
  (equal (aignet-hash-iff lit1 lit2
                          gatesimp strash (node-list-fix aignet))
         (aignet-hash-iff lit1 lit2 gatesimp strash aignet)))

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

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