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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)