• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
      • Base-api
      • Aignet-construction
        • Gatesimp
        • Aignet-hash-mux
        • Aignet-hash-xor
        • Aignet-hash-and
        • Aignet-hash-or
        • Aignet-hash-iff
        • Aignet-build
        • Patbind-aignet-build
      • Representation
      • Aignet-copy-init
      • Aignet-simplify-with-tracking
      • Aignet-simplify-marked-with-tracking
      • Aignet-cnf
      • Aignet-simplify-marked
      • Aignet-complete-copy
      • Aignet-transforms
      • Aignet-eval
      • Semantics
      • Aignet-read-aiger
      • Aignet-write-aiger
      • Aignet-abc-interface
      • Utilities
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Aignet-construction

Aignet-hash-and

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

Signature

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

and-lit — Type (litp and-lit).

See aignet-construction.

Definitions and Theorems

Function: aignet-hash-and

(defun aignet-hash-and (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-and))
    (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))
         ((mv code key lit1 lit2)
          (aignet-and-gate-simp/strash
               lit1 lit2 gatesimp strash aignet)))
      (aignet-install-gate code
                           key lit1 lit2 gatesimp strash aignet))))

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

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

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

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

Theorem: aignet-litp-of-aignet-hash-and

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

Theorem: deps-of-aignet-hash-and

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

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

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

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

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

(defthm unsigned-byte-p-of-aignet-hash-and
  (b* (((mv ?and-lit ?new-strash ?new-aignet)
        (aignet-hash-and lit1 lit2 gatesimp strash aignet)))
    (implies (and (< (fanin-count aignet) 536870911)
                  (natp n)
                  (<= 30 n))
             (unsigned-byte-p n and-lit))))

Theorem: fanin-count-of-aignet-hash-and

(defthm fanin-count-of-aignet-hash-and
  (b* (((mv ?and-lit ?new-strash ?new-aignet)
        (aignet-hash-and lit1 lit2 gatesimp strash aignet)))
    (<= (fanin-count new-aignet)
        (+ 1 (fanin-count aignet))))
  :rule-classes :linear)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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