• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
      • Base-api
      • Aignet-construction
      • Representation
      • Aignet-copy-init
      • Aignet-simplify-with-tracking
      • Aignet-simplify-marked-with-tracking
      • Aignet-cnf
      • Aignet-simplify-marked
      • Aignet-complete-copy
      • Aignet-transforms
        • Aignet-output-ranges
        • Aignet-comb-transforms
          • Fraig
          • Parametrize
          • Observability-fix
            • Observability-fix-hyps/concls
            • Observability-fix-input-copies
            • Observability-fixed-inputs
            • Observability-fixed-regs
            • Observability-fix-hyp/concl
            • Observability-fix-lit
            • M-assum-n-output-observability
            • Observability-fix-outs
            • Observability-fix-nxsts
            • Observability-split-supergate-aux
            • Observability-fix-core
            • Observability-split-supergate
            • Aignet-build-wide-and
            • Observability-config
            • Observability-fix!
            • Observability-size-check
            • M-assum-n-output-observability-config
          • Constprop
          • Apply-m-assumption-n-output-output-transform-default
          • Balance
          • Apply-n-output-comb-transform-default
          • Apply-comb-transform-default
          • Obs-constprop
          • Rewrite
          • Comb-transform
          • Abc-comb-simplify
          • Prune
          • Rewrite!
          • M-assumption-n-output-comb-transform->name
          • N-output-comb-transform->name
          • Comb-transform->name
          • N-output-comb-transformlist
          • M-assumption-n-output-comb-transformlist
          • Comb-transformlist
          • Apply-comb-transform
        • Aignet-m-assumption-n-output-transforms
        • Aignet-n-output-comb-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

• Observability-fix

Observability-fix-hyps/concls

Signature

(observability-fix-hyps/concls hyps concls aignet 
                               copy gatesimp strash aignet2 state) 
 
  → 
(mv hyp-copy new-hyps new-concls new-copy 
    new-strash new-aignet2 new-state) 

Arguments

hyps — Guard (lit-listp hyps).

concls — Guard (lit-listp concls).

gatesimp — Guard (gatesimp-p gatesimp).

Returns

hyp-copy — Type (litp hyp-copy).

new-hyps — Type (lit-listp new-hyps).

new-concls — Type (lit-listp new-concls).

Definitions and Theorems

Function: observability-fix-hyps/concls

(defun observability-fix-hyps/concls
       (hyps concls aignet
             copy gatesimp strash aignet2 state)
 (declare (xargs :stobjs (aignet copy strash aignet2 state)))
 (declare (xargs :guard (and (lit-listp hyps)
                             (lit-listp concls)
                             (gatesimp-p gatesimp))))
 (declare (xargs :guard (and (<= (num-fanins aignet)
                                 (lits-length copy))
                             (aignet-copies-in-bounds copy aignet2)
                             (aignet-lit-listp hyps aignet)
                             (aignet-lit-listp concls aignet)
                             (<= (num-ins aignet) (num-ins aignet2))
                             (<= (num-regs aignet)
                                 (num-regs aignet2)))))
 (let ((__function__ 'observability-fix-hyps/concls))
  (declare (ignorable __function__))
  (b*
   (((mv copy strash aignet2)
     (b*
       (((local-stobjs mark)
         (mv mark copy strash aignet2))
        (mark (resize-bits (num-fanins aignet) mark))
        ((mv mark copy strash aignet2)
         (aignet-copy-dfs-list hyps aignet
                               mark copy strash gatesimp aignet2)))
       (mv mark copy strash aignet2)))
    (hyp-copies (lit-list-copies hyps copy))
    ((mv hyp-copy strash aignet2)
     (aignet-hash-and-supergate hyp-copies gatesimp strash aignet2))
    ((mv ?status copy strash aignet2 state)
     (observability-fix-input-copies
          hyp-copy
          aignet copy strash aignet2 state))
    ((when (eq status :unsat))
     (mv 0 hyp-copies
         (make-list (len concls)
                    :initial-element 0)
         copy strash aignet2 state))
    ((mv copy strash aignet2)
     (b* (((local-stobjs mark)
           (mv mark copy strash aignet2))
          (mark (resize-bits (num-fanins aignet) mark)))
       (aignet-copy-dfs-list concls aignet
                             mark copy strash gatesimp aignet2)))
    (concl-copies (lit-list-copies concls copy)))
   (mv hyp-copy hyp-copies concl-copies
       copy strash aignet2 state))))

Theorem: litp-of-observability-fix-hyps/concls.hyp-copy

(defthm litp-of-observability-fix-hyps/concls.hyp-copy
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (litp hyp-copy))
  :rule-classes :rewrite)

Theorem: lit-listp-of-observability-fix-hyps/concls.new-hyps

(defthm lit-listp-of-observability-fix-hyps/concls.new-hyps
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (lit-listp new-hyps))
  :rule-classes :rewrite)

Theorem: lit-listp-of-observability-fix-hyps/concls.new-concls

(defthm lit-listp-of-observability-fix-hyps/concls.new-concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (lit-listp new-concls))
  :rule-classes :rewrite)

Theorem: aignet-extension-of-observability-fix-hyps/concls

(defthm aignet-extension-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (aignet-extension-p new-aignet2 aignet2)))

Theorem: stype-counts-of-observability-fix-hyps/concls

(defthm stype-counts-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (not (equal (stype-fix stype) (and-stype)))
                  (not (equal (stype-fix stype) (xor-stype))))
             (equal (stype-count stype new-aignet2)
                    (stype-count stype aignet2)))))

Theorem: copy-length-of-observability-fix-hyps/concls

(defthm copy-length-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (<= (num-fanins aignet) (len copy))
                  (aignet-lit-listp hyps aignet)
                  (aignet-lit-listp concls aignet))
             (equal (len new-copy) (len copy)))))

Theorem: copies-in-bounds-of-observability-fix-hyps/concls

(defthm copies-in-bounds-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (implies (and (aignet-copies-in-bounds copy aignet2)
                  (aignet-lit-listp hyps aignet)
                  (aignet-lit-listp concls aignet)
                  (<= (num-ins aignet) (num-ins aignet2))
                  (<= (num-regs aignet)
                      (num-regs aignet2)))
             (and (aignet-copies-in-bounds new-copy new-aignet2)
                  (aignet-litp hyp-copy new-aignet2)
                  (aignet-lit-listp new-hyps new-aignet2)
                  (aignet-lit-listp new-concls new-aignet2)))))

Theorem: dfs-copy-onto-invar-of-empty-mark

(defthm dfs-copy-onto-invar-of-empty-mark
  (dfs-copy-onto-invar aignet (resize-list nil n 0)
                       copy aignet2))

Theorem: new-concls-len-of-observability-fix-hyps/concls

(defthm new-concls-len-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (equal (len new-concls) (len concls))))

Theorem: new-hyps-len-of-observability-fix-hyps/concls

(defthm new-hyps-len-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (equal (len new-hyps) (len hyps))))

Theorem: new-concls-consp-of-observability-fix-hyps/concls

(defthm new-concls-consp-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (equal (consp new-concls)
           (consp concls))))

Theorem: new-hyps-consp-of-observability-fix-hyps/concls

(defthm new-hyps-consp-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (equal (consp new-hyps) (consp hyps))))

Theorem: hyp-eval-of-observability-fix-hyps/concls

(defthm hyp-eval-of-observability-fix-hyps/concls
 (b* (((mv ?hyp-copy
           ?new-hyps ?new-concls ?new-copy
           ?new-strash ?new-aignet2 ?new-state)
       (observability-fix-hyps/concls
            hyps concls aignet
            copy gatesimp strash aignet2 state)))
  (implies
   (and (aignet-copies-in-bounds copy aignet2)
        (aignet-lit-listp hyps aignet)
        (<= (num-ins aignet) (num-ins aignet2))
        (<= (num-regs aignet)
            (num-regs aignet2)))
   (and
    (equal
       (lit-eval hyp-copy invals regvals new-aignet2)
       (aignet-eval-conjunction
            hyps
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet))
    (equal
       (lit-eval-list new-hyps invals regvals new-aignet2)
       (lit-eval-list
            hyps
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet))))))

Theorem: eval-of-observability-fix-hyps/concls

(defthm eval-of-observability-fix-hyps/concls
 (b* (((mv ?hyp-copy
           ?new-hyps ?new-concls ?new-copy
           ?new-strash ?new-aignet2 ?new-state)
       (observability-fix-hyps/concls
            hyps concls aignet
            copy gatesimp strash aignet2 state)))
  (implies
   (and
    (aignet-copies-in-bounds copy aignet2)
    (aignet-lit-listp concls aignet)
    (aignet-lit-listp hyps aignet)
    (<= (num-ins aignet) (num-ins aignet2))
    (<= (num-regs aignet)
        (num-regs aignet2))
    (equal
       (aignet-eval-conjunction
            hyps
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)
       1))
   (equal
       (lit-eval-list new-concls invals regvals new-aignet2)
       (lit-eval-list
            concls
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)))))

Theorem: nth-hyp-eval-of-observability-fix-hyps/concls

(defthm nth-hyp-eval-of-observability-fix-hyps/concls
 (b* (((mv ?hyp-copy
           ?new-hyps ?new-concls ?new-copy
           ?new-strash ?new-aignet2 ?new-state)
       (observability-fix-hyps/concls
            hyps concls aignet
            copy gatesimp strash aignet2 state)))
  (implies
   (and (aignet-copies-in-bounds copy aignet2)
        (aignet-lit-listp hyps aignet)
        (<= (num-ins aignet) (num-ins aignet2))
        (<= (num-regs aignet)
            (num-regs aignet2)))
   (equal
       (lit-eval (nth n new-hyps)
                 invals regvals new-aignet2)
       (lit-eval
            (nth n hyps)
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)))))

Theorem: nth-concl-eval-of-observability-fix-hyps/concls

(defthm nth-concl-eval-of-observability-fix-hyps/concls
 (b* (((mv ?hyp-copy
           ?new-hyps ?new-concls ?new-copy
           ?new-strash ?new-aignet2 ?new-state)
       (observability-fix-hyps/concls
            hyps concls aignet
            copy gatesimp strash aignet2 state)))
  (implies
   (and
    (aignet-copies-in-bounds copy aignet2)
    (aignet-lit-listp concls aignet)
    (aignet-lit-listp hyps aignet)
    (<= (num-ins aignet) (num-ins aignet2))
    (<= (num-regs aignet)
        (num-regs aignet2))
    (equal
       (aignet-eval-conjunction
            hyps
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)
       1))
   (equal
       (lit-eval (nth n new-concls)
                 invals regvals new-aignet2)
       (lit-eval
            (nth n concls)
            (input-copy-values 0 invals regvals aignet copy aignet2)
            (reg-copy-values 0 invals regvals aignet copy aignet2)
            aignet)))))

Theorem: w-state-of-observability-fix-hyps/concls

(defthm w-state-of-observability-fix-hyps/concls
  (b* (((mv ?hyp-copy
            ?new-hyps ?new-concls ?new-copy
            ?new-strash ?new-aignet2 ?new-state)
        (observability-fix-hyps/concls
             hyps concls aignet
             copy gatesimp strash aignet2 state)))
    (equal (w new-state) (w state))))

Theorem: observability-fix-hyps/concls-of-lit-list-fix-hyps

(defthm observability-fix-hyps/concls-of-lit-list-fix-hyps
 (equal
  (observability-fix-hyps/concls (lit-list-fix hyps)
                                 concls aignet
                                 copy gatesimp strash aignet2 state)
  (observability-fix-hyps/concls
       hyps concls aignet
       copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyps/concls-lit-list-equiv-congruence-on-hyps

(defthm
    observability-fix-hyps/concls-lit-list-equiv-congruence-on-hyps
  (implies (satlink::lit-list-equiv hyps hyps-equiv)
           (equal (observability-fix-hyps/concls
                       hyps concls aignet
                       copy gatesimp strash aignet2 state)
                  (observability-fix-hyps/concls
                       hyps-equiv concls aignet
                       copy gatesimp strash aignet2 state)))
  :rule-classes :congruence)

Theorem: observability-fix-hyps/concls-of-lit-list-fix-concls

(defthm observability-fix-hyps/concls-of-lit-list-fix-concls
 (equal
  (observability-fix-hyps/concls hyps (lit-list-fix concls)
                                 aignet
                                 copy gatesimp strash aignet2 state)
  (observability-fix-hyps/concls
       hyps concls aignet
       copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyps/concls-lit-list-equiv-congruence-on-concls

(defthm
  observability-fix-hyps/concls-lit-list-equiv-congruence-on-concls
  (implies (satlink::lit-list-equiv concls concls-equiv)
           (equal (observability-fix-hyps/concls
                       hyps concls aignet
                       copy gatesimp strash aignet2 state)
                  (observability-fix-hyps/concls
                       hyps concls-equiv aignet
                       copy gatesimp strash aignet2 state)))
  :rule-classes :congruence)

Theorem: observability-fix-hyps/concls-of-node-list-fix-aignet

(defthm observability-fix-hyps/concls-of-node-list-fix-aignet
 (equal
  (observability-fix-hyps/concls hyps concls (node-list-fix aignet)
                                 copy gatesimp strash aignet2 state)
  (observability-fix-hyps/concls
       hyps concls aignet
       copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyps/concls-node-list-equiv-congruence-on-aignet

(defthm
 observability-fix-hyps/concls-node-list-equiv-congruence-on-aignet
 (implies (node-list-equiv aignet aignet-equiv)
          (equal (observability-fix-hyps/concls
                      hyps concls aignet
                      copy gatesimp strash aignet2 state)
                 (observability-fix-hyps/concls
                      hyps concls aignet-equiv
                      copy gatesimp strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyps/concls-of-gatesimp-fix-gatesimp

(defthm observability-fix-hyps/concls-of-gatesimp-fix-gatesimp
 (equal
  (observability-fix-hyps/concls hyps concls
                                 aignet copy (gatesimp-fix gatesimp)
                                 strash aignet2 state)
  (observability-fix-hyps/concls
       hyps concls aignet
       copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyps/concls-gatesimp-equiv-congruence-on-gatesimp

(defthm
 observability-fix-hyps/concls-gatesimp-equiv-congruence-on-gatesimp
 (implies (gatesimp-equiv gatesimp gatesimp-equiv)
          (equal (observability-fix-hyps/concls
                      hyps concls aignet
                      copy gatesimp strash aignet2 state)
                 (observability-fix-hyps/concls
                      hyps concls aignet copy
                      gatesimp-equiv strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-hyps/concls-of-node-list-fix-aignet2

(defthm observability-fix-hyps/concls-of-node-list-fix-aignet2
  (equal (observability-fix-hyps/concls
              hyps concls aignet copy
              gatesimp strash (node-list-fix aignet2)
              state)
         (observability-fix-hyps/concls
              hyps concls aignet
              copy gatesimp strash aignet2 state)))

Theorem: observability-fix-hyps/concls-node-list-equiv-congruence-on-aignet2

(defthm
 observability-fix-hyps/concls-node-list-equiv-congruence-on-aignet2
 (implies (node-list-equiv aignet2 aignet2-equiv)
          (equal (observability-fix-hyps/concls
                      hyps concls aignet
                      copy gatesimp strash aignet2 state)
                 (observability-fix-hyps/concls
                      hyps concls aignet copy
                      gatesimp strash aignet2-equiv state)))
 :rule-classes :congruence)