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• Observability-fix

Observability-fixed-regs

Signature

(observability-fixed-regs n regvals regmasks hyp-lit 
                          aignet copy gatesimp strash aignet2) 
 
  → 
(mv new-copy new-strash new-aignet2)

Arguments

n — Guard (natp n).

hyp-lit — Guard (litp hyp-lit).

gatesimp — Guard (gatesimp-p gatesimp).

Definitions and Theorems

Function: observability-fixed-regs

(defun observability-fixed-regs
       (n regvals regmasks hyp-lit
          aignet copy gatesimp strash aignet2)
 (declare
      (xargs :stobjs (regvals regmasks aignet copy strash aignet2)))
 (declare (xargs :guard (and (natp n)
                             (litp hyp-lit)
                             (gatesimp-p gatesimp))))
 (declare (xargs :guard (and (<= (nfix n) (num-regs aignet))
                             (fanin-litp hyp-lit aignet2)
                             (<= (num-regs aignet)
                                 (num-regs aignet2))
                             (<= (num-regs aignet)
                                 (bits-length regvals))
                             (<= (num-regs aignet)
                                 (bits-length regmasks))
                             (aignet-copies-in-bounds copy aignet2)
                             (<= (num-fanins aignet)
                                 (lits-length copy)))))
 (let ((__function__ 'observability-fixed-regs))
  (declare (ignorable __function__))
  (b* (((when (mbe :logic (zp (- (num-regs aignet) (nfix n)))
                   :exec (eql (num-regs aignet) n)))
        (b* ((aignet2 (aignet-fix aignet2)))
          (mv copy strash aignet2)))
       (reg-lit (get-lit (regnum->id n aignet) copy))
       ((mv fixed-lit strash aignet2)
        (if (eql 1 (get-bit n regmasks))
            (aignet-hash-mux hyp-lit reg-lit (get-bit n regvals)
                             gatesimp strash aignet2)
          (mv reg-lit strash aignet2)))
       (orig-id (regnum->id n aignet))
       (copy (set-lit orig-id fixed-lit copy)))
   (observability-fixed-regs (1+ (lnfix n))
                             regvals regmasks hyp-lit
                             aignet copy gatesimp strash aignet2))))

Theorem: copies-in-bounds-of-observability-fixed-regs

(defthm copies-in-bounds-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies (and (aignet-copies-in-bounds copy aignet2)
                (aignet-litp hyp-lit aignet2)
                (<= (num-regs aignet)
                    (num-regs aignet2)))
           (aignet-copies-in-bounds new-copy new-aignet2))))

Theorem: copy-length-of-observability-fixed-regs

(defthm copy-length-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies (<= (num-fanins aignet) (len copy))
           (equal (len new-copy) (len copy)))))

Theorem: aignet-extension-p-of-observability-fixed-regs

(defthm aignet-extension-p-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (aignet-extension-p new-aignet2 aignet2)))

Theorem: stypes-preserved-of-observability-fixed-regs

(defthm stypes-preserved-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (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: non-reg-copy-of-observability-fixed-inputs

(defthm non-reg-copy-of-observability-fixed-inputs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies (not (equal (stype (car (lookup-id id aignet)))
                       :reg))
           (equal (nth-lit id new-copy)
                  (nth-lit id copy)))))

Theorem: reg-copy-of-observability-fixed-regs

(defthm reg-copy-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies
   (and (<= (nfix n) (nfix regnum))
        (< (nfix regnum) (num-regs aignet))
        (aignet-litp hyp-lit aignet2)
        (aignet-copies-in-bounds copy aignet2)
        (<= (num-regs aignet)
            (num-regs aignet2))
        (equal 1
               (lit-eval hyp-lit
                         some-invals some-regvals aignet2)))
   (equal
       (lit-eval
            (nth-lit (fanin-count (lookup-stype regnum :reg aignet))
                     new-copy)
            some-invals some-regvals new-aignet2)
       (lit-eval
            (nth-lit (fanin-count (lookup-stype regnum :reg aignet))
                     copy)
            some-invals some-regvals aignet2)))))

Theorem: reg-copy-values-of-observability-fixed-regs

(defthm reg-copy-values-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies
       (and (aignet-litp hyp-lit aignet2)
            (aignet-copies-in-bounds copy aignet2)
            (<= (num-regs aignet)
                (num-regs aignet2))
            (equal 1
                   (lit-eval hyp-lit
                             some-invals some-regvals aignet2)))
       (equal (reg-copy-values n some-invals some-regvals
                               aignet new-copy new-aignet2)
              (reg-copy-values n some-invals
                               some-regvals aignet copy aignet2)))))

Theorem: input-copy-values-of-observability-fixed-regs

(defthm input-copy-values-of-observability-fixed-regs
 (b*
  (((mv ?new-copy ?new-strash ?new-aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
  (implies
     (and (aignet-copies-in-bounds copy aignet2)
          (aignet-litp hyp-lit aignet2)
          (<= (num-regs aignet)
              (num-regs aignet2)))
     (equal (input-copy-values 0 some-invals some-regvals
                               aignet new-copy new-aignet2)
            (input-copy-values 0 some-invals
                               some-regvals aignet copy aignet2)))))

Theorem: observability-fixed-regs-of-nfix-n

(defthm observability-fixed-regs-of-nfix-n
 (equal
    (observability-fixed-regs (nfix n)
                              regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-regs-nat-equiv-congruence-on-n

(defthm observability-fixed-regs-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)
    (observability-fixed-regs n-equiv regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-regs-of-lit-fix-hyp-lit

(defthm observability-fixed-regs-of-lit-fix-hyp-lit
 (equal
    (observability-fixed-regs n regvals regmasks (lit-fix hyp-lit)
                              aignet copy gatesimp strash aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-regs-lit-equiv-congruence-on-hyp-lit

(defthm observability-fixed-regs-lit-equiv-congruence-on-hyp-lit
 (implies
  (lit-equiv hyp-lit hyp-lit-equiv)
  (equal
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit-equiv
                              aignet copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-regs-of-node-list-fix-aignet

(defthm observability-fixed-regs-of-node-list-fix-aignet
 (equal
   (observability-fixed-regs n regvals
                             regmasks hyp-lit (node-list-fix aignet)
                             copy gatesimp strash aignet2)
   (observability-fixed-regs n regvals regmasks hyp-lit
                             aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-regs-node-list-equiv-congruence-on-aignet

(defthm
      observability-fixed-regs-node-list-equiv-congruence-on-aignet
 (implies
  (node-list-equiv aignet aignet-equiv)
  (equal
   (observability-fixed-regs n regvals regmasks hyp-lit
                             aignet copy gatesimp strash aignet2)
   (observability-fixed-regs n regvals regmasks hyp-lit aignet-equiv
                             copy gatesimp strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-regs-of-gatesimp-fix-gatesimp

(defthm observability-fixed-regs-of-gatesimp-fix-gatesimp
 (equal
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy (gatesimp-fix gatesimp)
                              strash aignet2)
    (observability-fixed-regs n regvals regmasks hyp-lit
                              aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-regs-gatesimp-equiv-congruence-on-gatesimp

(defthm
     observability-fixed-regs-gatesimp-equiv-congruence-on-gatesimp
 (implies
  (gatesimp-equiv gatesimp gatesimp-equiv)
  (equal
     (observability-fixed-regs n regvals regmasks hyp-lit
                               aignet copy gatesimp strash aignet2)
     (observability-fixed-regs n regvals regmasks hyp-lit aignet
                               copy gatesimp-equiv strash aignet2)))
 :rule-classes :congruence)

Theorem: observability-fixed-regs-of-node-list-fix-aignet2

(defthm observability-fixed-regs-of-node-list-fix-aignet2
 (equal
  (observability-fixed-regs n regvals regmasks hyp-lit aignet copy
                            gatesimp strash (node-list-fix aignet2))
  (observability-fixed-regs n regvals regmasks hyp-lit
                            aignet copy gatesimp strash aignet2)))

Theorem: observability-fixed-regs-node-list-equiv-congruence-on-aignet2

(defthm
     observability-fixed-regs-node-list-equiv-congruence-on-aignet2
 (implies
  (node-list-equiv aignet2 aignet2-equiv)
  (equal
     (observability-fixed-regs n regvals regmasks hyp-lit
                               aignet copy gatesimp strash aignet2)
     (observability-fixed-regs n regvals regmasks hyp-lit aignet
                               copy gatesimp strash aignet2-equiv)))
 :rule-classes :congruence)