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• Observability-fix

Observability-fix-outs

Signature

(observability-fix-outs n config aignet copy strash aignet2 state) 
  → 
(mv new-copy new-strash new-aignet2 new-aignet new-state)

Arguments

n — Guard (natp n).

config — Guard (observability-config-p config).

Definitions and Theorems

Function: observability-fix-outs

(defun observability-fix-outs
       (n config aignet copy strash aignet2 state)
 (declare (xargs :stobjs (aignet copy strash aignet2 state)))
 (declare (xargs :guard (and (natp n)
                             (observability-config-p config))))
 (declare (xargs :guard (and (<= (num-ins aignet) (num-ins aignet2))
                             (<= (num-regs aignet)
                                 (num-regs aignet2))
                             (aignet-copies-in-bounds copy aignet2)
                             (<= n (num-outs aignet)))))
 (let ((__function__ 'observability-fix-outs))
   (declare (ignorable __function__))
   (b* ((aignet (aignet-fix aignet))
        (aignet2 (aignet-fix aignet2))
        ((when (mbe :logic (zp (- (num-outs aignet) (nfix n)))
                    :exec (eql (num-outs aignet) n)))
         (mv copy strash aignet2 aignet state))
        (fanin-lit (outnum->fanin n aignet))
        ((mv copy-lit
             copy strash aignet2 aignet state)
         (observability-fix-lit fanin-lit config
                                aignet copy strash aignet2 state))
        (aignet2 (aignet-add-out copy-lit aignet2)))
     (observability-fix-outs (1+ (lnfix n))
                             config
                             aignet copy strash aignet2 state))))

Theorem: observability-fix-outs-of-nfix-n

(defthm observability-fix-outs-of-nfix-n
 (equal
    (observability-fix-outs (nfix n)
                            config aignet copy strash aignet2 state)
    (observability-fix-outs n config
                            aignet copy strash aignet2 state)))

Theorem: observability-fix-outs-nat-equiv-congruence-on-n

(defthm observability-fix-outs-nat-equiv-congruence-on-n
 (implies
  (nat-equiv n n-equiv)
  (equal
    (observability-fix-outs n
                            config aignet copy strash aignet2 state)
    (observability-fix-outs n-equiv config
                            aignet copy strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-outs-of-observability-config-fix-config

(defthm observability-fix-outs-of-observability-config-fix-config
  (equal (observability-fix-outs n (observability-config-fix config)
                                 aignet copy strash aignet2 state)
         (observability-fix-outs n config
                                 aignet copy strash aignet2 state)))

Theorem: observability-fix-outs-observability-config-equiv-congruence-on-config

(defthm
 observability-fix-outs-observability-config-equiv-congruence-on-config
 (implies
  (observability-config-equiv config config-equiv)
  (equal
    (observability-fix-outs n
                            config aignet copy strash aignet2 state)
    (observability-fix-outs n config-equiv
                            aignet copy strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-outs-of-node-list-fix-aignet

(defthm observability-fix-outs-of-node-list-fix-aignet
  (equal (observability-fix-outs n config (node-list-fix aignet)
                                 copy strash aignet2 state)
         (observability-fix-outs n config
                                 aignet copy strash aignet2 state)))

Theorem: observability-fix-outs-node-list-equiv-congruence-on-aignet

(defthm observability-fix-outs-node-list-equiv-congruence-on-aignet
 (implies
  (node-list-equiv aignet aignet-equiv)
  (equal
    (observability-fix-outs n
                            config aignet copy strash aignet2 state)
    (observability-fix-outs n config aignet-equiv
                            copy strash aignet2 state)))
 :rule-classes :congruence)

Theorem: observability-fix-outs-of-node-list-fix-aignet2

(defthm observability-fix-outs-of-node-list-fix-aignet2
  (equal (observability-fix-outs n config aignet
                                 copy strash (node-list-fix aignet2)
                                 state)
         (observability-fix-outs n config
                                 aignet copy strash aignet2 state)))

Theorem: observability-fix-outs-node-list-equiv-congruence-on-aignet2

(defthm observability-fix-outs-node-list-equiv-congruence-on-aignet2
 (implies
  (node-list-equiv aignet2 aignet2-equiv)
  (equal
    (observability-fix-outs n
                            config aignet copy strash aignet2 state)
    (observability-fix-outs n config aignet
                            copy strash aignet2-equiv state)))
 :rule-classes :congruence)

Theorem: aignet-extension-p-of-observability-fix-outs-2

(defthm aignet-extension-p-of-observability-fix-outs-2
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (aignet-extension-p new-aignet2 aignet2)))

Theorem: aignet-extension-p-of-observability-fix-outs-1

(defthm aignet-extension-p-of-observability-fix-outs-1
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (aignet-extension-p new-aignet aignet)))

Theorem: stype-counts-of-observability-fix-outs-2

(defthm stype-counts-of-observability-fix-outs-2
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (implies (and (and (not (equal (stype-fix stype) (and-stype)))
                       (not (equal (stype-fix stype) (xor-stype))))
                  (not (equal (stype-fix stype) :po)))
             (equal (stype-count stype new-aignet2)
                    (stype-count stype aignet2)))))

Theorem: stype-counts-of-observability-fix-outs-1

(defthm stype-counts-of-observability-fix-outs-1
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (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: copies-in-bounds-of-observability-fix-outs

(defthm copies-in-bounds-of-observability-fix-outs
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (implies (and (aignet-copies-in-bounds copy aignet2)
                  (<= (num-ins aignet) (num-ins aignet2))
                  (<= (num-regs aignet)
                      (num-regs aignet2)))
             (aignet-copies-in-bounds new-copy new-aignet2))))

Theorem: num-outs-of-observability-fix-outs

(defthm num-outs-of-observability-fix-outs
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (equal (stype-count :po new-aignet2)
           (+ (max 0 (- (num-outs aignet) (nfix n)))
              (num-outs aignet2)))))

Theorem: output-eval-of-observability-fix-outs

(defthm output-eval-of-observability-fix-outs
 (b* (((mv ?new-copy ?new-strash
           ?new-aignet2 ?new-aignet ?new-state)
       (observability-fix-outs n config
                               aignet copy strash aignet2 state)))
   (implies (and (<= (num-ins aignet) (num-ins aignet2))
                 (<= (num-regs aignet)
                     (num-regs aignet2))
                 (aignet-copies-in-bounds copy aignet2))
            (equal (output-eval m invals regvals new-aignet2)
                   (if (or (< (nfix m) (num-outs aignet2))
                           (<= (+ (num-outs aignet2)
                                  (- (num-outs aignet) (nfix n)))
                               (nfix m)))
                       (output-eval m invals regvals aignet2)
                     (output-eval (+ (- (nfix m) (num-outs aignet2))
                                     (nfix n))
                                  invals regvals aignet))))))

Theorem: w-state-of-observability-fix-outs

(defthm w-state-of-observability-fix-outs
  (b* (((mv ?new-copy ?new-strash
            ?new-aignet2 ?new-aignet ?new-state)
        (observability-fix-outs n config
                                aignet copy strash aignet2 state)))
    (equal (w new-state) (w state))))