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• Fraig

Fraig-finish-copy-nonstrict

Signature

(fraig-finish-copy-nonstrict strict-count 
                             output-ranges save-candidate-equivs-as 
                             remove-candidate-equivs 
                             classes aignet copy aignet2) 
 
  → 
(mv new-output-ranges new-aignet2)

Arguments

strict-count — Guard (acl2::maybe-natp strict-count).

output-ranges — Guard (aignet-output-range-map-p output-ranges).

save-candidate-equivs-as — Guard (symbolp save-candidate-equivs-as).

remove-candidate-equivs — Guard (symbolp remove-candidate-equivs).

Returns

new-output-ranges — Type (aignet-output-range-map-p new-output-ranges).

Definitions and Theorems

Function: fraig-finish-copy-nonstrict

(defun fraig-finish-copy-nonstrict
       (strict-count output-ranges save-candidate-equivs-as
                     remove-candidate-equivs
                     classes aignet copy aignet2)
 (declare (xargs :stobjs (classes aignet copy aignet2)))
 (declare
      (xargs :guard (and (acl2::maybe-natp strict-count)
                         (aignet-output-range-map-p output-ranges)
                         (symbolp save-candidate-equivs-as)
                         (symbolp remove-candidate-equivs))))
 (declare
  (xargs
   :guard (and (<= (num-fanins aignet)
                   (lits-length copy))
               (<= (num-regs aignet)
                   (num-regs aignet2))
               (or (not strict-count)
                   (<= strict-count (num-outs aignet)))
               (aignet-copies-in-bounds copy aignet2)
               (equal (aignet-output-range-map-length output-ranges)
                      (num-outs aignet))
               (classes-wellformed classes)
               (equal (classes-size classes)
                      (num-fanins aignet)))))
 (let ((__function__ 'fraig-finish-copy-nonstrict))
  (declare (ignorable __function__))
  (b*
   ((save-candidate-equivs-as
         (mbe :logic (acl2::symbol-fix save-candidate-equivs-as)
              :exec save-candidate-equivs-as))
    (remove-candidate-equivs
         (mbe :logic (acl2::symbol-fix remove-candidate-equivs)
              :exec remove-candidate-equivs))
    (output-ranges (aignet-output-range-map-fix output-ranges))
    ((when (not strict-count))
     (b* ((aignet2 (finish-copy-comb aignet copy aignet2)))
       (mv output-ranges aignet2)))
    ((mv first-ranges rest-ranges)
     (split-output-ranges strict-count output-ranges))
    (first-ranges-length
         (aignet-output-range-map-length first-ranges))
    (initial-segment (mbe :logic (max (nfix strict-count)
                                      first-ranges-length)
                          :exec first-ranges-length))
    (aignet2
     (aignet-copy-outs-range 0 initial-segment aignet copy aignet2))
    ((mv new-rest-ranges aignet2)
     (fraig-finish-copy-outs initial-segment
                             rest-ranges save-candidate-equivs-as
                             remove-candidate-equivs
                             classes aignet copy aignet2))
    (aignet2 (aignet-copy-nxsts aignet copy aignet2)))
   (mv (append first-ranges new-rest-ranges)
       aignet2))))

Theorem: aignet-output-range-map-p-of-fraig-finish-copy-nonstrict.new-output-ranges

(defthm
 aignet-output-range-map-p-of-fraig-finish-copy-nonstrict.new-output-ranges
 (b* (((mv ?new-output-ranges ?new-aignet2)
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)))
   (aignet-output-range-map-p new-output-ranges))
 :rule-classes :rewrite)

Theorem: aignet-extension-p-of-fraig-finish-copy-nonstrict

(defthm aignet-extension-p-of-fraig-finish-copy-nonstrict
  (b* (((mv ?new-output-ranges ?new-aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))
    (aignet-extension-p new-aignet2 aignet2)))

Theorem: output-range-length-of-fraig-finish-copy-nonstrict

(defthm output-range-length-of-fraig-finish-copy-nonstrict
 (b* (((mv ?new-output-ranges ?new-aignet2)
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)))
  (implies strict-count
           (equal (aignet-output-range-map-length new-output-ranges)
                  (- (stype-count :po new-aignet2)
                     (stype-count :po aignet2))))))

Theorem: stype-count-of-fraig-finish-copy-nonstrict

(defthm stype-count-of-fraig-finish-copy-nonstrict
  (b* (((mv ?new-output-ranges ?new-aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))
    (implies (and (not (equal (stype-fix stype) :po))
                  (not (equal (stype-fix stype) :nxst)))
             (equal (stype-count stype new-aignet2)
                    (stype-count stype aignet2)))))

Theorem: num-outs-of-fraig-finish-copy-nonstrict

(defthm num-outs-of-fraig-finish-copy-nonstrict
  (b* (((mv ?new-output-ranges ?new-aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))
    (implies (not strict-count)
             (equal (stype-count :po new-aignet2)
                    (+ (stype-count :po aignet2)
                       (stype-count :po aignet))))))

Theorem: num-outs-lower-bound-of-fraig-finish-copy-nonstrict-nonstrict

(defthm
      num-outs-lower-bound-of-fraig-finish-copy-nonstrict-nonstrict
  (b* (((mv ?new-output-ranges ?new-aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))
    (implies strict-count
             (<= (nfix strict-count)
                 (stype-count :po new-aignet2))))
  :rule-classes :linear)

Theorem: nxst-eval-of-fraig-finish-copy-nonstrict

(defthm nxst-eval-of-fraig-finish-copy-nonstrict
 (b* (((mv ?new-output-ranges ?new-aignet2)
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)))
  (implies
     (and (aignet-copies-in-bounds copy aignet2)
          (equal (stype-count :reg aignet2)
                 (stype-count :reg aignet))
          (equal (stype-count :nxst aignet2) 0)
          (equal (lit-copy 0 copy) 0)
          (aignet-copy-is-comb-equivalent (+ 1 (fanin-count aignet))
                                          aignet copy aignet2))
     (equal (nxst-eval n invals regvals new-aignet2)
            (nxst-eval n invals regvals aignet)))))

Theorem: output-eval-of-fraig-finish-copy-nonstrict

(defthm output-eval-of-fraig-finish-copy-nonstrict
 (b* (((mv ?new-output-ranges ?new-aignet2)
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)))
  (implies
     (and (aignet-copies-in-bounds copy aignet2)
          (equal (stype-count :po aignet2) 0)
          (equal (lit-copy 0 copy) 0)
          (or (not strict-count)
              (and (< (nfix n) (nfix strict-count))))
          (aignet-copy-is-comb-equivalent (+ 1 (fanin-count aignet))
                                          aignet copy aignet2))
     (equal (output-eval n invals regvals new-aignet2)
            (output-eval n invals regvals aignet)))))

Theorem: comb-equiv-when-strict-of-fraig-finish-copy-nonstrict

(defthm comb-equiv-when-strict-of-fraig-finish-copy-nonstrict
  (b* (((mv ?new-output-ranges ?new-aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))
    (implies (and (not strict-count)
                  (output-fanins-comb-equiv aignet copy aignet2)
                  (nxst-fanins-comb-equiv aignet copy aignet2)
                  (aignet-copies-in-bounds copy aignet2)
                  (equal (stype-count :po aignet2) 0)
                  (equal (stype-count :nxst aignet2) 0)
                  (equal (stype-count :reg aignet)
                         (stype-count :reg aignet2)))
             (comb-equiv new-aignet2 aignet))))

Theorem: fraig-finish-copy-nonstrict-when-strict

(defthm fraig-finish-copy-nonstrict-when-strict
 (b* (((mv ?new-output-ranges ?new-aignet2)
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)))
   (implies
        (not strict-count)
        (and (equal new-aignet2
                    (finish-copy-comb aignet copy aignet2))
             (equal new-output-ranges
                    (aignet-output-range-map-fix output-ranges))))))

Theorem: fraig-finish-copy-nonstrict-of-maybe-natp-fix-strict-count

(defthm fraig-finish-copy-nonstrict-of-maybe-natp-fix-strict-count
  (equal (fraig-finish-copy-nonstrict
              (acl2::maybe-natp-fix strict-count)
              output-ranges save-candidate-equivs-as
              remove-candidate-equivs
              classes aignet copy aignet2)
         (fraig-finish-copy-nonstrict
              strict-count
              output-ranges save-candidate-equivs-as
              remove-candidate-equivs
              classes aignet copy aignet2)))

Theorem: fraig-finish-copy-nonstrict-maybe-nat-equiv-congruence-on-strict-count

(defthm
 fraig-finish-copy-nonstrict-maybe-nat-equiv-congruence-on-strict-count
 (implies (acl2::maybe-nat-equiv strict-count strict-count-equiv)
          (equal (fraig-finish-copy-nonstrict
                      strict-count
                      output-ranges save-candidate-equivs-as
                      remove-candidate-equivs
                      classes aignet copy aignet2)
                 (fraig-finish-copy-nonstrict
                      strict-count-equiv
                      output-ranges save-candidate-equivs-as
                      remove-candidate-equivs
                      classes aignet copy aignet2)))
 :rule-classes :congruence)

Theorem: fraig-finish-copy-nonstrict-of-aignet-output-range-map-fix-output-ranges

(defthm
 fraig-finish-copy-nonstrict-of-aignet-output-range-map-fix-output-ranges
 (equal (fraig-finish-copy-nonstrict
             strict-count
             (aignet-output-range-map-fix output-ranges)
             save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))

Theorem: fraig-finish-copy-nonstrict-aignet-output-range-map-equiv-congruence-on-output-ranges

(defthm
 fraig-finish-copy-nonstrict-aignet-output-range-map-equiv-congruence-on-output-ranges
 (implies
  (aignet-output-range-map-equiv output-ranges output-ranges-equiv)
  (equal
       (fraig-finish-copy-nonstrict
            strict-count
            output-ranges save-candidate-equivs-as
            remove-candidate-equivs
            classes aignet copy aignet2)
       (fraig-finish-copy-nonstrict strict-count output-ranges-equiv
                                    save-candidate-equivs-as
                                    remove-candidate-equivs
                                    classes aignet copy aignet2)))
 :rule-classes :congruence)

Theorem: fraig-finish-copy-nonstrict-of-symbol-fix-save-candidate-equivs-as

(defthm
 fraig-finish-copy-nonstrict-of-symbol-fix-save-candidate-equivs-as
 (equal (fraig-finish-copy-nonstrict
             strict-count output-ranges
             (acl2::symbol-fix save-candidate-equivs-as)
             remove-candidate-equivs
             classes aignet copy aignet2)
        (fraig-finish-copy-nonstrict
             strict-count
             output-ranges save-candidate-equivs-as
             remove-candidate-equivs
             classes aignet copy aignet2)))

Theorem: fraig-finish-copy-nonstrict-symbol-equiv-congruence-on-save-candidate-equivs-as

(defthm
 fraig-finish-copy-nonstrict-symbol-equiv-congruence-on-save-candidate-equivs-as
 (implies
  (acl2::symbol-equiv save-candidate-equivs-as
                      save-candidate-equivs-as-equiv)
  (equal (fraig-finish-copy-nonstrict
              strict-count
              output-ranges save-candidate-equivs-as
              remove-candidate-equivs
              classes aignet copy aignet2)
         (fraig-finish-copy-nonstrict strict-count output-ranges
                                      save-candidate-equivs-as-equiv
                                      remove-candidate-equivs
                                      classes aignet copy aignet2)))
 :rule-classes :congruence)

Theorem: fraig-finish-copy-nonstrict-of-symbol-fix-remove-candidate-equivs

(defthm
  fraig-finish-copy-nonstrict-of-symbol-fix-remove-candidate-equivs
  (equal (fraig-finish-copy-nonstrict
              strict-count
              output-ranges save-candidate-equivs-as
              (acl2::symbol-fix remove-candidate-equivs)
              classes aignet copy aignet2)
         (fraig-finish-copy-nonstrict
              strict-count
              output-ranges save-candidate-equivs-as
              remove-candidate-equivs
              classes aignet copy aignet2)))

Theorem: fraig-finish-copy-nonstrict-symbol-equiv-congruence-on-remove-candidate-equivs

(defthm
 fraig-finish-copy-nonstrict-symbol-equiv-congruence-on-remove-candidate-equivs
 (implies (acl2::symbol-equiv remove-candidate-equivs
                              remove-candidate-equivs-equiv)
          (equal (fraig-finish-copy-nonstrict
                      strict-count
                      output-ranges save-candidate-equivs-as
                      remove-candidate-equivs
                      classes aignet copy aignet2)
                 (fraig-finish-copy-nonstrict
                      strict-count
                      output-ranges save-candidate-equivs-as
                      remove-candidate-equivs-equiv
                      classes aignet copy aignet2)))
 :rule-classes :congruence)