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• Constprop

Aignet-constprop-sweep-invar

Signature

(aignet-constprop-sweep-invar n invals regvals aignet copy aignet2) 
  → 
*

Arguments

n — Guard (natp n).

Definitions and Theorems

Function: aignet-constprop-sweep-invar

(defun aignet-constprop-sweep-invar
       (n invals regvals aignet copy aignet2)
  (declare (xargs :stobjs (invals regvals aignet copy aignet2)))
  (declare (xargs :guard (natp n)))
  (declare
       (xargs :guard (and (<= n (num-fanins aignet))
                          (<= (num-ins aignet)
                              (bits-length invals))
                          (<= (num-ins aignet2)
                              (bits-length invals))
                          (<= (num-regs aignet)
                              (bits-length regvals))
                          (<= (num-regs aignet2)
                              (bits-length regvals))
                          (<= n (lits-length copy))
                          (aignet-copies-in-bounds copy aignet2))))
  (let ((__function__ 'aignet-constprop-sweep-invar))
    (declare (ignorable __function__))
    (if (zp n)
        t
      (let ((n (1- n)))
        (and (equal (id-eval n invals regvals aignet)
                    (lit-eval (get-lit n copy)
                              invals regvals aignet2))
             (aignet-constprop-sweep-invar
                  n
                  invals regvals aignet copy aignet2))))))

Theorem: aignet-constprop-sweep-invar-implies

(defthm aignet-constprop-sweep-invar-implies
  (implies (and (aignet-constprop-sweep-invar
                     n invals regvals aignet copy aignet2)
                (< (nfix m) (nfix n)))
           (equal (lit-eval (nth-lit m copy)
                            invals regvals aignet2)
                  (id-eval m invals regvals aignet))))

Theorem: aignet-constprop-sweep-invar-implies-lit-eval-copy

(defthm aignet-constprop-sweep-invar-implies-lit-eval-copy
  (implies (and (aignet-constprop-sweep-invar
                     n invals regvals aignet copy aignet2)
                (< (lit->var m) (nfix n)))
           (equal (lit-eval (lit-copy m copy)
                            invals regvals aignet2)
                  (lit-eval m invals regvals aignet))))

Theorem: aignet-constprop-sweep-invar-of-aignet-extension

(defthm aignet-constprop-sweep-invar-of-aignet-extension
 (implies
  (and
    (aignet-extension-binding)
    (aignet-constprop-sweep-invar n invals regvals aignet copy orig)
    (aignet-copies-in-bounds copy orig))
  (aignet-constprop-sweep-invar n invals regvals aignet copy new)))

Theorem: aignet-constprop-sweep-invar-of-update-later

(defthm aignet-constprop-sweep-invar-of-update-later
 (implies
    (and (aignet-constprop-sweep-invar
              n invals regvals aignet copy aignet2)
         (<= (nfix n) (nfix m)))
    (aignet-constprop-sweep-invar n invals regvals
                                  aignet (update-nth-lit m lit copy)
                                  aignet2)))

Theorem: aignet-constprop-sweep-invar-1

(defthm aignet-constprop-sweep-invar-1
  (implies (equal 0 (nth-lit 0 copy))
           (aignet-constprop-sweep-invar
                1 invals regvals aignet copy aignet2)))

Theorem: aignet-constprop-sweep-invar-when-greater

(defthm aignet-constprop-sweep-invar-when-greater
  (implies (and (aignet-constprop-sweep-invar
                     n invals regvals aignet copy aignet2)
                (<= (nfix m) (nfix n)))
           (aignet-constprop-sweep-invar
                m invals regvals aignet copy aignet2)))

Theorem: aignet-constprop-sweep-invar-of-nfix-n

(defthm aignet-constprop-sweep-invar-of-nfix-n
 (equal
   (aignet-constprop-sweep-invar (nfix n)
                                 invals regvals aignet copy aignet2)
   (aignet-constprop-sweep-invar
        n invals regvals aignet copy aignet2)))

Theorem: aignet-constprop-sweep-invar-nat-equiv-congruence-on-n

(defthm aignet-constprop-sweep-invar-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (aignet-constprop-sweep-invar
                       n invals regvals aignet copy aignet2)
                  (aignet-constprop-sweep-invar
                       n-equiv
                       invals regvals aignet copy aignet2)))
  :rule-classes :congruence)

Theorem: aignet-constprop-sweep-invar-of-node-list-fix-aignet

(defthm aignet-constprop-sweep-invar-of-node-list-fix-aignet
  (equal (aignet-constprop-sweep-invar
              n invals regvals (node-list-fix aignet)
              copy aignet2)
         (aignet-constprop-sweep-invar
              n invals regvals aignet copy aignet2)))

Theorem: aignet-constprop-sweep-invar-node-list-equiv-congruence-on-aignet

(defthm
  aignet-constprop-sweep-invar-node-list-equiv-congruence-on-aignet
  (implies (node-list-equiv aignet aignet-equiv)
           (equal (aignet-constprop-sweep-invar
                       n invals regvals aignet copy aignet2)
                  (aignet-constprop-sweep-invar
                       n invals
                       regvals aignet-equiv copy aignet2)))
  :rule-classes :congruence)

Theorem: aignet-constprop-sweep-invar-of-node-list-fix-aignet2

(defthm aignet-constprop-sweep-invar-of-node-list-fix-aignet2
 (equal
  (aignet-constprop-sweep-invar n invals regvals
                                aignet copy (node-list-fix aignet2))
  (aignet-constprop-sweep-invar
       n invals regvals aignet copy aignet2)))

Theorem: aignet-constprop-sweep-invar-node-list-equiv-congruence-on-aignet2

(defthm
 aignet-constprop-sweep-invar-node-list-equiv-congruence-on-aignet2
 (implies (node-list-equiv aignet2 aignet2-equiv)
          (equal (aignet-constprop-sweep-invar
                      n invals regvals aignet copy aignet2)
                 (aignet-constprop-sweep-invar
                      n invals
                      regvals aignet copy aignet2-equiv)))
 :rule-classes :congruence)