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• Network

Fanin

(fanin which aignet) gets the specified fanin from the first node of the input network and fixes it to be a valid fanin literal of the rest of the network.

Signature

(fanin which aignet) → lit

Arguments

which — Guard (bitp which).

aignet — Guard (node-listp aignet).

Returns

lit — Type (litp lit).

Definitions and Theorems

Function: fanin

(defun fanin (which aignet)
  (declare (xargs :guard (and (bitp which) (node-listp aignet))))
  (declare (xargs :guard (and (consp aignet)
                              (or (eq (ctype (stype (car aignet)))
                                      :output)
                                  (eq (ctype (stype (car aignet)))
                                      :gate)))))
  (let ((__function__ 'fanin))
    (declare (ignorable __function__))
    (aignet-lit-fix (if (eq (ctype (stype (car aignet)))
                            :output)
                        (co-node->fanin (car aignet))
                      (if (bit->bool which)
                          (gate-node->fanin1 (car aignet))
                        (gate-node->fanin0 (car aignet))))
                    (cdr aignet))))

Theorem: litp-of-fanin

(defthm litp-of-fanin
  (b* ((lit (fanin which aignet)))
    (litp lit))
  :rule-classes :type-prescription)

Theorem: fanin-id-lte-fanin-count

(defthm fanin-id-lte-fanin-count
  (b* ((satlink::?lit (fanin which aignet)))
    (<= (lit-id lit)
        (fanin-count (cdr aignet))))
  :rule-classes :linear)

Theorem: fanin-id-lte-fanin-count-strong

(defthm fanin-id-lte-fanin-count-strong
  (b* ((satlink::?lit (fanin which aignet)))
    (implies (and (consp aignet)
                  (fanin-node-p (car aignet)))
             (< (lit-id lit) (fanin-count aignet))))
  :rule-classes :linear)

Theorem: aignet-litp-of-fanin

(defthm aignet-litp-of-fanin
  (b* ((satlink::?lit (fanin which aignet)))
    (aignet-litp lit aignet)))

Theorem: aignet-litp-in-extension-of-fanin

(defthm aignet-litp-in-extension-of-fanin
  (b* ((satlink::?lit (fanin which aignet)))
    (implies (aignet-extension-p new aignet)
             (aignet-litp lit new))))

Theorem: fanin-of-cons

(defthm fanin-of-cons
  (equal (fanin which (cons node aignet))
         (aignet-lit-fix (if (eq (ctype (stype node)) :output)
                             (co-node->fanin node)
                           (if (bit->bool which)
                               (gate-node->fanin1 node)
                             (gate-node->fanin0 node)))
                         aignet)))

Theorem: fanin-of-bfix-which

(defthm fanin-of-bfix-which
  (equal (fanin (bfix which) aignet)
         (fanin which aignet)))

Theorem: fanin-bit-equiv-congruence-on-which

(defthm fanin-bit-equiv-congruence-on-which
  (implies (bit-equiv which which-equiv)
           (equal (fanin which aignet)
                  (fanin which-equiv aignet)))
  :rule-classes :congruence)

Theorem: fanin-of-node-list-fix-aignet

(defthm fanin-of-node-list-fix-aignet
  (equal (fanin which (node-list-fix aignet))
         (fanin which aignet)))

Theorem: fanin-node-list-equiv-congruence-on-aignet

(defthm fanin-node-list-equiv-congruence-on-aignet
  (implies (node-list-equiv aignet aignet-equiv)
           (equal (fanin which aignet)
                  (fanin which aignet-equiv)))
  :rule-classes :congruence)