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Aignet-fanins

Signature

(aignet-fanins aignet) → fanins

Arguments

aignet — Guard (node-listp aignet).

Returns

fanins — Type (node-listp fanins).

Definitions and Theorems

Function: aignet-fanins

(defun aignet-fanins (aignet)
       (declare (xargs :guard (node-listp aignet)))
       (let ((__function__ 'aignet-fanins))
            (declare (ignorable __function__))
            (if (atom aignet)
                nil
                (if (fanin-node-p (car aignet))
                    (cons (node-fix (car aignet))
                          (aignet-fanins (cdr aignet)))
                    (aignet-fanins (cdr aignet))))))

Theorem: node-listp-of-aignet-fanins

(defthm node-listp-of-aignet-fanins
        (b* ((fanins (aignet-fanins aignet)))
            (node-listp fanins))
        :rule-classes :rewrite)

Theorem: fanin-count-of-aignet-fanins

(defthm fanin-count-of-aignet-fanins
        (b* ((?fanins (aignet-fanins aignet)))
            (equal (fanin-count fanins)
                   (fanin-count aignet))))

Theorem: lookup-id-of-aignet-fanins

(defthm lookup-id-of-aignet-fanins
        (b* ((?fanins (aignet-fanins aignet)))
            (equal (lookup-id n fanins)
                   (aignet-fanins (lookup-id n aignet)))))

Theorem: stype-count-of-aignet-fanins

(defthm stype-count-of-aignet-fanins
        (b* ((?fanins (aignet-fanins aignet)))
            (equal (stype-count stype fanins)
                   (if (equal (ctype stype) (out-ctype))
                       0 (stype-count stype aignet)))))

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

(defthm aignet-fanins-of-node-list-fix-aignet
        (equal (aignet-fanins (node-list-fix aignet))
               (aignet-fanins aignet)))

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

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

Theorem: lookup-stype-of-aignet-fanins

(defthm
    lookup-stype-of-aignet-fanins
    (b* ((?fanins (aignet-fanins aignet)))
        (equal (lookup-stype n stype fanins)
               (if (equal (ctype stype) (out-ctype))
                   nil
                   (aignet-fanins (lookup-stype n stype aignet))))))

Theorem: car-of-aignet-fanins

(defthm car-of-aignet-fanins
        (b* ((?fanins (aignet-fanins aignet)))
            (implies (fanin-node-p (car aignet))
                     (equal (car fanins)
                            (node-fix (car aignet))))))

Theorem: cdr-of-aignet-fanins

(defthm cdr-of-aignet-fanins
        (b* ((?fanins (aignet-fanins aignet)))
            (implies (fanin-node-p (car aignet))
                     (equal (cdr fanins)
                            (aignet-fanins (cdr aignet))))))

Theorem: aignet-fanins-of-append-non-fanins

(defthm aignet-fanins-of-append-non-fanins
        (implies (equal (fanin-count first) 0)
                 (equal (aignet-fanins (append first x))
                        (aignet-fanins x))))

Theorem: aignet-fanins-idempotent

(defthm aignet-fanins-idempotent
        (equal (aignet-fanins (aignet-fanins x))
               (aignet-fanins x)))

Theorem: fanin-of-aignet-fanins

(defthm fanin-of-aignet-fanins
        (implies (fanin-node-p (car aignet))
                 (equal (fanin ftype (aignet-fanins aignet))
                        (fanin ftype aignet))))

Theorem: aignet-fanins-of-cons

(defthm aignet-fanins-of-cons
        (equal (aignet-fanins (cons node x))
               (if (fanin-node-p node)
                   (cons (node-fix node) (aignet-fanins x))
                   (aignet-fanins x))))