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• Network

Lookup-id

Core function for looking up an AIG node in the logical AIG network by its ID.

Signature

(lookup-id id aignet) → suffix

Arguments

id — Guard (natp id).

aignet — Guard (node-listp aignet).

Returns

suffix — Tail of the aignet up to (and including) the idth node.
    Type (node-listp suffix).

Definitions and Theorems

Function: lookup-id

(defun lookup-id (id aignet)
  (declare (xargs :guard (and (natp id) (node-listp aignet))))
  (let ((__function__ 'lookup-id))
    (declare (ignorable __function__))
    (cond ((endp aignet) (node-list-fix aignet))
          ((and (fanin-node-p (car aignet))
                (equal (fanin-count aignet) (lnfix id)))
           (node-list-fix aignet))
          (t (lookup-id id (cdr aignet))))))

Theorem: node-listp-of-lookup-id

(defthm node-listp-of-lookup-id
  (b* ((suffix (lookup-id id aignet)))
    (node-listp suffix))
  :rule-classes :rewrite)

Theorem: lookup-id-of-nfix-id

(defthm lookup-id-of-nfix-id
  (equal (lookup-id (nfix id) aignet)
         (lookup-id id aignet)))

Theorem: lookup-id-nat-equiv-congruence-on-id

(defthm lookup-id-nat-equiv-congruence-on-id
  (implies (nat-equiv id id-equiv)
           (equal (lookup-id id aignet)
                  (lookup-id id-equiv aignet)))
  :rule-classes :congruence)

Theorem: lookup-id-of-node-list-fix-aignet

(defthm lookup-id-of-node-list-fix-aignet
  (equal (lookup-id id (node-list-fix aignet))
         (lookup-id id aignet)))

Theorem: lookup-id-node-list-equiv-congruence-on-aignet

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

Theorem: fanin-count-of-lookup-id

(defthm fanin-count-of-lookup-id
  (implies (<= (nfix n) (fanin-count aignet))
           (equal (fanin-count (lookup-id n aignet))
                  (nfix n))))

Theorem: fanin-count-of-cdr-lookup-id

(defthm fanin-count-of-cdr-lookup-id
  (implies (consp (lookup-id n aignet))
           (equal (fanin-count (cdr (lookup-id n aignet)))
                  (+ -1 (nfix n)))))

Theorem: output-ctype-of-lookup-id

(defthm output-ctype-of-lookup-id
  (not (equal (ctype (stype (car (lookup-id id aignet))))
              (out-ctype))))

Theorem: output-stype-of-lookup-id

(defthm output-stype-of-lookup-id
  (and (not (equal (stype (car (lookup-id id aignet)))
                   :po))
       (not (equal (stype (car (lookup-id id aignet)))
                   :nxst))))

Theorem: fanin-node-p-of-lookup-id

(defthm fanin-node-p-of-lookup-id
  (fanin-node-p (car (lookup-id id aignet))))

Theorem: lookup-id-0

(defthm lookup-id-0
  (equal (lookup-id 0 aignet) nil))

Theorem: lookup-id-in-bounds

(defthm lookup-id-in-bounds
  (iff (consp (lookup-id n aignet))
       (and (< 0 (nfix n))
            (<= (nfix n) (fanin-count aignet)))))

Theorem: lookup-id-in-bounds-when-positive

(defthm lookup-id-in-bounds-when-positive
  (implies (posp n)
           (iff (consp (lookup-id n aignet))
                (<= (nfix n) (fanin-count aignet)))))

Theorem: lookup-id-aignet-extension-p

(defthm lookup-id-aignet-extension-p
  (aignet-extension-p aignet (lookup-id id aignet)))

Theorem: lookup-id-in-extension

(defthm lookup-id-in-extension
  (implies (and (aignet-extension-p new orig)
                (<= (nfix id) (fanin-count orig)))
           (equal (lookup-id id new)
                  (lookup-id id orig))))

Theorem: lookup-id-in-extension-inverse

(defthm lookup-id-in-extension-inverse
  (implies (and (aignet-extension-bind-inverse)
                (<= (nfix id) (fanin-count orig)))
           (equal (lookup-id id orig)
                  (lookup-id id new))))

Theorem: fanin-count-of-cdr-lookup-bound-by-id

(defthm fanin-count-of-cdr-lookup-bound-by-id
  (implies (consp (lookup-id id aignet))
           (< (fanin-count (cdr (lookup-id id aignet)))
              (nfix id)))
  :rule-classes :linear)

Theorem: lookup-id-of-fanin-count-of-suffix

(defthm lookup-id-of-fanin-count-of-suffix
  (implies (and (aignet-extension-p y x)
                (consp x)
                (fanin-node-p (car x)))
           (equal (lookup-id (fanin-count x) y)
                  (node-list-fix x))))

Theorem: true-listp-lookup-id-of-node-listp

(defthm true-listp-lookup-id-of-node-listp
  (implies (node-listp aignet)
           (true-listp (lookup-id id aignet)))
  :rule-classes :type-prescription)

Theorem: lookup-id-of-nil

(defthm lookup-id-of-nil
  (equal (lookup-id x nil) nil))

Theorem: lookup-id-of-cons

(defthm lookup-id-of-cons
  (equal (lookup-id id (cons node rest))
         (if (and (fanin-node-p node)
                  (equal (nfix id)
                         (+ 1 (fanin-count rest))))
             (cons (node-fix node)
                   (node-list-fix rest))
           (lookup-id id rest))))

Theorem: lookup-id-of-fanin-count

(defthm lookup-id-of-fanin-count
  (implies (fanin-node-p (car x))
           (equal (lookup-id (fanin-count x) x)
                  (node-list-fix x))))

Theorem: fanin-count-of-lookup-id-when-consp

(defthm fanin-count-of-lookup-id-when-consp
  (implies (consp (lookup-id id aignet))
           (equal (fanin-count (lookup-id id aignet))
                  id)))

Theorem: posp-when-consp-of-lookup-id

(defthm posp-when-consp-of-lookup-id
  (implies (consp (lookup-id id aignet))
           (posp id))
  :rule-classes :forward-chaining)

Theorem: lookup-id-consp-forward-to-id-bound-nfix

(defthm lookup-id-consp-forward-to-id-bound-nfix
  (implies (and (consp (lookup-id id aignet)))
           (<= (nfix id) (fanin-count aignet)))
  :rule-classes :forward-chaining)

Theorem: lookup-id-consp-forward-to-id-bound

(defthm lookup-id-consp-forward-to-id-bound
  (implies (and (consp (lookup-id id aignet))
                (natp id))
           (<= id (fanin-count aignet)))
  :rule-classes :forward-chaining)

Theorem: lookup-id-out-of-bounds

(defthm lookup-id-out-of-bounds
  (implies (< (fanin-count aignet) (nfix id))
           (equal (lookup-id id aignet) nil)))