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• Gate-elim

Vl-modulelist-gate-elim-aux

Extends vl-module-gate-elim across a module list.

Signature

(vl-modulelist-gate-elim-aux x primalist) → (mv new-x addmods)

Arguments

x — Guard (vl-modulelist-p x).

primalist — Mapping from gate types to primitive modules.
    Guard (vl-primalist-p primalist).

Returns

new-x — Type (vl-modulelist-p new-x), given the guard.

addmods — Type (vl-modulelist-p addmods), given the guard.

Definitions and Theorems

Function: vl-modulelist-gate-elim-aux

(defun vl-modulelist-gate-elim-aux (x primalist)
  (declare (xargs :guard (and (vl-modulelist-p x)
                              (vl-primalist-p primalist))))
  (let ((__function__ 'vl-modulelist-gate-elim-aux))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (mv nil nil))
         ((mv car-prime car-addmods)
          (vl-module-gate-elim (car x) primalist))
         ((mv cdr-prime cdr-addmods)
          (vl-modulelist-gate-elim-aux (cdr x)
                                       primalist)))
      (mv (cons car-prime cdr-prime)
          (append car-addmods cdr-addmods)))))

Theorem: vl-modulelist-p-of-vl-modulelist-gate-elim-aux.new-x

(defthm vl-modulelist-p-of-vl-modulelist-gate-elim-aux.new-x
  (implies (and (force (vl-modulelist-p x))
                (force (vl-primalist-p primalist)))
           (b* (((mv ?new-x ?addmods)
                 (vl-modulelist-gate-elim-aux x primalist)))
             (vl-modulelist-p new-x)))
  :rule-classes :rewrite)

Theorem: vl-modulelist-p-of-vl-modulelist-gate-elim-aux.addmods

(defthm vl-modulelist-p-of-vl-modulelist-gate-elim-aux.addmods
  (implies (and (force (vl-modulelist-p x))
                (force (vl-primalist-p primalist)))
           (b* (((mv ?new-x ?addmods)
                 (vl-modulelist-gate-elim-aux x primalist)))
             (vl-modulelist-p addmods)))
  :rule-classes :rewrite)

Theorem: vl-modulelist-gate-elim-aux-mvtypes-0

(defthm vl-modulelist-gate-elim-aux-mvtypes-0
  (true-listp (mv-nth 0
                      (vl-modulelist-gate-elim-aux x primalist)))
  :rule-classes :type-prescription)

Theorem: vl-modulelist-gate-elim-aux-mvtypes-1

(defthm vl-modulelist-gate-elim-aux-mvtypes-1
  (true-listp (mv-nth 1
                      (vl-modulelist-gate-elim-aux x primalist)))
  :rule-classes :type-prescription)