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• Bed-mk1

Mk-op-x-x

Construct a reduced BED for op(arg, arg).

Signature

(mk-op-x-x op arg) → bed

Arguments

op — The operator being applied.
    Guard (bed-op-p op).

arg — First and second argument to the operator (a bed).

Definitions and Theorems

Function: mk-op-x-x

(defun mk-op-x-x (op arg)
  (declare (xargs :guard (bed-op-p op)))
  (let ((__function__ 'mk-op-x-x))
    (declare (ignorable __function__))
    (b* ((op (bed-op-fix$ op))
         ((when (eql op (bed-op-true))) t)
         ((when (eql op (bed-op-ior))) arg)
         ((when (eql op (bed-op-orc2))) t)
         ((when (eql op (bed-op-arg1))) arg)
         ((when (eql op (bed-op-orc1))) t)
         ((when (eql op (bed-op-arg2))) arg)
         ((when (eql op (bed-op-eqv))) t)
         ((when (eql op (bed-op-and))) arg)
         ((when (eql op (bed-op-nand)))
          (mk-not arg))
         ((when (eql op (bed-op-xor))) nil)
         ((when (eql op (bed-op-not2)))
          (mk-not arg))
         ((when (eql op (bed-op-andc2))) nil)
         ((when (eql op (bed-op-not1)))
          (mk-not arg))
         ((when (eql op (bed-op-andc1))) nil)
         ((when (eql op (bed-op-nor)))
          (mk-not arg))
         ((when (eql op (bed-op-false))) nil))
      (mk-op-raw op arg arg))))

Theorem: bed-eval-of-mk-op-x-x

(defthm bed-eval-of-mk-op-x-x
  (equal (bed-eval (mk-op-x-x op arg) env)
         (bed-eval (mk-op-raw op arg arg) env)))