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• Abstract-syntax-operations

Binary-op-strictp

Check if a binary operator is strict.

Signature

(binary-op-strictp op) → yes/no

Arguments

op — Guard (binary-opp op).

Returns

yes/no — Type (booleanp yes/no).

These are all the operators that are not non-strict, i.e. that are strict.

Definitions and Theorems

Function: binary-op-strictp

(defun binary-op-strictp (op)
  (declare (xargs :guard (binary-opp op)))
  (let ((__function__ 'binary-op-strictp))
    (declare (ignorable __function__))
    (not (binary-op-nonstrictp op))))

Theorem: booleanp-of-binary-op-strictp

(defthm booleanp-of-binary-op-strictp
  (b* ((yes/no (binary-op-strictp op)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: binary-op-strictp-of-binary-op-fix-op

(defthm binary-op-strictp-of-binary-op-fix-op
  (equal (binary-op-strictp (binary-op-fix op))
         (binary-op-strictp op)))

Theorem: binary-op-strictp-binary-op-equiv-congruence-on-op

(defthm binary-op-strictp-binary-op-equiv-congruence-on-op
  (implies (binary-op-equiv op op-equiv)
           (equal (binary-op-strictp op)
                  (binary-op-strictp op-equiv)))
  :rule-classes :congruence)