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Integer-operations

Int-add

Addition of signed integer values.

Signature
(int-add left-operand right-operand) → result
Arguments: left-operand — Guard (intp left-operand).; right-operand — Guard (intp right-operand).
Returns: result — Type (intp result).

Definitions and Theorems

Function: int-add

(defun int-add (left-operand right-operand)
  (declare (xargs :guard (and (intp left-operand)
                              (intp right-operand))))
  (b* ((size (int->size left-operand))
       (x (int->value left-operand))
       (y (int->value right-operand)))
    (make-int :size (int->size left-operand)
              :value (logext size (+ x y)))))

Theorem: intp-of-int-add

(defthm intp-of-int-add
  (b* ((result (int-add left-operand right-operand)))
    (intp result))
  :rule-classes :rewrite)

Theorem: int-add-of-int-fix-left-operand

(defthm int-add-of-int-fix-left-operand
  (equal (int-add (int-fix left-operand)
                  right-operand)
         (int-add left-operand right-operand)))

Theorem: int-add-int-equiv-congruence-on-left-operand

(defthm int-add-int-equiv-congruence-on-left-operand
  (implies (int-equiv left-operand left-operand-equiv)
           (equal (int-add left-operand right-operand)
                  (int-add left-operand-equiv right-operand)))
  :rule-classes :congruence)

Theorem: int-add-of-int-fix-right-operand

(defthm int-add-of-int-fix-right-operand
  (equal (int-add left-operand (int-fix right-operand))
         (int-add left-operand right-operand)))

Theorem: int-add-int-equiv-congruence-on-right-operand

(defthm int-add-int-equiv-congruence-on-right-operand
  (implies (int-equiv right-operand right-operand-equiv)
           (equal (int-add left-operand right-operand)
                  (int-add left-operand right-operand-equiv)))
  :rule-classes :congruence)