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• Primitive-widening-conversions

Byte-to-short

Widening conversion from byte to short [JLS14:5.1.2].

Signature

(byte-to-short operand) → result

Arguments

operand — Guard (byte-valuep operand).

Returns

result — Type (short-valuep result).

Definitions and Theorems

Function: byte-to-short

(defun byte-to-short (operand)
  (declare (xargs :guard (byte-valuep operand)))
  (b* ((x (byte-value->int operand)))
    (short-value x)))

Theorem: short-valuep-of-byte-to-short

(defthm short-valuep-of-byte-to-short
  (b* ((result (byte-to-short operand)))
    (short-valuep result))
  :rule-classes :rewrite)

Theorem: byte-to-short-of-byte-value-fix-operand

(defthm byte-to-short-of-byte-value-fix-operand
  (equal (byte-to-short (byte-value-fix operand))
         (byte-to-short operand)))

Theorem: byte-to-short-byte-value-equiv-congruence-on-operand

(defthm byte-to-short-byte-value-equiv-congruence-on-operand
  (implies (byte-value-equiv operand operand-equiv)
           (equal (byte-to-short operand)
                  (byte-to-short operand-equiv)))
  :rule-classes :congruence)