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Instruction

Instruction-fix

Fixing function for instruction structures.

Signature
(instruction-fix x) → new-x
Arguments: x — Guard (instructionp x).
Returns: new-x — Type (instructionp new-x).

Definitions and Theorems

Function: instruction-fix$inline

(defun instruction-fix$inline (x)
 (declare (xargs :guard (instructionp x)))
 (let ((__function__ 'instruction-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (case (instruction-kind x)
       (:unary (b* ((op (unary-op-fix (std::da-nth 0 (cdr x))))
                    (arg (operand-fix (std::da-nth 1 (cdr x))))
                    (into (register-fix (std::da-nth 2 (cdr x)))))
                 (cons :unary (list op arg into))))
       (:binary (b* ((op (binary-op-fix (std::da-nth 0 (cdr x))))
                     (arg1 (operand-fix (std::da-nth 1 (cdr x))))
                     (arg2 (operand-fix (std::da-nth 2 (cdr x))))
                     (into (register-fix (std::da-nth 3 (cdr x)))))
                  (cons :binary (list op arg1 arg2 into))))
       (:ternary (b* ((op (ternary-op-fix (std::da-nth 0 (cdr x))))
                      (arg1 (operand-fix (std::da-nth 1 (cdr x))))
                      (arg2 (operand-fix (std::da-nth 2 (cdr x))))
                      (arg3 (operand-fix (std::da-nth 3 (cdr x))))
                      (into (register-fix (std::da-nth 4 (cdr x)))))
                   (cons :ternary (list op arg1 arg2 arg3 into))))
       (:equal (b* ((op (equal-op-fix (std::da-nth 0 (cdr x))))
                    (arg1 (operand-fix (std::da-nth 1 (cdr x))))
                    (arg2 (operand-fix (std::da-nth 2 (cdr x))))
                    (into (register-fix (std::da-nth 3 (cdr x)))))
                 (cons :equal (list op arg1 arg2 into))))
       (:assert (b* ((op (assert-op-fix (std::da-nth 0 (cdr x))))
                     (arg1 (operand-fix (std::da-nth 1 (cdr x))))
                     (arg2 (operand-fix (std::da-nth 2 (cdr x)))))
                  (cons :assert (list op arg1 arg2))))
       (:commit (b* ((op (commit-op-fix (std::da-nth 0 (cdr x))))
                     (arg1 (operand-fix (std::da-nth 1 (cdr x))))
                     (arg2 (operand-fix (std::da-nth 2 (cdr x))))
                     (into (register-fix (std::da-nth 3 (cdr x)))))
                  (cons :commit (list op arg1 arg2 into))))
       (:hash (b* ((op (hash-op-fix (std::da-nth 0 (cdr x))))
                   (arg (operand-fix (std::da-nth 1 (cdr x))))
                   (into (register-fix (std::da-nth 2 (cdr x)))))
                (cons :hash (list op arg into))))
       (:cast (b* ((args (operand-list-fix (std::da-nth 0 (cdr x))))
                   (into (register-fix (std::da-nth 1 (cdr x))))
                   (as (register-type-fix (std::da-nth 2 (cdr x)))))
                (cons :cast (list args into as))))
       (:call (b* ((ref (reference-fix (std::da-nth 0 (cdr x))))
                   (args (operand-list-fix (std::da-nth 1 (cdr x))))
                   (into (register-fix (std::da-nth 2 (cdr x)))))
                (cons :call (list ref args into)))))
     :exec x)))

Theorem: instructionp-of-instruction-fix

(defthm instructionp-of-instruction-fix
  (b* ((new-x (instruction-fix$inline x)))
    (instructionp new-x))
  :rule-classes :rewrite)

Theorem: instruction-fix-when-instructionp

(defthm instruction-fix-when-instructionp
  (implies (instructionp x)
           (equal (instruction-fix x) x)))

Function: instruction-equiv$inline

(defun instruction-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (instructionp acl2::x)
                              (instructionp acl2::y))))
  (equal (instruction-fix acl2::x)
         (instruction-fix acl2::y)))

Theorem: instruction-equiv-is-an-equivalence

(defthm instruction-equiv-is-an-equivalence
  (and (booleanp (instruction-equiv x y))
       (instruction-equiv x x)
       (implies (instruction-equiv x y)
                (instruction-equiv y x))
       (implies (and (instruction-equiv x y)
                     (instruction-equiv y z))
                (instruction-equiv x z)))
  :rule-classes (:equivalence))

Theorem: instruction-equiv-implies-equal-instruction-fix-1

(defthm instruction-equiv-implies-equal-instruction-fix-1
  (implies (instruction-equiv acl2::x x-equiv)
           (equal (instruction-fix acl2::x)
                  (instruction-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: instruction-fix-under-instruction-equiv

(defthm instruction-fix-under-instruction-equiv
  (instruction-equiv (instruction-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-instruction-fix-1-forward-to-instruction-equiv

(defthm equal-of-instruction-fix-1-forward-to-instruction-equiv
  (implies (equal (instruction-fix acl2::x)
                  acl2::y)
           (instruction-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-instruction-fix-2-forward-to-instruction-equiv

(defthm equal-of-instruction-fix-2-forward-to-instruction-equiv
  (implies (equal acl2::x (instruction-fix acl2::y))
           (instruction-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: instruction-equiv-of-instruction-fix-1-forward

(defthm instruction-equiv-of-instruction-fix-1-forward
  (implies (instruction-equiv (instruction-fix acl2::x)
                              acl2::y)
           (instruction-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: instruction-equiv-of-instruction-fix-2-forward

(defthm instruction-equiv-of-instruction-fix-2-forward
  (implies (instruction-equiv acl2::x (instruction-fix acl2::y))
           (instruction-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: instruction-kind$inline-of-instruction-fix-x

(defthm instruction-kind$inline-of-instruction-fix-x
  (equal (instruction-kind$inline (instruction-fix x))
         (instruction-kind$inline x)))

Theorem: instruction-kind$inline-instruction-equiv-congruence-on-x

(defthm instruction-kind$inline-instruction-equiv-congruence-on-x
  (implies (instruction-equiv x x-equiv)
           (equal (instruction-kind$inline x)
                  (instruction-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-instruction-fix

(defthm consp-of-instruction-fix
  (consp (instruction-fix x))
  :rule-classes :type-prescription)