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• Instr

Instr-fix

Fixing function for instr structures.

Signature

(instr-fix x) → new-x

Arguments

x — Guard (instrp x).

Returns

new-x — Type (instrp new-x).

Definitions and Theorems

Function: instr-fix$inline

(defun instr-fix$inline (x)
 (declare (xargs :guard (instrp x)))
 (let ((__function__ 'instr-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (instr-kind x)
    (:op-imm (b* ((funct (op-imm-funct-fix (std::da-nth 0 (cdr x))))
                  (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
                  (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
                  (imm (ubyte12-fix (std::da-nth 3 (cdr x)))))
               (cons :op-imm (list funct rd rs1 imm))))
    (:op-imms32
         (b* ((funct (op-imms-funct-fix (std::da-nth 0 (cdr x))))
              (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
              (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
              (imm (ubyte5-fix (std::da-nth 3 (cdr x)))))
           (cons :op-imms32 (list funct rd rs1 imm))))
    (:op-imms64
         (b* ((funct (op-imms-funct-fix (std::da-nth 0 (cdr x))))
              (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
              (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
              (imm (ubyte6-fix (std::da-nth 3 (cdr x)))))
           (cons :op-imms64 (list funct rd rs1 imm))))
    (:op-imm-32
         (b* ((funct (op-imm-32-funct-fix (std::da-nth 0 (cdr x))))
              (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
              (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
              (imm (ubyte12-fix (std::da-nth 3 (cdr x)))))
           (cons :op-imm-32 (list funct rd rs1 imm))))
    (:op-imms-32
         (b* ((funct (op-imms-32-funct-fix (std::da-nth 0 (cdr x))))
              (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
              (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
              (imm (ubyte5-fix (std::da-nth 3 (cdr x)))))
           (cons :op-imms-32 (list funct rd rs1 imm))))
    (:lui (b* ((rd (ubyte5-fix (std::da-nth 0 (cdr x))))
               (imm (ubyte20-fix (std::da-nth 1 (cdr x)))))
            (cons :lui (list rd imm))))
    (:auipc (b* ((rd (ubyte5-fix (std::da-nth 0 (cdr x))))
                 (imm (ubyte20-fix (std::da-nth 1 (cdr x)))))
              (cons :auipc (list rd imm))))
    (:op (b* ((funct (op-funct-fix (std::da-nth 0 (cdr x))))
              (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
              (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
              (rs2 (ubyte5-fix (std::da-nth 3 (cdr x)))))
           (cons :op (list funct rd rs1 rs2))))
    (:op-32 (b* ((funct (op-32-funct-fix (std::da-nth 0 (cdr x))))
                 (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
                 (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
                 (rs2 (ubyte5-fix (std::da-nth 3 (cdr x)))))
              (cons :op-32 (list funct rd rs1 rs2))))
    (:jal (b* ((rd (ubyte5-fix (std::da-nth 0 (cdr x))))
               (imm (ubyte20-fix (std::da-nth 1 (cdr x)))))
            (cons :jal (list rd imm))))
    (:jalr (b* ((rd (ubyte5-fix (std::da-nth 0 (cdr x))))
                (rs1 (ubyte5-fix (std::da-nth 1 (cdr x))))
                (imm (ubyte12-fix (std::da-nth 2 (cdr x)))))
             (cons :jalr (list rd rs1 imm))))
    (:branch (b* ((funct (branch-funct-fix (std::da-nth 0 (cdr x))))
                  (rs1 (ubyte5-fix (std::da-nth 1 (cdr x))))
                  (rs2 (ubyte5-fix (std::da-nth 2 (cdr x))))
                  (imm (ubyte12-fix (std::da-nth 3 (cdr x)))))
               (cons :branch (list funct rs1 rs2 imm))))
    (:load (b* ((funct (load-funct-fix (std::da-nth 0 (cdr x))))
                (rd (ubyte5-fix (std::da-nth 1 (cdr x))))
                (rs1 (ubyte5-fix (std::da-nth 2 (cdr x))))
                (imm (ubyte12-fix (std::da-nth 3 (cdr x)))))
             (cons :load (list funct rd rs1 imm))))
    (:store (b* ((funct (store-funct-fix (std::da-nth 0 (cdr x))))
                 (rs1 (ubyte5-fix (std::da-nth 1 (cdr x))))
                 (rs2 (ubyte5-fix (std::da-nth 2 (cdr x))))
                 (imm (ubyte12-fix (std::da-nth 3 (cdr x)))))
              (cons :store (list funct rs1 rs2 imm)))))
   :exec x)))

Theorem: instrp-of-instr-fix

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

Theorem: instr-fix-when-instrp

(defthm instr-fix-when-instrp
  (implies (instrp x)
           (equal (instr-fix x) x)))

Function: instr-equiv$inline

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

Theorem: instr-equiv-is-an-equivalence

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

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

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

Theorem: instr-fix-under-instr-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-instr-fix

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