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Semantics64

Exec64-op

Semantics of the instructions with the OP opcode [ISA:2.4.2] [ISA:4.2.2] [ISA:13.1] [ISA:13.2].

Signature
(exec64-op funct rd rs1 rs2 stat) → new-stat
Arguments: funct — Guard (op-funct-p funct).; rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

Definitions and Theorems

Function: exec64-op

(defun exec64-op (funct rd rs1 rs2 stat)
  (declare (xargs :guard (and (op-funct-p funct)
                              (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state64p stat))))
  (let ((__function__ 'exec64-op))
    (declare (ignorable __function__))
    (op-funct-case funct
                   :add (exec64-add rd rs1 rs2 stat)
                   :sub (exec64-sub rd rs1 rs2 stat)
                   :slt (exec64-slt rd rs1 rs2 stat)
                   :sltu (exec64-sltu rd rs1 rs2 stat)
                   :and (exec64-and rd rs1 rs2 stat)
                   :or (exec64-or rd rs1 rs2 stat)
                   :xor (exec64-xor rd rs1 rs2 stat)
                   :sll (exec64-sll rd rs1 rs2 stat)
                   :srl (exec64-srl rd rs1 rs2 stat)
                   :sra (exec64-sra rd rs1 rs2 stat)
                   :mul (exec64-mul rd rs1 rs2 stat)
                   :mulh (exec64-mulh rd rs1 rs2 stat)
                   :mulhu (exec64-mulhu rd rs1 rs2 stat)
                   :mulhsu (exec64-mulhsu rd rs1 rs2 stat)
                   :div (exec64-div rd rs1 rs2 stat)
                   :divu (exec64-divu rd rs1 rs2 stat)
                   :rem (exec64-rem rd rs1 rs2 stat)
                   :remu (exec64-remu rd rs1 rs2 stat))))

Theorem: state64p-of-exec64-op

(defthm state64p-of-exec64-op
  (b* ((new-stat (exec64-op funct rd rs1 rs2 stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: exec64-op-of-op-funct-fix-funct

(defthm exec64-op-of-op-funct-fix-funct
  (equal (exec64-op (op-funct-fix funct)
                    rd rs1 rs2 stat)
         (exec64-op funct rd rs1 rs2 stat)))

Theorem: exec64-op-op-funct-equiv-congruence-on-funct

(defthm exec64-op-op-funct-equiv-congruence-on-funct
  (implies (op-funct-equiv funct funct-equiv)
           (equal (exec64-op funct rd rs1 rs2 stat)
                  (exec64-op funct-equiv rd rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-of-ubyte5-fix-rd

(defthm exec64-op-of-ubyte5-fix-rd
  (equal (exec64-op funct (ubyte5-fix rd)
                    rs1 rs2 stat)
         (exec64-op funct rd rs1 rs2 stat)))

Theorem: exec64-op-ubyte5-equiv-congruence-on-rd

(defthm exec64-op-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec64-op funct rd rs1 rs2 stat)
                  (exec64-op funct rd-equiv rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-of-ubyte5-fix-rs1

(defthm exec64-op-of-ubyte5-fix-rs1
  (equal (exec64-op funct rd (ubyte5-fix rs1)
                    rs2 stat)
         (exec64-op funct rd rs1 rs2 stat)))

Theorem: exec64-op-ubyte5-equiv-congruence-on-rs1

(defthm exec64-op-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec64-op funct rd rs1 rs2 stat)
                  (exec64-op funct rd rs1-equiv rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-of-ubyte5-fix-rs2

(defthm exec64-op-of-ubyte5-fix-rs2
  (equal (exec64-op funct rd rs1 (ubyte5-fix rs2)
                    stat)
         (exec64-op funct rd rs1 rs2 stat)))

Theorem: exec64-op-ubyte5-equiv-congruence-on-rs2

(defthm exec64-op-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec64-op funct rd rs1 rs2 stat)
                  (exec64-op funct rd rs1 rs2-equiv stat)))
  :rule-classes :congruence)

Theorem: exec64-op-of-state64-fix-stat

(defthm exec64-op-of-state64-fix-stat
  (equal (exec64-op funct rd rs1 rs2 (state64-fix stat))
         (exec64-op funct rd rs1 rs2 stat)))

Theorem: exec64-op-state64-equiv-congruence-on-stat

(defthm exec64-op-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (exec64-op funct rd rs1 rs2 stat)
                  (exec64-op funct rd rs1 rs2 stat-equiv)))
  :rule-classes :congruence)