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Semantics32

Exec32-op-imm

Semantics of the non-shift instructions with the OP-IMM opcode [ISA:2.4.1].

Signature
(exec32-op-imm funct rd rs1 imm stat) → new-stat
Arguments: funct — Guard (op-imm-funct-p funct).; rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte12p imm).; stat — Guard (state32p stat).
Returns: new-stat — Type (state32p new-stat).

Definitions and Theorems

Function: exec32-op-imm

(defun exec32-op-imm (funct rd rs1 imm stat)
  (declare (xargs :guard (and (op-imm-funct-p funct)
                              (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte12p imm)
                              (state32p stat))))
  (let ((__function__ 'exec32-op-imm))
    (declare (ignorable __function__))
    (op-imm-funct-case funct
                       :addi (exec32-addi rd rs1 imm stat)
                       :slti (exec32-slti rd rs1 imm stat)
                       :sltiu (exec32-sltiu rd rs1 imm stat)
                       :andi (exec32-andi rd rs1 imm stat)
                       :ori (exec32-ori rd rs1 imm stat)
                       :xori (exec32-xori rd rs1 imm stat))))

Theorem: state32p-of-exec32-op-imm

(defthm state32p-of-exec32-op-imm
  (b* ((new-stat (exec32-op-imm funct rd rs1 imm stat)))
    (state32p new-stat))
  :rule-classes :rewrite)

Theorem: exec32-op-imm-of-op-imm-funct-fix-funct

(defthm exec32-op-imm-of-op-imm-funct-fix-funct
  (equal (exec32-op-imm (op-imm-funct-fix funct)
                        rd rs1 imm stat)
         (exec32-op-imm funct rd rs1 imm stat)))

Theorem: exec32-op-imm-op-imm-funct-equiv-congruence-on-funct

(defthm exec32-op-imm-op-imm-funct-equiv-congruence-on-funct
  (implies (op-imm-funct-equiv funct funct-equiv)
           (equal (exec32-op-imm funct rd rs1 imm stat)
                  (exec32-op-imm funct-equiv rd rs1 imm stat)))
  :rule-classes :congruence)

Theorem: exec32-op-imm-of-ubyte5-fix-rd

(defthm exec32-op-imm-of-ubyte5-fix-rd
  (equal (exec32-op-imm funct (ubyte5-fix rd)
                        rs1 imm stat)
         (exec32-op-imm funct rd rs1 imm stat)))

Theorem: exec32-op-imm-ubyte5-equiv-congruence-on-rd

(defthm exec32-op-imm-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec32-op-imm funct rd rs1 imm stat)
                  (exec32-op-imm funct rd-equiv rs1 imm stat)))
  :rule-classes :congruence)

Theorem: exec32-op-imm-of-ubyte5-fix-rs1

(defthm exec32-op-imm-of-ubyte5-fix-rs1
  (equal (exec32-op-imm funct rd (ubyte5-fix rs1)
                        imm stat)
         (exec32-op-imm funct rd rs1 imm stat)))

Theorem: exec32-op-imm-ubyte5-equiv-congruence-on-rs1

(defthm exec32-op-imm-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec32-op-imm funct rd rs1 imm stat)
                  (exec32-op-imm funct rd rs1-equiv imm stat)))
  :rule-classes :congruence)

Theorem: exec32-op-imm-of-ubyte12-fix-imm

(defthm exec32-op-imm-of-ubyte12-fix-imm
  (equal (exec32-op-imm funct rd rs1 (ubyte12-fix imm)
                        stat)
         (exec32-op-imm funct rd rs1 imm stat)))

Theorem: exec32-op-imm-ubyte12-equiv-congruence-on-imm

(defthm exec32-op-imm-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec32-op-imm funct rd rs1 imm stat)
                  (exec32-op-imm funct rd rs1 imm-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-op-imm-of-state32-fix-stat

(defthm exec32-op-imm-of-state32-fix-stat
  (equal (exec32-op-imm funct rd rs1 imm (state32-fix stat))
         (exec32-op-imm funct rd rs1 imm stat)))

Theorem: exec32-op-imm-state32-equiv-congruence-on-stat

(defthm exec32-op-imm-state32-equiv-congruence-on-stat
  (implies (state32-equiv stat stat-equiv)
           (equal (exec32-op-imm funct rd rs1 imm stat)
                  (exec32-op-imm funct rd rs1 imm stat-equiv)))
  :rule-classes :congruence)