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Semantics64

Exec64-op-imms

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

Signature
(exec64-op-imms funct rd rs1 imm stat) → new-stat
Arguments: funct — Guard (op-imms-funct-p funct).; rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte6p imm).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

Definitions and Theorems

Function: exec64-op-imms

(defun exec64-op-imms (funct rd rs1 imm stat)
  (declare (xargs :guard (and (op-imms-funct-p funct)
                              (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte6p imm)
                              (state64p stat))))
  (let ((__function__ 'exec64-op-imms))
    (declare (ignorable __function__))
    (op-imms-funct-case funct
                        :slli (exec64-slli rd rs1 imm stat)
                        :srli (exec64-srli rd rs1 imm stat)
                        :srai (exec64-srai rd rs1 imm stat))))

Theorem: state64p-of-exec64-op-imms

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: exec64-op-imms-of-ubyte6-fix-imm

(defthm exec64-op-imms-of-ubyte6-fix-imm
  (equal (exec64-op-imms funct rd rs1 (ubyte6-fix imm)
                         stat)
         (exec64-op-imms funct rd rs1 imm stat)))

Theorem: exec64-op-imms-ubyte6-equiv-congruence-on-imm

(defthm exec64-op-imms-ubyte6-equiv-congruence-on-imm
  (implies (acl2::ubyte6-equiv imm imm-equiv)
           (equal (exec64-op-imms funct rd rs1 imm stat)
                  (exec64-op-imms funct rd rs1 imm-equiv stat)))
  :rule-classes :congruence)

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

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

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

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