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Semantics32

Exec32-branch

Semantics of the instructions with the BRANCH opcode [ISA:2.5.2].

Signature
(exec32-branch funct rs1 rs2 imm pc stat) → new-stat
Arguments: funct — Guard (branch-funct-p funct).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; imm — Guard (ubyte12p imm).; pc — Guard (ubyte32p pc).; stat — Guard (state32p stat).
Returns: new-stat — Type (state32p new-stat).

Definitions and Theorems

Function: exec32-branch

(defun exec32-branch (funct rs1 rs2 imm pc stat)
  (declare (xargs :guard (and (branch-funct-p funct)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (ubyte12p imm)
                              (ubyte32p pc)
                              (state32p stat))))
  (let ((__function__ 'exec32-branch))
    (declare (ignorable __function__))
    (branch-funct-case funct
                       :beq (exec32-beq rs1 rs2 imm pc stat)
                       :bne (exec32-bne rs1 rs2 imm pc stat)
                       :blt (exec32-blt rs1 rs2 imm pc stat)
                       :bltu (exec32-bltu rs1 rs2 imm pc stat)
                       :bge (exec32-bge rs1 rs2 imm pc stat)
                       :bgeu (exec32-bgeu rs1 rs2 imm pc stat))))

Theorem: state32p-of-exec32-branch

(defthm state32p-of-exec32-branch
  (b* ((new-stat (exec32-branch funct rs1 rs2 imm pc stat)))
    (state32p new-stat))
  :rule-classes :rewrite)

Theorem: exec32-branch-of-branch-funct-fix-funct

(defthm exec32-branch-of-branch-funct-fix-funct
  (equal (exec32-branch (branch-funct-fix funct)
                        rs1 rs2 imm pc stat)
         (exec32-branch funct rs1 rs2 imm pc stat)))

Theorem: exec32-branch-branch-funct-equiv-congruence-on-funct

(defthm exec32-branch-branch-funct-equiv-congruence-on-funct
  (implies (branch-funct-equiv funct funct-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct-equiv rs1 rs2 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-branch-of-ubyte5-fix-rs1

(defthm exec32-branch-of-ubyte5-fix-rs1
  (equal (exec32-branch funct (ubyte5-fix rs1)
                        rs2 imm pc stat)
         (exec32-branch funct rs1 rs2 imm pc stat)))

Theorem: exec32-branch-ubyte5-equiv-congruence-on-rs1

(defthm exec32-branch-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct rs1-equiv rs2 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-branch-of-ubyte5-fix-rs2

(defthm exec32-branch-of-ubyte5-fix-rs2
  (equal (exec32-branch funct rs1 (ubyte5-fix rs2)
                        imm pc stat)
         (exec32-branch funct rs1 rs2 imm pc stat)))

Theorem: exec32-branch-ubyte5-equiv-congruence-on-rs2

(defthm exec32-branch-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct rs1 rs2-equiv imm pc stat)))
  :rule-classes :congruence)

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

(defthm exec32-branch-of-ubyte12-fix-imm
  (equal (exec32-branch funct rs1 rs2 (ubyte12-fix imm)
                        pc stat)
         (exec32-branch funct rs1 rs2 imm pc stat)))

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

(defthm exec32-branch-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct rs1 rs2 imm-equiv pc stat)))
  :rule-classes :congruence)

Theorem: exec32-branch-of-ubyte32-fix-pc

(defthm exec32-branch-of-ubyte32-fix-pc
  (equal (exec32-branch funct rs1 rs2 imm (ubyte32-fix pc)
                        stat)
         (exec32-branch funct rs1 rs2 imm pc stat)))

Theorem: exec32-branch-ubyte32-equiv-congruence-on-pc

(defthm exec32-branch-ubyte32-equiv-congruence-on-pc
  (implies (acl2::ubyte32-equiv pc pc-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct rs1 rs2 imm pc-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-branch-of-state32-fix-stat

(defthm exec32-branch-of-state32-fix-stat
  (equal (exec32-branch funct rs1 rs2 imm pc (state32-fix stat))
         (exec32-branch funct rs1 rs2 imm pc stat)))

Theorem: exec32-branch-state32-equiv-congruence-on-stat

(defthm exec32-branch-state32-equiv-congruence-on-stat
  (implies (state32-equiv stat stat-equiv)
           (equal (exec32-branch funct rs1 rs2 imm pc stat)
                  (exec32-branch funct rs1 rs2 imm pc stat-equiv)))
  :rule-classes :congruence)