• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
    • Farray
    • Rp-rewriter
    • Riscv
      • Semantics
      • Features
      • States
      • Instructions
      • Decoding
      • Encoding
        • Encode
        • Decoding-of-encoding
          • Decode-of-encode-of-instr
          • Get-opcode-of-encode-of-instr
          • Get-funct3-of-encode-of-instr
          • Get-rd-of-encode-of-instr
          • Get-rs1-of-encode-of-instr
          • Get-fields-itype-of-encode-of-instr
          • Get-imm-itype-of-encode-of-instr
          • Get-rs2-of-encode-of-instr
          • Get-fields-rtype-of-encode-of-instr
          • Encode-injective
          • Get-funct7-of-encode-of-instr
          • Get-fields-utype-of-encode-of-instr
          • Get-imm-utype-of-encode-of-instr
          • Decode-of-encode
          • Get-fields-stype-of-encode-of-instr
          • Get-fields-btype-of-encode-of-instr
          • Get-imm-stype-of-encode-of-instr
          • Get-imm-jtype-of-encode-of-instr
          • Get-imm-btype-of-encode-of-instr
          • Get-fields-jtype-of-encode-of-instr
        • Encode-load-funct
        • Encode-store-funct
        • Encode-op-imms-32-funct
        • Encode-op-funct
        • Encode-op-32-funct
        • Encode-op-imms64-funct
        • Encode-op-imms32-funct
        • Encode-op-imm-funct
        • Encode-op-imm-32-funct
        • Encode-branch-funct
      • Reads-over-writes
      • Rv32im
      • Rv64im
      • Execution
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Community
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Encoding
• Decoding

Decoding-of-encoding

Theorems about decoding applied to encoding.

We show that decoding is left inverse of encoding over valid instructions: encoding a valid instruction and then decoding it yields the original instruction. As a consequence, encoding is injective over valid instructions: if two different instructions were encoded in the same way, the decoder would have to restore both from the same encoding, which is impossible since decoding is a function.

Subtopics

Decode-of-encode-of-instr

Theorems about decode applied to the encoding of different instructions.

Get-opcode-of-encode-of-instr

Theorems about get-opcode applied to the encoding of different instructions.

Get-funct3-of-encode-of-instr

Theorems about get-funct3 applied to the encoding of different instructions.

Get-rd-of-encode-of-instr

Theorems about get-rd applied to the encoding of different instructions.

Get-rs1-of-encode-of-instr

Theorems about get-rs1 applied to the encoding of different instructions.

Get-fields-itype-of-encode-of-instr

Theorems about get-fields-itype applied to the encoding of different instructions.

Get-imm-itype-of-encode-of-instr

Theorems about get-imm-itype applied to the encoding of different instructions.

Get-rs2-of-encode-of-instr

Theorems about get-rs2 applied to the encoding of different instructions.

Get-fields-rtype-of-encode-of-instr

Theorems about get-fields-rtype applied to the encoding of different instructions.

Encode-injective

Injectivity of encoding.

Get-funct7-of-encode-of-instr

Theorems about get-funct7 applied to the encoding of different instructions.

Get-fields-utype-of-encode-of-instr

Theorems about get-fields-utype applied to the encoding of different instructions.

Get-imm-utype-of-encode-of-instr

Theorems about get-imm-utype applied to the encoding of different instructions.

Decode-of-encode

Decoding the encoding of a valid instruction yields the original instruction.

Get-fields-stype-of-encode-of-instr

Theorems about get-fields-stype applied to the encoding of different instructions.

Get-fields-btype-of-encode-of-instr

Theorems about get-fields-btype applied to the encoding of different instructions.

Get-imm-stype-of-encode-of-instr

Theorems about get-imm-stype applied to the encoding of different instructions.

Get-imm-jtype-of-encode-of-instr

Theorems about get-imm-jtype applied to the encoding of different instructions.

Get-imm-btype-of-encode-of-instr

Theorems about get-imm-btype applied to the encoding of different instructions.

Get-fields-jtype-of-encode-of-instr

Theorems about get-fields-utype applied to the encoding of different instructions.