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  • Intro
    • Welcome
    • The Benefits of BSV Blockchain
    • What Can I Do?
    • Overview of GitHub repositories
    • Quick Start
  • Protocol
    • Introduction
    • BSV Blockchain
      • Blocks
      • Transactions
      • Proof of Work
      • Capabilities
      • Economic Model of Governance
      • Digital Asset Recovery
    • Network Policies
      • High-Level Architecture
      • Mining
      • Standard and Local Policies
      • Consensus Rules
      • Local Policies
    • Node Operations
      • Node Software
      • Bitcoin Server Network (BSN)
      • ChainTracker
      • Transaction Validation
      • UTXO Storage
      • Mempool
      • Block Assembler
      • Block Validation
      • Mining Software
      • Pruning transactions
      • Responsibilities of a Node
    • SPV Wallets, Overlays and SPV Processes
      • Simplified Payment Verification (SPV)
      • Instant Payments
      • Integrity Checks
      • SPV Wallets & Overlays
    • Transaction Lifecycle
      • Transaction Inputs and Outputs
      • Script
      • Transaction Flow
      • Constructing a transaction
      • Sequence Number and Time Locking
      • Transaction Templates
      • Transaction Processing
      • Opcodes used in Script
    • Privacy
      • Keys and Identity
      • Private vs Anonymous
      • Digital Signatures
      • Privacy on the Public Blockchain
  • Network Access Rules
    • Rules
      • Table of Contents
      • Background to the Rules
      • PART I - MASTER RULES
      • PART II - GENERAL RULES
      • PART III - ENFORCEMENT RULES
      • PART IV - DISPUTE RESOLUTION RULES
      • PART V - INTERPRETIVE RULES
    • FAQs
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  • Important Concepts
    • High Level
      • Web3
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      • UTXO vs Account Based
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        • Deep Dive
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  • Network Topology
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  • paymail
    • Overview
    • BRFC Specifications
      • Specification Documents
      • BRFC ID Assignment
    • Service Discovery
      • Host Discovery
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    • Public Key Infrastructure
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      • Basic Address Resolution
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      • PayTo Protocol Prefix
    • Verify Public Key Owner
    • Recommendations
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    • Local Blockchain Stack
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    • Business Use Cases
      • Creating a Tranche of Event Tickets
    • SDKs
      • Concepts
        • BEEF
        • Fees
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        • Transactions
        • Op Codes
        • Script Templates
        • Signatures
        • Verification
      • TypeScript
        • Node, CommonJS
        • React
        • Low Level
          • Verification
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          • Numbers & Points
          • Signatures
          • 42
          • ECDSA
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          • Scripts
        • Examples
          • Creating a Simple Transaction
          • Verifying a BEEF Structure
          • Creating Transactions with Inputs, Outputs and Templates
          • Creating the R-puzzle Script Template
          • Message Encryption and Decryption
          • Message Signing
          • Building a Custom Transaction Broadcast Client
          • Verifying Spends with Script Intrepreter
          • BIP32 Key Derivation with HD Wallets
          • Using Type 42 Key Derivation for Bitcoin Wallet Management
          • Creating a Custom Transaction Fee Model
          • Building a Pulse Block Headers Client
          • Using ECIES Encryption
      • Go
        • Examples
          • Simple Tx
          • Keys
          • Encryption
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      • Python
        • Examples
          • Simple Tx
          • Verifying BEEF
          • Complex Tx
          • Script Templates
          • Encryption
          • Message Signing
          • Building A Custom Broadcaster
          • HD Wallets
          • Linked Keys
          • Fees
          • Merkle Path Verification
          • ECIES
  • BSV Academy
    • Getting Started
    • BSV Basics: Protocol and Design
      • Introduction
        • Bit-Coin
      • The BSV Ledger
        • The Ledger
        • Triple Entry Accounting
        • Example
      • Coins and Transactions
        • Coins
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      • Theory
      • Conclusion
    • BSV Enterprise
      • Introduction
      • About BSV Blockchain
        • Introduction
        • Safe, Instant Transactions at a Predictably Low Cost
          • Reliably Low Fees
          • Comparison to Legacy Transaction Systems
          • Payment Channels
        • Scalability to Accommodate Global Demand
          • Big Blocks Show Big Potential
        • A Plan for Regulatory Acceptance
          • Ready-made Compliance
          • The Open BSV License
        • Protocol Stability
          • Building Foundations on a Bedrock of Stone
      • Technical Details
        • The Network
          • The Small World Network
          • Robust In Its Unstructured Simplicity
        • The Bitcoin SV Node Client
          • Teranode - The Future of BSV
        • The Protocol - Simple, Robust and Unbounded
          • What is the BSV Protocol?
        • Proof of Work
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        • Privacy and Identity
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        • The Working Blockchain
          • Pruning to Create a Working Blockchain
          • Building a Working Blockchain from a List of Block Headers
          • A World View Backed by Proof of Work
    • Hash Functions
      • What are Hash Functions?
        • The Differences Between Hashing and Encryption
        • The Three Important Properties of Hash Functions
        • The Hash Functions Found in BSV
      • Base58 and Base58Check
        • What is Base58 and Why Does Bitcoin use it?
        • What is Base58 and How Does BSV use it?
      • SHA256
        • BSV Transactions and SHA-256
        • BSV Blocks and SHA-256
        • Proof-of-Work and HASH-256
      • Walkthrough Implementation of SHA-256 in Golang
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      • RIPEMD-160
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      • Walkthrough Implementation of RIPEMD-160 in Golang
        • Overview of RIPEMD-160
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      • Doubla Hashing and BSV's Security
        • Why is Double Hashing Used in BSV
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    • Merkle Trees
      • The Merkle Tree
        • What is a Merkle Tree?
        • Why use a Merkle Tree?
        • Merkle Trees in Action
      • Merkles Trees in BSV
        • The Data Elements
        • Transaction Merkle Trees
        • Transaction Merkle Trees in Action
      • Merkle Trees and the Block Header
        • What is the Block Header
        • The Hash Puzzle
        • Proof-of-Work in Action
      • Merkle trees and Verifying Proof of Work
        • Broadcasting the Block
        • The Coinbase Transaction
        • Data Integrity of the Block
        • Saving Disk Space
      • Standarised Merkle Proof
        • What is a Merkle Proof?
        • The BSV Unified Merkle Path (BUMP) Standard
        • Simple and Composite Proofs
      • Merkle Trees and Simplified Payment Verification
        • SPV
        • Offline Payments
    • Digital Signatures
      • What are Digital Signatures
        • Background
        • Introduction
        • Digital Signatures Protocol
        • Properties of Digital Signatures
      • ECDSA Prerequisites
        • Disclaimer
        • Modular Arithmetic
        • Groups, Rings and Finite Fields
        • Discrete Logarithm Problem
        • Elliptic Curve Cryptography (ECC)
        • Discrete Logarithm Problem with Elliptic Curves
      • ECDSA
        • Introduction
        • ECDSA
        • Further Discussion
      • BSV and Digital Signatures
        • Introduction
        • BSV Transaction
        • ECDSA (secp256k1) for BSV Transaction
        • Summary
        • Signed Messages
        • Miner Identification and Digital Signatures
    • BSV Theory
      • Abstract
        • Peer-to-Peer Cash
        • Digital Signatures and Trusted Third Parties
        • Peer-to-Peer Network
        • Timechain and Proof-of-Work
        • CPU Power
        • Cooperation in the Network
        • Network Structure
        • Messaging Between Nodes
      • Introduction
        • Commerce on the Internet
        • Non Reversible Transactions
        • Privacy in Commerce
        • The Paradigm of Fraud Acceptance
        • What is Needed...
        • Protecting Sellers From Fraud
        • Proposed Solution
        • Security and Honesty
      • Transactions
        • Electronic Coins
        • Spending a Coin
        • Payee Verification
        • Existing Solutions
        • First Seen Rule
        • Broadcasting Transactions
        • Achieving Consensus
        • Proof of Acceptance
      • Timestamp Server
        • Timestamped Hashes
        • A Chain of Timestamped Hashes
      • Proof of Work
        • Hashcash
        • Scanning Random Space
        • Nonce
        • Immutable Work
        • Chain Effort
        • One CPU, One Vote
        • The Majority Decision
        • The Honest Chain
        • Attacking the Longest Chain
        • Controlling the Block Discovery Rate
      • Network
        • Running the Network
        • The Longest Chain
        • Simultaneous Blocks
        • Breaking the Tie
        • Missed Messages
      • Incentive
        • The Coinbase Transaction
        • Coin Distribution
        • Mining Analogy
        • Transaction Fees
        • The End of Inflation
        • Encouraging Honesty
        • The Attacker's Dilemma
      • Reclaiming Disk Space
        • Spent Transactions
        • The Merkle Tree
        • Compacting Blocks
        • Block Headers
      • Simplified Payment Verification
        • Full Network Nodes
        • Merkle Branches
        • Transaction Acceptance
        • Verification During Attack Situations
        • Maintaining an Attack
        • Invalid Block Relay System
        • Businesses Running Nodes
      • Combining and Splitting Value
        • Dynamically Sized Coins
        • Inputs and Outputs
        • A Typical Example
        • Fan Out
      • Privacy
        • Traditional Models
        • Privacy in Bitcoin
        • Public Records
        • Stock Exchange Comparison
        • Key Re-Use
        • Privacy - Assessment 2
        • Linking Inputs
        • Linking the Owner
      • Calculations
        • Attacking the Chain
        • Things the Attacker Cannot Achieve
        • The Only Thing an Attacker Can Achieve
        • The Binomial Random Walk
        • The Gambler's Ruin
        • Exponential Odds
        • Waiting For Confirmation
        • Attack Via Proof of Work
        • Vanishing Probabilities
      • Conclusion
        • Conclusion Explained
    • Introduction to Bitcoin Script
      • Chapter 1: About Bitcoin Script
        • 01 - Introduction
        • 02 - FORTH: A Precursor to Bitcoin Script
        • 03 - From FORTH to Bitcoin Script
        • 04 - Bitcoin's Transaction Protocol
        • 05 - Transaction Breakdown
        • 06 - nLockTime
        • 07 - The Script Evaluator
      • Chapter 2: Basic Script Syntax
        • 01 - Introduction
        • 02 - Rules Around Data and Scripting Grammar
        • 03 - The Stacks
      • Chapter 3: The Opcodes
        • 01 - Introduction
        • 02 - Constant Value and PUSHDATA Opcodes
        • 03 - IF Loops
        • 04 - OP_NOP, OP_VERIFY and its Derivatives
        • 05 - OP_RETURN
        • 06 - Stack Operations
        • 07 - Data transformation
        • 08 - Stack Data Queries
        • 09 - Bitwise transformations and Arithmetic
        • 10 - Cryptographic Functions
        • 11 - Disabled and Removed Opcodes
      • Chapter 4: Simple Scripts
        • 01 - Introduction
        • 01 - Pay to Public Key (P2PK)
        • 02 - Pay to Hash Puzzle
        • 03 - Pay to Public Key Hash (P2PKH)
        • 04 - Pay to MultiSig (P2MS)
        • 05 - Pay to MultiSignature Hash (P2MSH)
        • 06 - R-Puzzles
      • Chapter 5: OP_PUSH_TX
        • 01 - Turing Machines
        • 02 - Elliptic Curve Signatures in Bitcoin
        • 03 - OP_PUSH_TX
        • 04 - Signing and Checking the Pre-Image
        • 05 - nVersion
        • 06 - hashPrevouts
        • 07 - hashSequence
        • 08 - Outpoint
        • 09 - scriptLen and scriptPubKey
        • 10 - value
        • 11 - nSequence
        • 12 - hashOutputs
        • 13 - nLocktime
        • 14 - SIGHASH flags
      • Chapter 6: Conclusion
        • Conclusion
    • BSV Infrastructure
      • The Instructions
        • The Whitepaper
        • Steps to Run the Network
        • Step 1
        • Step 2
        • Step 3
        • Step 4
        • Step 5
        • Step 6
      • Rules and their Enforcement
        • Introduction
        • Consensus Rules
        • Block Consensus Rules
        • Transaction Consensus Rules
        • Script Language Rules
        • Standard Local Policies
      • Transactions, Payment Channels and Mempools
      • Block Assembly
      • The Small World Network
        • The Decentralisation of Power
        • Incentive Driven Behaviour
        • Lightspeed Propagation of Transactions
        • Ensuring Rapid Receipt and Propagation of New Blocks
        • Hardware Developments to Meet User Demand
        • Novel Service Delivery Methods
        • MinerID
      • Conclusion
  • Research and Development
    • BRCs
    • Technical Standards
  • Support & Contribution
    • Join Our Discord
    • GitHub
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On this page
  • Formal Grammar for Bitcoin Script
  • Validity of Script Rule
  • Numeric Value Size Rule
  • Clean Stack Rule
  • Other rules

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  1. BSV Academy
  2. Introduction to Bitcoin Script
  3. Chapter 2: Basic Script Syntax

02 - Rules Around Data and Scripting Grammar

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Last updated 3 months ago

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All data items in Bitcoin Script are a byte sequence. Some operations interpret their parameters as numeric or boolean values and require the item to fulfil the specifications of those types. Some operations produce items on the stack which are valid numeric or boolean values.

A byte sequence has a length and a value. The length of the byte sequence must be an integer greater or equal to zero and less than or equal to 2^32-1 (UINT32_MAX).

When a value is being treated as an integer, the most significant bit of the value is used to represent sign, with 1 indicating a negative value, and 0 indicating a positive value. The magnitude of its value is the same regardless of the sign bit's status.

Hexadecimal values 0x80, 0x0080, 0x00000080 are treated by arithmetic opcodes as 'negative zero'. Note the little endian notation. A script that terminates with a negative zero value on its stack will fail.

The byte sequence of length zero is called a “null item”.

Any data item can be interpreted as a boolean value. If the data item consists entirely of bytes with value zero (including negative zero), or the data item is a null item, then the boolean value of the item is false. Otherwise, the boolean value of the item is true.

A data item can be interpreted as a numeric value. The numeric value is encoded in a byte sequence using little-endian notation. When script items are processed using opcodes that perform mathematical functions, the node will treat any byte sequence of up to 750,000 bytes length as a numeric value, allowing for 'bignum' calculations to be performed in script.

Formal Grammar for Bitcoin Script

The Formal Grammar for Bitcoin Script is defined as part of the Bitcoin protocol. This contains the full set of approved opcodes and their exact spelling and function.

Script components

The complete script consists of two sections, the unlockScript (scriptSig) and the lockScript (scriptPubKey). The locking script is from the transaction output that is being spent, while the unlocking script is included in the transaction input that is spending the output.

Valid opcodes for unlockScript elements

Current consensus rules state that an unlockScript can only contain the first 96 opcodes, which allow constants and data to be pushed onto the stack. This requirement is a part of Validity of Script Consensus Rule, defined later.

IF loops

A branching operator (OP_IF or OP_NOTIF) must have a matching OP_ENDIF.

An OP_ELSE can only be included between a branching operator and OP_ENDIF pair. There can only be at most one OP_ELSE between a branching operator and an OP_ENDIF.

OP_RETURN

OP_RETURN may appear at any location in a valid script. The functionality of OP_RETURN has been restored and is defined later in the section on opcodes. Grammatically, any bytes after an OP_RETURN that is not in a branch block are not evaluated and there are no grammatical requirements for those bytes.

Note that disabled operations are part of this grammar. A disabled operation is grammatically correct but will produce a failure if executed.

Validity of Script Rule

The inputs and outputs of a transaction must be grammatically valid, as defined by the formal grammar rules from the previous page.

The unlocking scripts used in transaction inputs may only contain PUSHDATA operations, as defined by the formal grammar above.

Currently, the following 5 opcodes are disabled: OP_2MUL, OP_2DIV, OP_VER, OP_VERIF, OP_VERNOTIF.

Numeric Value Size Rule

For a byte sequence to validly represent a numeric value, the length of the byte sequence must be less than or equal to 750,000 bytes. A byte sequence that is larger than this is a valid byte sequence but is not a valid numeric value.

Note that while some operations require parameters to be valid numeric values, they may produce byte sequences which are not valid numeric values (for example, OP_MUL may produce a byte sequence which is too large to validly represent a numeric value).

Clean Stack Rule

The Clean Stack Rule requires that a valid solution leave just one non-zero value on the stack. This means you must remove any other data items from the stack in order to be able to solve a script correctly.

The clean stack rule is a later addition to the node client system and is not a fixed element of the Bitcoin protocol. It is possible that this rule may be removed in future.

Other rules

There are a multitude of other rules that define usage of the Bitcoin network, which are both set protocol level rules that cannot change, and flexible, consensus generated usage limits that give node operators the flexibility to create a flexible and useful environment for network users. For a deeper insight into these rules, please consider doing Introduction to Bitcoin Infrastructure.

This animation is INCORRECT and must be fixed both here and in Introduction to Infrastructure