https://github.com/inferara/inference-language-spec

🌀 Inference programming language specification
https://github.com/inferara/inference-language-spec
formal-specification formal-verification programming-language
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🌀 Inference programming language specification
Host: GitHub
URL: https://github.com/inferara/inference-language-spec
Owner: Inferara
License: other
Created: 2024-06-30T09:42:01.000Z (over 1 year ago)
Default Branch: main
Last Pushed: 2025-12-14T04:58:40.000Z (3 months ago)
Last Synced: 2025-12-16T06:22:15.422Z (3 months ago)
Topics: formal-specification, formal-verification, programming-language
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Forks: 1
Open Issues: 1
Metadata Files:
- Readme: README.md
- Funding: .github/FUNDING.yml
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README

          ![alt text](./assets/inference-logo-oulined-shaped-font.svg)

# 🌀 Inference programming language specification

> [!WARNING]

> This document is a work in progress. The content is subject to change. Some sections may be incomplete or missing. Please stay tuned for updates.

Inference is a programming language that defines a high-assurance, deterministic computing model with non-deterministic extensions designed by [Inferara](https://inferara.com) for developing verifiable programs. It enables developers to write both executable code and formal specifications in a unified language, using a familiar syntax similar to imperative programming languages.

Inference allows formal proof of the correctness of the specified properties to be expressed as a theorem-prover theory and verified in an automated way. The compiler (`infc`) targets multiple backends: generating executable binaries (currently WASM via LLVM IR) for deployment and proof units (Rocq) for formal verification.

> [!IMPORTANT]

> Inference is designed for both high-assurance application development and formal specification. While Web3 applications are a primary use case, the language's safety guarantees (determinism, no floating-point, static typing) make it suitable for any critical system requiring formal verification.

This repository contains the specification of the Inference programming language. The specification is divided into several sections, each describing a specific aspect of the language. The language is designed to be simple and easy to learn, and its syntax is concise and similar to Rust.

## Table of contents

- [Foreword](./foreword.md)

- [§1](./introduction.md) Introduction

- [§2](./terms-and-definitions.md) Terms and definitions

  - [§2.1](./terms-and-definitions.md#21-dapp) DApp

  - [§2.2](./terms-and-definitions.md#22-infc) `infc`

  - [§2.3](./terms-and-definitions.md#23-module) Module

  - [§2.4](./terms-and-definitions.md#24-theory) Theory

  - [§2.5](./terms-and-definitions.md#25-proof-unit) Proof-Unit

- [§3](./general-description.md) General description

  - [§3.1](./general-description.md#31-non-deterministic-computations) Non-Deterministic Computations

    - [§3.1.1](./general-description.md#311-uzumaki) Uzumaki

    - [§3.1.2](./general-description.md#312-forall) Forall

    - [§3.1.3](./general-description.md#313-assume) Assume

    - [§3.1.4](./general-description.md#314-exists) Exists

    - [§3.1.5](./general-description.md#315-unique) Unique

    - [§3.1.6](./general-description.md#316-semantics) Semantics

    - [§3.1.7](./general-description.md#317-examples) Examples

  - [§3.2](./general-description.md#32-compiler-design) Compiler Design

  - [§3.3](./general-description.md#33-automated-theorem-proving) Automated Theorem Proving

  - [§3.4](./general-description.md#34-restrictions) Restrictions

- [§4](./lexical-structure.md) Lexical structure

  - [§4.1](./lexical-structure.md#41-comments) Comments

    - [§4.1.](./lexical-structure.md#411-description) Description

    - [§4.1.2](./lexical-structure.md#412-examples) Examples

  - [§4.2](./lexical-structure.md#42-keywords) Keywords

  - [§4.3](./lexical-structure.md#43-identifiers) Identifiers

    - [§4.3.1](./lexical-structure.md#431-description) Description

    - [§4.3.2](./lexical-structure.md#432-examples) Examples

  - [§4.4](./lexical-structure.md#44-reserved-identifiers) Reserved Identifiers

  - [§4.5](./lexical-structure.md#45-qualified-identifiers) Qualified Identifiers

    - [§4.5.1](./lexical-structure.md#451-description) Description

    - [§4.5.2](./lexical-structure.md#452-examples) Examples

  - [§4.6](./lexical-structure.md#46-member-access) Member Access

    - [§4.6.1](./lexical-structure.md#461-description) Description

    - [§4.6.2](./lexical-structure.md#462-examples) Examples

  - [§4.7](./lexical-structure.md#47-literals) Literals

    - [§4.7.1](./lexical-structure.md#471-bool) Bool

      - [§4.7.1.1](./lexical-structure.md#4711-description) Description

      - [§4.7.1.2](./lexical-structure.md#4712-examples) Examples

    - [§4.7.2](./lexical-structure.md#472-unit) Unit

      - [§4.7.2.1](./lexical-structure.md#4721-description) Description

      - [§4.7.2.2](./lexical-structure.md#4722-examples) Examples

  - [§4.8](./lexical-structure.md#48-right-arrow) Right Arrow

    - [§4.8.1](./lexical-structure.md#481-description) Description

    - [§4.8.2](./lexical-structure.md#482-examples) Examples

  - [§4.9](./lexical-structure.md#49-terminator) Terminator

    - [§4.9.1](./lexical-structure.md#491-description) Description

    - [§4.9.2](./lexical-structure.md#492-examples) Examples

  - [§4.10](./lexical-structure.md#410-braces) Braces

    - [§4.10.1](./lexical-structure.md#4101-curly-braces) Curly Braces

      - [§4.10.1.1](./lexical-structure.md#41011-description) Description

      - [§4.10.1.2](./lexical-structure.md#41012-examples) Examples

    - [§4.10.2](./lexical-structure.md#4102-parentheses) Parentheses

      - [§4.10.2.1](./lexical-structure.md#41021-description) Description

      - [§4.10.2.2](./lexical-structure.md#41022-examples) Examples

    - [§4.10.3](./lexical-structure.md#4103-square-brackets) Square Brackets

      - [§4.10.3.1](./lexical-structure.md#41031-description) Description

      - [§4.10.3.2](./lexical-structure.md#41032-examples) Examples

    - [§4.10.4](./lexical-structure.md#4104-prime-symbol) Prime Symbol

      - [§4.10.4.1](./lexical-structure.md#41041-description) Description

      - [§4.10.4.2](./lexical-structure.md#41042-examples) Examples

- [§5](./basic-concepts.md) Basic concepts

  - [§5.1](./basic-concepts.md#51-specification-definition) Specification Definition

  - [§5.2](./basic-concepts.md#52-specification-is-not-a-program) Specification Is Not a Program

  - [§5.3](./basic-concepts.md#53-execution-model) Execution Model

  - [§5.4](./basic-concepts.md#54-non-deterministic-execution) Non-deterministic Execution

  - [§5.5](./basic-concepts.md#55-platform-specific-execution) Platform-specific Execution

  - [§5.6](./basic-concepts.md#56-platform-agnostic-design) Platform Agnostic Design

  - [§5.7](./basic-concepts.md#57-automated-reasoning) Automated Reasoning

  - [§5.8](./basic-concepts.md#58-correctness-certificate) Correctness Certificate

- [§6](./types.md) Types

  - [§6.1](./types.md#61-unit) Unit

    - [§6.1.1](./types.md#611-description) Description

    - [§6.1.2](./types.md#612-examples) Examples

  - [§6.2](./types.md#62-elementary-types) Elementary Types

    - [§6.2.1](./types.md#621-boolean) Boolean

      - [§6.2.1.1](./types.md#6211-description) Description

      - [§6.2.1.2](./types.md#6212-examples) Examples

    - [§6.2.2](./types.md#622-integers) Integers

      - [§6.2.2.1](./types.md#6221-description) Description

      - [§6.2.2.2](./types.md#6222-examples) Examples

    - [§6.2.3](./types.md#623-unsigned-integers) Unsigned Integers

      - [§6.2.3.1](./types.md#6231-description) Description

      - [§6.2.3.2](./types.md#6232-examples) Examples

    - [§6.3](./types.md#63-array) Array

      - [§6.3.1](./types.md#631-description) Description

      - [§6.3.2](./types.md#632-examples) Examples

    - [§6.4](./types.md#64-function-type) Function type

      - [§6.4.1](./types.md#641-description) Description

      - [§6.4.2](./types.md#642-examples) Examples

    - [§6.5](./types.md#65-user-defined-types) User-defined Types

      - [§6.5.1](./types.md#651-description) Description

- [§7](./variables.md) Variables

  - [§7.1](./variables.md#71-general-description) General Description

  - [§7.2](./variables.md#72-variable-categories) Variable Categories

    - [§7.2.1](./variables.md#721-local-variables) Local Variables

      - [§7.2.1.1](./variables.md#7211-description) Description

      - [§7.2.1.2](./variables.md#7212-examples) Examples

    - [§7.2.2](./variables.md#722-array-elements) Array Elements

      - [§7.2.2.1](./variables.md#7221-description) Description

      - [§7.2.2.2](./variables.md#7222-examples) Examples

  - [§7.3](./variables.md#73-default-values) Default Values

    - [§7.3.1](./variables.md#731-description) Description

    - [§7.3.2](./variables.md#732-examples) Examples

  - [§7.4](./variables.md#74-variable-definition-and-assignment) Variable Definition and Assignment

    - [§7.4.1](./variables.md#741-description) Description

    - [§7.4.2](./variables.md#742-block-statement) Block Statement

      - [§7.4.2.1](./variables.md#7421-description) Description

      - [§7.4.2.2](./variables.md#7422-examples) Examples

    - [§7.4.3](./variables.md#743-loop-statement) Loop Statement

      - [§7.4.3.1](./variables.md#7431-description) Description

      - [§7.4.3.2](./variables.md#7432-examples) Examples

- [§8](./expressions.md) Expressions

  - [§8.1](./expressions.md#81-member-access) Member Access

    - [§8.1.1](./expressions.md#811-description) Description

    - [§8.1.2](./expressions.md#812-examples) Examples

  - [§8.2](./expressions.md#82-array-index-access) Array Index Access

    - [§8.2.1](./expressions.md#821-description) Description

    - [§8.2.2](./expressions.md#822-examples) Examples

  - [§8.3](./expressions.md#83-function-call) Function Call

    - [§8.3.1](./expressions.md#831-description) Description

    - [§8.3.2](./expressions.md#832-examples) Examples

  - [§8.4](./expressions.md#84-parenthesized) Parenthesized

    - [§8.4.1](./expressions.md#841-description) Description

    - [§8.4.2](./expressions.md#842-examples) Examples

  - [§8.5](./expressions.md#85-unary-operators) Unary Operators

    - [§8.5.1](./expressions.md#851-description) Description

    - [§8.5.2](./expressions.md#852-examples) Examples

  - [§8.6](./expressions.md#86-binary-operators) Binary Operators

    - [§8.6.1](./expressions.md#861-description) Description

    - [§8.6.2](./expressions.md#862-examples) Examples

- [§9](./statements.md#9-statements) Statements

  - [§9.1](./statements.md#91-assign) Assign

    - [§9.1.1](./statements.md#911-description) Description

    - [§9.1.2](./statements.md#912-examples) Examples

  - [§9.2](./statements.md#92-block) Block

    - [§9.2.1](./statements.md#921-description) Description

    - [§9.2.2](./statements.md#922-examples) Examples

  - [§9.3](./statements.md#93-return) Return

    - [§9.3.1](./statements.md#931-description) Description

    - [§9.3.2](./statements.md#932-examples) Examples

  - [§9.4](./statements.md#94-forall) Forall

  - [§9.5](./statements.md#95-exists) Exists

  - [§9.6](./statements.md#96-assume) Assume

    - [§9.6.1](./statements.md#961-description) Description

    - [§9.6.2](./statements.md#962-examples) Examples

  - [§9.7](./statements.md#97-unique) Unique

    - [§9.7.1](./statements.md#971-description) Description

    - [§9.7.2](./statements.md#972-examples) Examples

  - [§9.8](./statements.md#98-loop) Loop

    - [§9.8.1](./statements.md#981-description) Description

    - [§9.8.2](./statements.md#982-examples) Examples

  - [§9.9](./statements.md#99-if) If

    - [§9.9.1](./statements.md#991-description) Description

    - [§9.9.2](./statements.md#992-examples) Examples

  - [§9.10](./statements.md#910-variable-definition) Variable Definition

    - [§9.10.1](./statements.md#9101-description) Description

    - [§9.10.2](./statements.md#9102-value-modifiers) Value Modifiers

      - [§9.10.2.1](./statements.md#91021-uzumaki) Uzumaki

    - [§9.10.3](./statements.md#9103-examples) Examples

  - [§9.11](./statements.md#911-type-definition) Type Definition

    - [§9.11.1](./statements.md#9111-description) Description

    - [§9.11.2](./statements.md#9112-examples) Examples

  - [§9.12](./statements.md#912-assert) Assert

    - [§9.12.1](./statements.md#9121-description) Description

    - [§9.12.2](./statements.md#9122-examples) Examples

- [§10](./definitions.md) Definitions

  - [§10.1](./definitions.md#101-constant) Constant

    - [§10.1.1](./definitions.md#1011-description) Description

    - [§10.1.2](./definitions.md#1012-examples) Examples

  - [§10.2](./definitions.md#102-function) Function

    - [§10.2.1](./definitions.md#1021-description) Description

    - [§10.2.2](./definitions.md#1022-examples) Examples

  - [§10.3](./definitions.md#103-external-function) External Function

    - [§10.3.1](./definitions.md#1031-description) Description

    - [§10.3.2](./definitions.md#1032-examples) Examples

  - [§10.4](./definitions.md#104-type) Type

    - [§10.4.1](./definitions.md#1041-description) Description

    - [§10.4.2](./definitions.md#1042-examples) Examples

  - [§10.5](./definitions.md#105-spec) Spec

    - [§10.5.1](./definitions.md#1051-description) Description

    - [§10.5.2](./definitions.md#1052-examples) Examples

  - [§10.6](./definitions.md#106-enum) Enum

    - [§10.6.1](./definitions.md#1061-description) Description

    - [§10.6.2](./definitions.md#1062-examples) Examples

  - [§10.7](./definitions.md#107-struct) Struct

    - [§10.7.1](./definitions.md#1071-description) Description

    - [§10.7.2](./definitions.md#1072-examples) Examples

- [§11](./functions.md) Functions

  - [§11.1](./functions.md#111-function-definition) Function Definition

    - [§11.1.1](./functions.md#1111-description) Description

    - [§11.1.2](./functions.md#1112-declaring-a-function) Declaring a function

      - [§11.1.3](./functions.md#1113-modifiers) Modifiers

        - [§11.1.3.1](./functions.md#11131-forall) `forall`

    - [§11.1.4](./functions.md#1114-examples) Examples

  - [§11.2](./functions.md#112-external-function) External Function

    - [§11.2.1](./functions.md#1121-description) Description

    - [§11.2.2](./functions.md#1122-examples) Examples

  - [§11.3](./functions.md#113-high-order-functions) High-order Functions

    - [§11.3.1](./functions.md#1131-description) Description

    - [§11.3.2](./functions.md#1132-examples) Examples

- [§12](./constants.md) Constants

  - [§12.1](./constants.md#121-description) Description

  - [§12.2](./constants.md#122-examples) Examples

- [§13](./directives.md) Directives

  - [§13.1](./directives.md#131-use-directive) Use Directive

    - [§13.1.1](./directives.md#1311-description) Description

    - [§13.1.2](./directives.md#1312-examples) Examples

- [§A](./grammar.md) Grammar

- [§B](./standard-library.md) Standard Library

- [§C](./comments.md) Comments

  - [C001](./comments.md#c001)

  - [C002](./comments.md#c002)

- [§D](./examples.md) Examples

- [§E](./bibliography.md) Bibliography

  - [§E.1](./bibliography.md#e1-inferara-papers) Inferara Papers

  - [§E.2](./bibliography.md#e2-books) Books

  - [§E.3](./bibliography.md#e3-articles) Articles

  - [§E.4](./bibliography.md#e4-links) Links
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