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: 2024-10-22T13:16:13.000Z (about 1 year ago)
Last Synced: 2024-10-23T11:55:59.541Z (about 1 year ago)
Topics: formal-specification, formal-verification, programming-language
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- Readme: README.md
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# 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 domain-specific programming language designed by [Inferara](https://inferara.com) to enable Web3 developers to formulate properties of the native application algorithms in a familiar format similar to how unit tests are written.

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.

> [!IMPORTANT]

> Inference is a Web3 native applications-oriented, formal specification language.

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-forall) Forall

    - [§3.1.2](./general-description.md#312-exists) Exists

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

    - [§3.1.4](./general-description.md#314-uzumaki) Uzumaki

      - [§3.1.4.1](./general-description.md#3141-semantics) Semantics

      - [§3.1.4.2](./general-description.md#3142-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-angle-brackets) Angle Brackets

      - [§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-poly-blockchain-design) Poly-blockchain 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-assign) Assign

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

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

  - [§8.2](./expressions.md#82-member-access) Member Access

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

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

  - [§8.3](./expressions.md#83-array-index-access) Array Index Access

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

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

  - [§8.4](./expressions.md#84-function-call) Function Call

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

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

  - [§8.5](./expressions.md#85-parenthesized) Parenthesized

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

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

  - [§8.6](./expressions.md#86-unary-operators) Unary Operators

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

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

  - [§8.7](./expressions.md#87-binary-operators) Binary Operators

    - [§8.7.1](./expressions.md#871-description) Description

    - [§8.7.2](./expressions.md#872-examples) Examples

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

  - [§9.1](./statements.md#91-block) Block

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

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

  - [§9.2](./statements.md#92-return) Return

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

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

  - [§9.3](./statements.md#93-forall) Forall

  - [§9.4](./statements.md#94-exists) Exists

  - [§9.5](./statements.md#95-assume) Assume

    - [§9.5.1](./statements.md#951-description) Description

    - [§9.5.2](./statements.md#952-examples) Examples

  - [§9.6](./statements.md#96-unique) Unique

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

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

  - [§9.7](./statements.md#97-loop) Loop

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

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

  - [§9.8](./statements.md#98-if) If

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

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

  - [§9.9](./statements.md#99-variable-definition) Variable Definition

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

    - [§9.9.2](./statements.md#992-value-modifiers) Value Modifiers

      - [§9.9.2.1](./statements.md#9921-uzumaki) Uzumaki

    - [§9.9.3](./statements.md#993-examples) Examples

  - [§9.10](./statements.md#910-type-definition) Type Definition

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

    - [§9.10.2](./statements.md#9102-examples) Examples

  - [§9.11](./statements.md#911-assert) Assert

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

    - [§9.11.2](./statements.md#9112-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-modifiers) Modifiers

        - [§11.1.2.1](./functions.md#11121-forall) `forall`

    - [§11.1.3](./functions.md#1113-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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