Agda User Manual Release 2.6.2 The Agda Team Jun 19, 2021 Contents 1 Overview 3 2 Getting Started 5 2.1 What is Agda? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 ‘Hello world’ in Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 A Taste of Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Cubical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Welcome to Agda’s documentation! Overview Getting Started What is Agda? Prerequisites Installation ‘Hello world’ in Agda Quick Guide to Editing, Type Checking and Compiling Agda Code A List of Tutorials Tutorials Language Reference Abstract definitions Built-ins Coinduction Copatterns Core language Cubical Cumulativity Data Types Flat Modality Foreign Function Interface Function Definitions Function Types Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Agda Sized Types Syntactic Sugar Syntax Declarations Telescopes Termination Checking Universe Levels With-Abstraction

Welcome to Agda’s documentation! Overview Getting Started What is Agda? Prerequisites Installation ‘Hello world’ in Agda Quick Guide to Editing, Type Checking and Compiling Agda Code A List of Tutorials Tutorials Language Reference Abstract definitions Built-ins Coinduction Copatterns Core language Cubical Data Types Foreign Function Interface Function Definitions Function Types Generalization of Declared Pattern Synonyms Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Safe Agda Sized Types Syntactic Sugar Syntax Declarations Telescopes Termination Checking Universe Levels With-Abstraction

Welcome to Agda’s documentation! Overview Getting Started Prerequisites Installation Quick Guide to Editing, Type Checking and Compiling Agda Code Language Reference Abstract definitions Built-ins Recursion Pattern Synonyms Positivity Checking Postulates Pragmas Record Types Reflection Rewriting Safe Agda Sized Types Syntactic Sugar Telescopes Termination Checking Universe Levels With-Abstraction Without LaTeX Library Management Contribute Documentation The Agda License The Agda Team Indices and tables Index Search Page Overview Note The Agda User Manual is a work-in-progress and is still incomplete

Agda User Manual Release 2.6.0 The Agda Team Apr 12, 2019 Contents 1 Overview 1 2 Getting Started 3 2.1 What is Agda? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 ‘Hello world’ in Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Quick Guide to Editing, Type Checking and Compiling Agda Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6 Cubical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Agda User Manual Release 2.6.1.2 The Agda Team Feb 03, 2021 Contents 1 Overview 3 2 Getting Started 5 2.1 What is Agda? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 ‘Hello world’ in Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Quick Guide to Editing, Type Checking and Compiling Agda Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 Cubical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Agda User Manual Release 2.6.4.1 The Agda Team Nov 30, 2023 CONTENTS 1 Overview 3 2 Getting Started 5 2.1 What is Agda? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 ‘Hello world’ in Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 A Taste of Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.7 Cubical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.8 Cubical compatible . . . . . . . . . . . . . .

Agda User Manual Release 2.6.4.3 The Agda Team Mar 06, 2024 CONTENTS 1 Overview 3 2 Getting Started 5 2.1 What is Agda? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 ‘Hello world’ in Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 A Taste of Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Cubical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.8 Cubical compatible . . . . . . . . . . . . . .

Agda User Manual Release 2.5.4 The Agda Team Jun 02, 2018 Contents 1 Overview 1 2 Getting Started 3 2.1 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Quick Guide to Editing, Type Checking and Compiling Agda Code . . . . . . . . . . . . . . . . . . 6 3 Language Reference 9 3.1 Abstract definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.27 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Welcome to Agda’s documentation! Overview Getting Started What is Agda? Prerequisites Installation ‘Hello world’ in Agda Quick Guide to Editing, Type Checking and Compiling Agda Code A List of Tutorials Tutorials Language Reference Abstract definitions Built-ins Coinduction Copatterns Core language Cubical Cumulativity Data Types Flat Modality Foreign Function Interface Function Definitions Function Types Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Agda Sized Types Syntactic Sugar Syntax Declarations Telescopes Termination Checking Universe Levels With-Abstraction