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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 3.35 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

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 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 Search Definitions in Scope Contribute Documentation The Agda Team and License Indices and tables Index Search Page Overview Note The Agda User Manual is a work-in-progress and is still incomplete

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 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 LaTeX Library Management Contribute Documentation The Agda Team and License Indices and tables Index Search Page Overview Note The Agda User Manual is a work-in-progress and is still incomplete

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.30 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3.33 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 3.38 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 3.38 Safe Agda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 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 Search Definitions in Scope Contribute Documentation The Agda Team and License Indices and tables Index Search Page Overview Note The Agda User Manual is a work-in-progress and is still incomplete