Agda User Manual Release 2.6.2 The Agda Team Jun 19, 2021 Powered by TCPDF (www.tcpdf.org) ## Contents 1 Overview 3 2 Getting Started 5 2.1 What is Agda? 5 2.2 Installation 7 2.3 'Hello 'Hello world' in Agda 13 2.4 A Taste of Agda 14 2.5 A List of Tutorials 22 3 Language Reference 25 3.1 Abstract definitions 25 3.2 Built-ins 27 3.3 Coinduction 40 3.4 Copatterns 42 3.5 Core 80099a5fb/p5_1.jpg) Overview Note: The Agda User Manual is a work-in-progress and is still incomplete. Contributions, additions and corrections to the Agda manual are greatly appreciated. To do so,

## 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 • Language Reference ☐ Abstract definitions ☐ Built-ins ○ Coinduction • Copatterns • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes • Termination Checking

## Welcome to Agda's documentation! Overview Getting Started - What is Agda? - Prerequisites - Installation - 'Hello world' in Agda - Quick Guide Guide to Editing, Type Checking and Compiling Agda Code - A List of Tutorials Language Reference - Abstract definitions - Built-ins - Coinduction - Copatterns - Prop - Record Types - Reflection - Rewriting - Safe Agda - Sized Types o Syntactic Sugar ○ Syntax Declarations • Telescopes • Termination Checking

## Welcome to Agda's documentation! Overview Getting Started o Prerequisites o Installation o Quick Guide to Editing, Type Checking and Compiling Agda Code Language Reference Postulates o Pragmas o Record Types o Reflection o Rewriting o Safe Agda o Sized Types o Syntactic Sugar o Telescopes o Termination Checking Management • Contribute • Documentation • The Agda License • The Agda Team ## I ndices and tables • Index • Search Page ## Overview ## Note The Agda User Manual is a work-in-progress and is still

Agda User Manual Release 2.6.0 The Agda Team Apr 12, 2019 Powered by TCPDF (www.tcpdf.org) ## Contents 1 Overview 1 2 Getting Started 3 2.1 What is Agda? 3 2.2 Prerequisites 5 2.3 Installation Installation 5 2.4 'Hello world' in Agda 8 2.5 Quick Guide to Editing, Type Checking and Compiling Agda Code 9 2.6 A List of Tutorials 10 3 Language Reference 13 3.1 Abstract definitions Prop 97 3.27 Record Types ..... 99 3.28 Reflection ..... 105 3.29 Rewriting ..... 114 3.30 Safe Agda ..... 114 3.31 Sized Types ..... 115 3.32 Syntactic Sugar ..... 118 3.33 Syntax Declarations

Agda User Manual Release 2.6.1.2 The Agda Team Feb 03, 2021 Powered by TCPDF (www.tcpdf.org) ## Contents 1 Overview 3 2 Getting Started 5 2.1 What is Agda? 5 2.2 Prerequisites 7 2.3 Installation Installation 7 2.4 'Hello world' in Agda 11 2.5 Quick Guide to Editing, Type Checking and Compiling Agda Code 11 2.6 A List of Tutorials 13 3 Language Reference 17 3.1 Abstract definitions Reflection ..... 118 3.31 Rewriting ..... 128 3.32 Run-time Irrelevance ..... 130 3.33 Safe Agda ..... 132 3.34 Sized Types ..... 133 3.35 Syntactic Sugar ..... 135 3.36 Syntax Declarations

Agda User Manual Release 2.6.4.1 The Agda Team Nov 30, 2023 Powered by TCPDF (www.tcpdf.org) ## CONTENTS 1 Overview 3 2 Getting Started 5 2.1 What is Agda? 5 2.2 Installation 7 2.3 'Hello 'Hello world' in Agda 14 2.4 A Taste of Agda 15 2.5 A List of Tutorials 23 3 Language Reference 27 3.1 Abstract definitions 27 3.2 Built-ins 30 3.3 Coinduction 43 3.4 Copatterns 47 3.5 Reflection ..... 159 3.36 Rewriting ..... 173 3.37 Run-time Irrelevance ..... 175 3.38 Safe Agda ..... 179 3.39 Sized Types ..... 180 3.40 Sort System ..... 183 3.41 Syntactic Sugar ..... 189

Agda User Manual Release 2.6.4.3 The Agda Team Mar 06, 2024 Powered by TCPDF (www.tcpdf.org) ## CONTENTS 1 Overview 3 2 Getting Started 5 2.1 What is Agda? 5 2.2 Installation 7 2.3 'Hello 'Hello world' in Agda 14 2.4 A Taste of Agda 15 2.5 A List of Tutorials 23 3 Language Reference 27 3.1 Abstract definitions 27 3.2 Built-ins 30 3.3 Coinduction 43 3.4 Copatterns 47 3.5 Reflection ..... 160 3.36 Rewriting ..... 174 3.37 Run-time Irrelevance ..... 176 3.38 Safe Agda ..... 180 3.39 Sized Types ..... 181 3.40 Sort System ..... 183 3.41 Syntactic Sugar ..... 190

Agda User Manual Release 2.5.4 The Agda Team Jun 02, 2018 Powered by TCPDF (www.tcpdf.org) ## Contents 1 Overview 2 Getting Started 2.1 Prerequisites 2.2 Installation 2.3 Quick Guide to Editing Editing, Type Checking and Compiling Agda Code 3 Language Reference 3.1 Abstract definitions 3.2 Built-ins 3.3 Coinduction 3.4 Copatterns 3.5 Core language 3.6 Data Types 3.7 Foreign Function 3.22 Postulates 3.23 Pragmas 3.24 Record Types 3.25 Reflection 3.26 Rewriting 3.27 Safe Agda 3.28 Sized Types 3.29 Syntactic Sugar 3.30 Telescopes 98 3.31 Termination Checking 98 3.32

## 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 • Language Reference ☐ Abstract definitions ☐ Built-ins ○ Coinduction • Copatterns • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes • Termination Checking