Abstract definitions - Built-ins - Coinduction - Copatterns - Core language - Coverage Checking - Cubical - Cumulativity - Data Types - Flat Modality - Foreign Function Interface - Mixfix Operators - Module System - Mutual Recursion ○ Pattern Synonyms ○ Positivity Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance Sized Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations ○ Telescopes ○ Termination Checking ○ Universe Levels ○ With-Abstraction ○ Without K • Tools - Automatic Proof Search

3.2 Built-ins 27 3.3 Coinduction 40 3.4 Copatterns 42 3.5 Core language 45 3.6 Coverage Checking 48 3.7 Cubical 51 3.8 Cumulativity 64 3.9 Data Types 66 3.10 Flat Modality 68 3.11 Foreign 3.24 Module System 112 3.25 Mutual Recursion 117 3.26 Pattern Synonyms 120 3.27 Positivity Checking 121 3.28 Postulates  or issue on the GitHub Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related resources/tools. The latest PDF version of this manual

Getting Started o Prerequisites o Installation o Quick Guide to Editing, Type Checking and Compiling Agda Code Language Reference o Abstract definitions o Built-ins Operators o Module System o Mutual Recursion o Pattern Synonyms o Positivity Checking o Postulates o Pragmas o Record Types o Reflection o Rewriting o Safe Agda o Sized Types o Syntactic Sugar o Telescopes o Termination Checking o Universe Levels o With-Abstraction o Without K ## • Tools • Automatic Proof

Abstract definitions - Built-ins - Coinduction - Copatterns - Core language - Coverage Checking - Cubical - Cumulativity - Data Types - Flat Modality - Foreign Function Interface - Mixfix Operators - Module System - Mutual Recursion ○ Pattern Synonyms ○ Positivity Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance Sized Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations ○ Telescopes ○ Termination Checking ○ Universe Levels ○ With-Abstraction ○ Without K • Tools - Automatic Proof Search

3.2 Built-ins 27 3.3 Coinduction 40 3.4 Copatterns 42 3.5 Core language 45 3.6 Coverage Checking 48 3.7 Cubical 51 3.8 Cumulativity 64 3.9 Data Types 66 3.10 Flat Modality 69 3.11 Foreign 3.25 Module System 113 3.26 Mutual Recursion 118 3.27 Pattern Synonyms 121 3.28 Positivity Checking ..... 123 3.29 Postulates ..... 125 3.30 Pragmas ..... 126 3.31 Prop ..... 129 3.32 Record Syntactic Sugar ..... 162 3.40 Syntax Declarations ..... 166 3.41 Telescopes ..... 167 3.42 Termination Checking ..... 168 3.43 Universe Levels ..... 170 3.44 With-Abstraction ..... 172 3.45 Without

3.18 Module System 53 3.19 Mutual Recursion 58 3.20 Pattern Synonyms 59 3.21 Positivity Checking 59 3.22 Postulates 61 3.23 Pragmas 62 3.24 Record Types 62 3.25 Reflection 68 3.26 Rewriting Rewriting 76 3.27 Safe Agda 76 3.28 Sized Types 77 3.29 Telescopes 80 3.30 Termination Checking 80 3.31 Universe Levels 81 3.32 With-Abstraction ..... 81 3.33 Without K ..... 90 4 Tools or issue on the Github Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related tools. A description of the Agda language is given

Overview 2 Getting Started 2.1 Prerequisites 2.2 Installation 2.3 Quick Guide to Editing, Type Checking and Compiling Agda Code 3 Language Reference 3.1 Abstract definitions 3.2 Built-ins 3.3 Positivity Checking 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 or issue on the Github Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related tools. A description of the Agda language is given

Overview 2 Getting Started 2.1 Prerequisites 2.2 Installation 2.3 Quick Guide to Editing, Type Checking and Compiling Agda Code 3 Language Reference 3.1 Abstract definitions 3.2 Built-ins 3.3 Positivity Checking 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 or issue on the Github Agda page. This is the manual for the Agda programming language, its type checking, compilation and editing system and related tools. A description of the Agda language is given

definitions • Built-ins • Coinduction • Copatterns • Core language • Coverage Checking • Cubical • Cubical compatible • Cumulativity • Data Types • Flat Modality Unification • Mixfix Operators Module System Mutual Recursion Pattern Synonyms Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Safe Agda Sized Types Sort System Syntactic Sugar Syntax Declarations Telescopes Termination Checking Two-Level Type Theory Universe Levels With-Abstraction Without K Tools Automatic

3.2 Built-ins 30 3.3 Coinduction 43 3.4 Copatterns 47 3.5 Core language 51 3.6 Coverage Checking 54 3.7 Cubical 57 3.8 Cubical compatible 73 3.9 Cumulativity 73 3.10 Data Types 75 3.11 Mutual Recursion 133 3.28 Opaque definitions 137 3.29 Pattern Synonyms 141 3.30 Positivity Checking 143 3.31 Postulates ..... 145 3.32 Pragmas ..... 146 3.33 Prop ..... 150 3.34 Record Types Syntactic Sugar ..... 190 3.42 Syntax Declarations ..... 195 3.43 Telescopes ..... 196 3.44 Termination Checking ..... 196 3.45 Two-Level Type Theory ..... 199 3.46 Universe Levels ..... 200 3.47 With-Abstraction