Generalization of Declared Variables 64 3.14 Implicit Arguments 68 3.15 Instance Arguments 71 3.16 Irrelevance 77 3.17 Lambda Abstraction 82 3.18 Local Definitions: let and where 83 3.19 Lexical Structure 3.29 Record Types ..... 111 3.30 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 f, which lets you reason about programs using primForce, evaluates to refl when x is in whnf. At run-time, primForce e f is compiled (by the GHC backend) to let x = e in seq x (f x). For example, consider

Function Types Generalization of Declared Variables • Implicit Arguments ○ Instance Arguments o Irrelevance ○ Lambda Abstraction ☐ Local Definitions: let and where ☐ Lexical Structure ☐ Literal Overloading Checking • Postulates • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes Metavariables - Unification - Instance Arguments - Usage - Instance resolution - Irrelevance - Motivating example - Irrelevant function types - Irrelevant declarations - Irrelevant

Function Types Generalization of Declared Variables • Implicit Arguments ○ Instance Arguments o Irrelevance ○ Lambda Abstraction ☐ Local Definitions: let and where ☐ Lexical Structure ☐ Literal Overloading Checking • Postulates • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes Metavariables - Unification - Instance Arguments - Usage - Instance resolution - Irrelevance - Motivating example - Irrelevant function types - Irrelevant declarations - Irrelevant

Declared Variables • Guarded Cubical • Implicit Arguments • Instance Arguments • Irrelevance • Lambda Abstraction • Local Definitions: let and where • Lexical Structure Checking o Postulates o Pragmas o Prop o Record Types o Reflection o Rewriting o Run-time Irrelevance o Safe Agda o Sized Types o Sort System o Syntactic Sugar o Syntax Declarations Metavariables • Unification • Instance Arguments • Usage • Instance resolution • Irrelevance • Motivating example • Irrelevant function types • Irrelevant declarations

Function Types Generalization of Declared Variables • Implicit Arguments ○ Instance Arguments o Irrelevance ○ Lambda Abstraction ☐ Local Definitions: let and where ☐ Lexical Structure ☐ Literal Overloading Checking • Postulates • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes Metavariables - Unification - Instance Arguments - Usage - Instance resolution - Irrelevance - Motivating example - Irrelevant function types - Irrelevant declarations - Irrelevant

Function Types Generalization of Declared Variables • Implicit Arguments ○ Instance Arguments o Irrelevance ○ Lambda Abstraction ☐ Local Definitions: let and where ☐ Lexical Structure ☐ Literal Overloading Checking • Postulates • Pragmas • Prop • Record Types • Reflection • Rewriting • Run-time Irrelevance • Safe Agda • Sized Types • Syntactic Sugar • Syntax Declarations • Telescopes Metavariables - Unification - Instance Arguments - Usage - Instance resolution - Irrelevance - Motivating example - Irrelevant function types • Irrelevant declarations • Irrelevant

Declared Variables • Guarded Cubical • Implicit Arguments • Instance Arguments • Irrelevance • Lambda Abstraction • Local Definitions: let and where • Lexical Structure Positivity Checking Postulates Pragmas Prop Record Types Reflection Rewriting Run-time Irrelevance Safe Agda Sized Types Sort System Syntactic Sugar Syntax Declarations Telescopes Metavariables • Unification • Instance Arguments • Usage • Instance resolution • Irrelevance • Motivating example • Irrelevant function types • Irrelevant declarations

of Declared Variables - Guarded Cubical - Implicit Arguments - Instance Arguments - Irrelevance - Lambda Abstraction - Local Definitions: let and where - Lexical Structure - Literal Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance ○ Safe Agda ○ Sized Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations Metavariables • Unification • Instance Arguments • Usage • Instance resolution • Irrelevance • Motivating example • Irrelevant function types • Irrelevant declarations

of Declared Variables - Guarded Cubical - Implicit Arguments - Instance Arguments - Irrelevance - Lambda Abstraction - Local Definitions: let and where - Lexical Structure - Literal Checking ○ Postulates ○ Pragmas ○ Prop ○ Record Types ○ Reflection ○ Rewriting ○ Run-time Irrelevance ○ Safe Agda ○ Sized Types ○ Sort System ○ Syntactic Sugar ○ Syntax Declarations Metavariables • Unification • Instance Arguments • Usage • Instance resolution • Irrelevance • Motivating example • Irrelevant function types • Irrelevant declarations

3.16 Guarded Type Theory 95 3.17 Implicit Arguments 95 3.18 Instance Arguments 98 3.19 Irrelevance 105 3.20 Lambda Abstraction 110 3.21 Local Definitions: let and where 111 3.22 Lexical Structure 3.34 Record Types ..... 152 3.35 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 .... f, which lets you reason about programs using primForce, evaluates to refl when x is in whnf. At run-time, primForce e f is compiled (by the GHC backend) to let x = e in seq x (f x). For example, consider