Lambda Abstraction Local Definitions: let and where Lexical Structure Literal Overloading Lossy Unification Mixfix Operators Module System Mutual Recursion Pattern Synonyms Positivity Checking Postulates Interaction Modalities Guarded Cubical References Implicit Arguments Tactic arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function Literate Agda Literal Overloading Natural numbers Negative numbers Strings Restrictions Lossy Unification Heuristic Example Drawbacks Mixfix Operators Precedence Associativity Ambiguity and Scope Operators

Lambda Abstraction Local Definitions: let and where Lexical Structure Literal Overloading Lossy Unification Mixfix Operators Module System Mutual Recursion Pattern Synonyms Positivity Checking Postulates Interaction Modalities Guarded Cubical References Implicit Arguments Tactic arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function Literate Agda Literal Overloading Natural numbers Negative numbers Strings Restrictions Lossy Unification Heuristic Example Drawbacks Mixfix Operators Precedence Associativity Ambiguity and Scope Operators

Interaction Modalities Guarded Cubical References Implicit Arguments Tactic arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function indices of the datatype being matched on. For each constructor c that does not appear in a clause, unification of the indices of the type of the constructor with the indices of the datatype should end in a the pattern x ∷ xs is Vec A (suc n), which is unifiable with the type Vec A (suc m). Meanwhile, unification of the type Vec A 0 of the constructor [] with the type Vec A (suc n) results in a conflict between

Interaction Modalities Guarded Cubical References Implicit Arguments Tactic arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function indices of the datatype being matched on. For each constructor c that does not appear in a clause, unification of the indices of the type of the constructor with the indices of the datatype should end in a the pattern x ∷ xs is Vec A (suc n), which is unifiable with the type Vec A (suc m). Meanwhile, unification of the type Vec A 0 of the constructor [] with the type Vec A (suc n) results in a conflict between

patterns Case trees Function Types Notational conventions Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Examples Instance resolution

patterns Case trees Function Types Notational conventions Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Examples Instance resolution

patterns Case trees Function Types Notational conventions Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Examples Instance resolution

patterns Case trees Function Types Notational conventions Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Lambda Abstraction Pattern matching (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Examples Instance resolution

patterns Case trees Function Types Notational conventions Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Lambda Abstraction Pattern matching (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Examples Instance resolution

irrelevant variables Importing and exporting variables Interaction Implicit Arguments Metavariables Unification Instance Arguments Usage Instance resolution Irrelevance Motivating example Irrelevant function (x₁ : A₁) → … → (xₘ : Aₘ) → D j₁ … jₙ, Agda will attempt to unify i₁ … iₙ with j₁ … jₙ. When the unification algorithm instantiates a variable x with value t, the corresponding argument of the function can where we guarantee that they are solved rules out many useful cases in practice. Metavariables Unification Instance Arguments Usage Defining type classes Declaring instances Restricting instance search