Agda-2.4.2.3: A dependently typed functional programming language and proof assistant

Safe HaskellNone
LanguageHaskell98

Agda.Syntax.Abstract

Contents

Description

The abstract syntax. This is what you get after desugaring and scope analysis of the concrete syntax. The type checker works on abstract syntax, producing internal syntax (Agda.Syntax.Internal).

Synopsis

Documentation

type Color = Expr

type Arg a = Arg Color a

type Dom a = Dom Color a

type Args = [NamedArg Expr]

data Expr

Expressions after scope checking (operators parsed, names resolved).

Constructors

Var Name

Bound variable.

Def QName

Constant: axiom, function, data or record type.

Proj QName

Projection.

Con AmbiguousQName

Constructor.

PatternSyn QName

Pattern synonym.

Lit Literal

Literal.

QuestionMark MetaInfo InteractionId

Meta variable for interaction. The InteractionId is usually identical with the metaNumber of MetaInfo. However, if you want to print an interaction meta as just ? instead of ?n, you should set the metaNumber to Nothing while keeping the InteractionId.

Underscore MetaInfo

Meta variable for hidden argument (must be inferred locally).

App ExprInfo Expr (NamedArg Expr)

Ordinary (binary) application.

WithApp ExprInfo Expr [Expr]

With application.

Lam ExprInfo LamBinding Expr

λ bs → e.

AbsurdLam ExprInfo Hiding

λ() or λ{}.

ExtendedLam ExprInfo DefInfo QName [Clause] 
Pi ExprInfo Telescope Expr

Dependent function space Γ → A.

Fun ExprInfo (Arg Expr) Expr

Non-dependent function space.

Set ExprInfo Integer

Set, Set1, Set2, ...

Prop ExprInfo

Prop (no longer supported, used as dummy type).

Let ExprInfo [LetBinding] Expr

let bs in e.

ETel Telescope

Only used when printing telescopes.

Rec ExprInfo Assigns

Record construction.

RecUpdate ExprInfo Expr Assigns

Record update.

ScopedExpr ScopeInfo Expr

Scope annotation.

QuoteGoal ExprInfo Name Expr

Binds Name to current type in Expr.

QuoteContext ExprInfo Name Expr

Binds Name to current context in Expr.

Quote ExprInfo

Quote an identifier QName.

QuoteTerm ExprInfo

Quote a term.

Unquote ExprInfo

The splicing construct: unquote ...

DontCare Expr

For printing DontCare from Syntax.Internal.

type Assign = (Name, Expr)

Record field assignment f = e.

type Assigns = [Assign]

data Axiom

Is a type signature a postulate or a function signature?

Constructors

FunSig

A function signature.

NoFunSig

Not a function signature, i.e., a postulate (in user input) or another (e.g. data/record) type signature (internally).

Instances

type Ren a = [(a, a)]

Renaming (generic).

data Declaration

Constructors

Axiom Axiom DefInfo ArgInfo QName Expr

type signature (can be irrelevant and colored, but not hidden)

Field DefInfo QName (Arg Expr)

record field

Primitive DefInfo QName Expr

primitive function

Mutual MutualInfo [Declaration]

a bunch of mutually recursive definitions

Section ModuleInfo ModuleName [TypedBindings] [Declaration] 
Apply ModuleInfo ModuleName ModuleApplication (Ren QName) (Ren ModuleName) 
Import ModuleInfo ModuleName 
Pragma Range Pragma 
Open ModuleInfo ModuleName

only retained for highlighting purposes

FunDef DefInfo QName Delayed [Clause]

sequence of function clauses

DataSig DefInfo QName Telescope Expr

lone data signature ^ the LamBindings are DomainFree and binds the parameters of the datatype.

DataDef DefInfo QName [LamBinding] [Constructor]

the LamBindings are DomainFree and binds the parameters of the datatype.

RecSig DefInfo QName Telescope Expr

lone record signature

RecDef DefInfo QName (Maybe (Ranged Induction)) (Maybe QName) [LamBinding] Expr [Declaration]

The Expr gives the constructor type telescope, (x1 : A1)..(xn : An) -> Prop, and the optional name is the constructor's name.

PatternSynDef QName [Arg Name] Pattern

Only for highlighting purposes

UnquoteDecl MutualInfo DefInfo QName Expr 
ScopedDecl ScopeInfo [Declaration]

scope annotation

class GetDefInfo a where

Methods

getDefInfo :: a -> Maybe DefInfo

data LetBinding

Bindings that are valid in a let.

Constructors

LetBind LetInfo ArgInfo Name Expr Expr
LetBind info rel name type defn
LetPatBind LetInfo Pattern Expr

Irrefutable pattern binding.

LetApply ModuleInfo ModuleName ModuleApplication (Ren QName) (Ren ModuleName)

LetApply mi newM (oldM args) renaming moduleRenaming.

LetOpen ModuleInfo ModuleName

only for highlighting and abstractToConcrete

data TypedBinding

A typed binding. Appears in dependent function spaces, typed lambdas, and telescopes. It might be tempting to simplify this to only bind a single name at a time, and translate, say, (x y : A) to (x : A)(y : A) before type-checking. However, this would be slightly problematic:

  1. We would have to typecheck the type A several times.
  2. If A contains a meta variable or hole, it would be duplicated by such a translation.

While 1. is only slightly inefficient, 2. would be an outright bug. Duplicating A could not be done naively, we would have to make sure that the metas of the copy are aliases of the metas of the original.

Constructors

TBind Range [WithHiding Name] Expr

As in telescope (x y z : A) or type (x y z : A) -> B.

TLet Range [LetBinding]

E.g. (let x = e) or (let open M).

data Clause' lhs

We could throw away where clauses at this point and translate them to let. It's not obvious how to remember that the let was really a where clause though, so for the time being we keep it here.

Constructors

Clause 

data RHS

Constructors

RHS Expr 
AbsurdRHS 
WithRHS QName [Expr] [Clause]

The QName is the name of the with function.

RewriteRHS [(QName, Expr)] RHS [Declaration]

The QNames are the names of the generated with functions. One for each Expr. The RHS shouldn't be another RewriteRHS.

data SpineLHS

The lhs of a clause in spine view (inside-out). Projection patterns are contained in spLhsPats, represented as DefP d [].

Constructors

SpineLHS 

Fields

spLhsInfo :: LHSInfo

Range.

spLhsDefName :: QName

Name of function we are defining.

spLhsPats :: [NamedArg Pattern]

Function parameters (patterns).

spLhsWithPats :: [Pattern]

with patterns (after |).

data LHS

The lhs of a clause in focused (projection-application) view (outside-in). Projection patters are represented as LHSProjs.

Constructors

LHS 

Fields

lhsInfo :: LHSInfo

Range.

lhsCore :: LHSCore

Copatterns.

lhsWithPats :: [Pattern]

with patterns (after |).

data LHSCore' e

The lhs minus with-patterns in projection-application view. Parameterised over the type e of dot patterns.

Constructors

LHSHead

The head applied to ordinary patterns.

Fields

lhsDefName :: QName

Head f.

lhsPats :: [NamedArg (Pattern' e)]

Applied to patterns ps.

LHSProj

Projection

Fields

lhsDestructor :: QName

Record projection identifier.

lhsPatsLeft :: [NamedArg (Pattern' e)]

Indices of the projection. Currently none [], since we do not have indexed records.

lhsFocus :: NamedArg (LHSCore' e)

Main branch.

lhsPatsRight :: [NamedArg (Pattern' e)]

Further applied to patterns.

class LHSToSpine a b where

Convert a focused lhs to spine view and back.

Methods

lhsToSpine :: a -> b

spineToLhs :: b -> a

Instances

LHSToSpine LHS SpineLHS

LHS instance.

LHSToSpine Clause SpineClause

Clause instance.

LHSToSpine a b => LHSToSpine [a] [b]

List instance (for clauses).

lhsCoreApp :: LHSCore' e -> [NamedArg (Pattern' e)] -> LHSCore' e

Add applicative patterns (non-projection patterns) to the right.

lhsCoreAddSpine :: LHSCore' e -> [NamedArg (Pattern' e)] -> LHSCore' e

Add projection and applicative patterns to the right.

lhsCoreAllPatterns :: LHSCore' e -> [Pattern' e]

Used for checking pattern linearity.

lhsCoreToPattern :: LHSCore -> Pattern

Used in AbstractToConcrete.

Patterns

data Pattern' e

Parameterised over the type of dot patterns.

Constructors

VarP Name 
ConP ConPatInfo AmbiguousQName [NamedArg (Pattern' e)] 
DefP PatInfo QName [NamedArg (Pattern' e)]

Defined pattern: function definition f ps or destructor pattern d p ps.

WildP PatInfo

Underscore pattern entered by user.

AsP PatInfo Name (Pattern' e) 
DotP PatInfo e 
AbsurdP PatInfo 
LitP Literal 
ImplicitP PatInfo

Generated at type checking for implicit arguments.

PatternSynP PatInfo QName [NamedArg (Pattern' e)] 

class IsProjP a where

Check whether we are a projection pattern.

Methods

isProjP :: a -> Maybe QName

Instances

class AllNames a where

Extracts all the names which are declared in a Declaration. This does not include open public or let expressions, but it does include local modules, where clauses and the names of extended lambdas.

Methods

allNames :: a -> Seq QName

axiomName :: Declaration -> QName

The name defined by the given axiom.

Precondition: The declaration has to be a (scoped) Axiom.

class AnyAbstract a where

Are we in an abstract block?

In that case some definition is abstract.

Methods

anyAbstract :: a -> Bool

insertImplicitPatSynArgs :: HasRange a => (Range -> a) -> Range -> [Arg Name] -> [NamedArg a] -> Maybe ([(Name, a)], [Arg Name])