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GHC 9.10.3 · lts/ghc-9.10.x · c74966e · 2026-09-27

ModuleAgda-2.7.0.1Haskell2010

Agda.TypeChecking.SizedTypes.Syntax

Syntax of size expressions and constraints.

  • 18 types
  • 5 classes
  • 7 values
  • PackageAgda-2.7.0.1
  • Exports30
  • LanguageHaskell2010
  • LicenceMIT
  • SourceSyntax.hs

Syntax

8 declarations
newtypenewtype Offset
#

Constant finite sizes n >= 0.

Constructors

Instances17Enum, Eq, Num, Ord, Show, Generic, …
newtypenewtype Rigid
#

Fixed size variables i.

Constructors

Instances4Eq, Ord, Show, Pretty
  • Eq RigidDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord RigidDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Show RigidDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Pretty RigidDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
newtypenewtype Flex
#

Size meta variables X to solve for.

Constructors

Instances4Eq, Ord, Show, Pretty
  • Eq FlexDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord FlexDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Show FlexDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Pretty FlexDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
datadata SizeExpr' rigid flex
#

Size expressions appearing in constraints.

Constructors

Instances22Substitute, Functor, Foldable, Traversable, Eq, Ord, …
datadata Cmp
#

Comparison operator, e.g. for size expression.

Constructors

Instances12Bounded, Enum, Eq, Ord, Show, Generic, …
  • Bounded CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Enum CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Eq CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax

    Comparison operator is ordered Lt < Le.

  • Show CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Generic CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • NFData CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Pretty CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Dioid CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • MeetSemiLattice CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Top CmpDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • type Rep Cmp = D1 ('MetaData "Cmp" "Agda.TypeChecking.SizedTypes.Syntax" "Agda-2.7.0.1-DbbZpETDDF1KkwuzEZvfn8" 'False) (C1 ('MetaCons "Lt" 'PrefixI 'False) U1 :+: C1 ('MetaCons "Le" 'PrefixI 'False) U1)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
datadata Constraint' rigid flex
#

Constraint: an inequation between size expressions, e.g. X < ∞ or i + 3 ≤ j.

Constructors

Instances16Subst, PrettyTCM, Substitute, Functor, Foldable, Traversable, …

Polarities to specify solutions.

6 declarations
datadata Polarity
#

What type of solution are we looking for?

Instances3Eq, Ord, Pretty
  • Eq PolarityDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord PolarityDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Pretty PolarityDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax

Solutions.

3 declarations
newtypenewtype Solution rigid flex
#

Partial substitution from flexible variables to size expression.

Constructors

Instances4Substitute, Show, Pretty, Null
  • Ord f => Substitute r f (Solution r f)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • (Show flex, Show rigid) => Show (Solution rigid flex)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • (Pretty r, Pretty f) => Pretty (Solution r f)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Null (Solution rigid flex)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
classclass Substitute r f a where
#

Executing a substitution.

Methods

Instances5Substitute

Constraint simplification

4 declarations

Printing

0 declarations

Wellformedness

2 declarations

Computing variable sets

7 declarations
classclass Ord (RigidOf a) => Rigids a where
#

The rigid variables contained in a pice of syntax.

Associated types

Methods

Instances3Rigids
  • Rigids a => Rigids [a]Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord r => Rigids (Constraint' r f)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord r => Rigids (SizeExpr' r f)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
classclass Ord (FlexOf a) => Flexs a where
#

The flexibe variables contained in a pice of syntax.

Associated types

Methods

Instances4Flexs
  • Flexs HypSizeConstraintDefined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Flexs a => Flexs [a]Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord flex => Flexs (Constraint' rigid flex)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
  • Ord flex => Flexs (SizeExpr' rigid flex)Defined in Agda-2.7.0.1 · Agda.TypeChecking.SizedTypes.Syntax
datadata NamedRigid
#

Identifiers for rigid variables.

Constructors

Instances13Eq, Ord, Show, Generic, NFData, Pretty, …
datadata SizeMeta
#

Size metas in size expressions.

Constructors

Instances15Eq, Ord, Show, Generic, NFData, Pretty, …
datadata HypSizeConstraint
#

Size constraint with de Bruijn indices.

Constructors

Instances7Show, Generic, NFData, PrettyTCM, Flexs, Rep, …