Agda-2.5.1.2: A dependently typed functional programming language and proof assistant

Agda.TypeChecking.Telescope

Contents

Synopsis

# Documentation

Strips all Pi's and return the head definition name, if possible.

renameP :: Subst t a => Permutation -> a -> a Source #

The permutation should permute the corresponding telescope. (left-to-right list)

renaming :: forall a. DeBruijn a => Permutation -> Substitution' a Source #

If permute π : [a]Γ -> [a]Δ, then applySubst (renaming π) : Term Γ -> Term Δ

If permute π : [a]Γ -> [a]Δ, then applySubst (renamingR π) : Term Δ -> Term Γ

Flatten telescope: (Γ : Tel) -> [Type Γ]

Order a flattened telescope in the correct dependeny order: Γ -> Permutation (Γ -> Γ~)

Since reorderTel tel uses free variable analysis of type in tel, the telescope should be normalised.

unflattenTel :: [ArgName] -> [Dom Type] -> Telescope Source #

Unflatten: turns a flattened telescope into a proper telescope. Must be properly ordered.

Get the suggested names from a telescope

Permute telescope: permutes or drops the types in the telescope according to the given permutation. Assumes that the permutation preserves the dependencies in the telescope.

Recursively computes dependencies of a set of variables in a given telescope. Any dependencies outside of the telescope are ignored.

data SplitTel Source #

A telescope split in two.

Constructors

 SplitTel FieldsfirstPart :: Telescope secondPart :: Telescope splitPerm :: PermutationThe permutation takes us from the original telescope to firstPart ++ secondPart.

Arguments

 :: VarSet A set of de Bruijn indices. -> Telescope Original telescope. -> SplitTel firstPart mentions the given variables, secondPart not.

Split a telescope into the part that defines the given variables and the part that doesn't.

See prop_splitTelescope.

Arguments

 :: [Int] A list of de Bruijn indices -> Telescope The telescope to split -> Maybe SplitTel firstPart mentions the given variables in the given order, secondPart contains all other variables

As splitTelescope, but fails if any additional variables or reordering would be needed to make the first part well-typed.

Arguments

 :: Telescope ⊢ Γ -> Int Γ ⊢ var k : A -> Term Γ ⊢ u : A -> Maybe (Telescope, PatternSubstitution, Permutation)

Try to instantiate one variable in the telescope (given by its de Bruijn level) with the given value, returning the new telescope and a substitution to the old one. Returns Nothing if the given value depends (directly or indirectly) on the variable.

Try to eta-expand one variable in the telescope (given by its de Bruijn level)

telViewUpTo n t takes off the first n function types of t. Takes off all if n < 0.

telViewUpTo' :: Int -> (Dom Type -> Bool) -> Type -> TCM TelView Source #

telViewUpTo' n p t takes off $t$ the first n (or arbitrary many if n < 0) function domains as long as they satify p.

mustBePi :: MonadTCM tcm => Type -> tcm (Dom Type, Abs Type) Source #

Decomposing a function type.

ifPi :: MonadTCM tcm => Term -> (Dom Type -> Abs Type -> tcm a) -> (Term -> tcm a) -> tcm a Source #

If the given type is a Pi, pass its parts to the first continuation. If not (or blocked), pass the reduced type to the second continuation.

ifPiType :: MonadTCM tcm => Type -> (Dom Type -> Abs Type -> tcm a) -> (Type -> tcm a) -> tcm a Source #

If the given type is a Pi, pass its parts to the first continuation. If not (or blocked), pass the reduced type to the second continuation.

ifNotPi :: MonadTCM tcm => Term -> (Term -> tcm a) -> (Dom Type -> Abs Type -> tcm a) -> tcm a Source #

If the given type is blocked or not a Pi, pass it reduced to the first continuation. If it is a Pi, pass its parts to the second continuation.

ifNotPiType :: MonadTCM tcm => Type -> (Type -> tcm a) -> (Dom Type -> Abs Type -> tcm a) -> tcm a Source #

If the given type is blocked or not a Pi, pass it reduced to the first continuation. If it is a Pi, pass its parts to the second continuation.

A safe variant of piApply.

piApply1 :: MonadTCM tcm => Type -> Term -> tcm Type Source #

intro1 :: MonadTCM tcm => Type -> (Type -> tcm a) -> tcm a Source #

Given a function type, introduce its domain into the context and continue with its codomain.

# Instance definitions

Try to solve the instance definitions whose type is not yet known, report an error if it doesn't work and return the instance table otherwise.