| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Agda.TypeChecking.Telescope
Contents
Synopsis
- flattenTel :: TermSubst a => Tele (Dom a) -> [Dom a]
- reorderTel :: [Dom Type] -> Maybe Permutation
- reorderTel_ :: [Dom Type] -> Permutation
- unflattenTel :: [ArgName] -> [Dom Type] -> Telescope
- renameTel :: [Maybe ArgName] -> Telescope -> Telescope
- teleNames :: Telescope -> [ArgName]
- teleArgNames :: Telescope -> [Arg ArgName]
- teleArgs :: DeBruijn a => Tele (Dom t) -> [Arg a]
- teleDoms :: DeBruijn a => Tele (Dom t) -> [Dom a]
- teleNamedArgs :: DeBruijn a => Telescope -> [NamedArg a]
- tele2NamedArgs :: DeBruijn a => Telescope -> Telescope -> [NamedArg a]
- splitTelescopeAt :: Int -> Telescope -> (Telescope, Telescope)
- permuteTel :: Permutation -> Telescope -> Telescope
- varDependencies :: Telescope -> IntSet -> IntSet
- varDependents :: Telescope -> IntSet -> IntSet
- data SplitTel = SplitTel {}
- splitTelescope :: VarSet -> Telescope -> SplitTel
- splitTelescopeExact :: [Int] -> Telescope -> Maybe SplitTel
- instantiateTelescope :: Telescope -> Int -> DeBruijnPattern -> Maybe (Telescope, PatternSubstitution, Permutation)
- expandTelescopeVar :: Telescope -> Int -> Telescope -> ConHead -> (Telescope, PatternSubstitution)
- telView :: (MonadReduce m, MonadAddContext m) => Type -> m TelView
- telViewUpTo :: (MonadReduce m, MonadAddContext m) => Int -> Type -> m TelView
- telViewUpTo' :: (MonadReduce m, MonadAddContext m) => Int -> (Dom Type -> Bool) -> Type -> m TelView
- telViewPath :: PureTCM m => Type -> m TelView
- telViewUpToPath :: PureTCM m => Int -> Type -> m TelView
- type Boundary = Boundary' (Term, Term)
- type Boundary' a = [(Term, a)]
- telViewUpToPathBoundary' :: PureTCM m => Int -> Type -> m (TelView, Boundary)
- fullBoundary :: Telescope -> Boundary -> Boundary
- telViewUpToPathBoundary :: PureTCM m => Int -> Type -> m (TelView, Boundary)
- telViewUpToPathBoundaryP :: PureTCM m => Int -> Type -> m (TelView, Boundary)
- telViewPathBoundaryP :: PureTCM m => Type -> m (TelView, Boundary)
- teleElims :: DeBruijn a => Telescope -> Boundary' (a, a) -> [Elim' a]
- pathViewAsPi :: PureTCM m => Type -> m (Either (Dom Type, Abs Type) Type)
- pathViewAsPi' :: PureTCM m => Type -> m (Either ((Dom Type, Abs Type), (Term, Term)) Type)
- pathViewAsPi'whnf :: HasBuiltins m => m (Type -> Either ((Dom Type, Abs Type), (Term, Term)) Type)
- piOrPath :: HasBuiltins m => Type -> m (Either (Dom Type, Abs Type) Type)
- telView'UpToPath :: Int -> Type -> TCM TelView
- telView'Path :: Type -> TCM TelView
- isPath :: PureTCM m => Type -> m (Maybe (Dom Type, Abs Type))
- telePatterns :: DeBruijn a => Telescope -> Boundary -> [NamedArg (Pattern' a)]
- telePatterns' :: DeBruijn a => (forall a. DeBruijn a => Telescope -> [NamedArg a]) -> Telescope -> Boundary -> [NamedArg (Pattern' a)]
- mustBePi :: MonadReduce m => Type -> m (Dom Type, Abs Type)
- ifPi :: MonadReduce m => Term -> (Dom Type -> Abs Type -> m a) -> (Term -> m a) -> m a
- ifPiType :: MonadReduce m => Type -> (Dom Type -> Abs Type -> m a) -> (Type -> m a) -> m a
- ifNotPi :: MonadReduce m => Term -> (Term -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
- ifNotPiType :: MonadReduce m => Type -> (Type -> m a) -> (Dom Type -> Abs Type -> m a) -> m a
- ifNotPiOrPathType :: (MonadReduce tcm, HasBuiltins tcm) => Type -> (Type -> tcm a) -> (Dom Type -> Abs Type -> tcm a) -> tcm a
- class PiApplyM a where
- piApplyM' :: (MonadReduce m, HasBuiltins m) => m Empty -> Type -> a -> m Type
- piApplyM :: (MonadReduce m, HasBuiltins m) => Type -> a -> m Type
- typeArity :: Type -> TCM Nat
- data OutputTypeName
- getOutputTypeName :: Type -> TCM (Telescope, OutputTypeName)
- addTypedInstance :: QName -> Type -> TCM ()
- resolveUnknownInstanceDefs :: TCM ()
- getInstanceDefs :: TCM InstanceTable
Documentation
flattenTel :: TermSubst a => Tele (Dom a) -> [Dom a] Source #
Flatten telescope: (Γ : Tel) -> [Type Γ]
reorderTel :: [Dom Type] -> Maybe Permutation Source #
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.
reorderTel_ :: [Dom Type] -> Permutation Source #
unflattenTel :: [ArgName] -> [Dom Type] -> Telescope Source #
Unflatten: turns a flattened telescope into a proper telescope. Must be properly ordered.
renameTel :: [Maybe ArgName] -> Telescope -> Telescope Source #
Rename the variables in the telescope to the given names
Precondition: size xs == size tel.
tele2NamedArgs :: DeBruijn a => Telescope -> Telescope -> [NamedArg a] Source #
A variant of teleNamedArgs which takes the argument names (and the argument info)
from the first telescope and the variable names from the second telescope.
Precondition: the two telescopes have the same length.
splitTelescopeAt :: Int -> Telescope -> (Telescope, Telescope) Source #
Split the telescope at the specified position.
permuteTel :: Permutation -> Telescope -> Telescope Source #
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.
For example (Andreas, 2016-12-18, issue #2344):
tel = (A : Set) (X : _18 A) (i : Fin (_m_23 A X))
tel (de Bruijn) = 2:Set, 1:_18 0, 0:Fin(_m_23 1 0)
flattenTel tel = 2:Set, 1:_18 0, 0:Fin(_m_23 1 0) |- [ Set, _18 2, Fin (_m_23 2 1) ]
perm = 0,1,2 -> 0,1 (picks the first two)
renaming _ perm = [var 0, var 1, error] -- THE WRONG RENAMING!
renaming _ (flipP perm) = [error, var 1, var 0] -- The correct renaming!
apply to flattened tel = ... |- [ Set, _18 1, Fin (_m_23 1 0) ]
permute perm it = ... |- [ Set, _18 1 ]
unflatten (de Bruijn) = 1:Set, 0: _18 0
unflatten = (A : Set) (X : _18 A)
varDependencies :: Telescope -> IntSet -> IntSet Source #
Recursively computes dependencies of a set of variables in a given telescope. Any dependencies outside of the telescope are ignored.
varDependents :: Telescope -> IntSet -> IntSet Source #
Computes the set of variables in a telescope whose type depend on one of the variables in the given set (including recursive dependencies). Any dependencies outside of the telescope are ignored.
A telescope split in two.
Constructors
| SplitTel | |
Fields
| |
Arguments
| :: VarSet | A set of de Bruijn indices. |
| -> Telescope | Original telescope. |
| -> SplitTel |
|
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 |
|
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 de Bruijn _level_ |
| -> DeBruijnPattern | 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.
expandTelescopeVar :: Telescope -> Int -> Telescope -> ConHead -> (Telescope, PatternSubstitution) Source #
Try to eta-expand one variable in the telescope (given by its de Bruijn level)
telView :: (MonadReduce m, MonadAddContext m) => Type -> m TelView Source #
Gather leading Πs of a type in a telescope.
telViewUpTo :: (MonadReduce m, MonadAddContext m) => Int -> Type -> m TelView Source #
telViewUpTo n t takes off the first n function types of t.
Takes off all if n < 0.
telViewUpTo' :: (MonadReduce m, MonadAddContext m) => Int -> (Dom Type -> Bool) -> Type -> m 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.
telViewUpToPath :: PureTCM m => Int -> Type -> m TelView Source #
telViewUpToPath n t takes off $t$
the first n (or arbitrary many if n < 0) function domains or Path types.
telViewUpToPathBoundary' :: PureTCM m => Int -> Type -> m (TelView, Boundary) Source #
Like telViewUpToPath but also returns the Boundary expected
by the Path types encountered. The boundary terms live in the
telescope given by the TelView.
Each point of the boundary has the type of the codomain of the Path type it got taken from, see fullBoundary.
telViewUpToPathBoundary :: PureTCM m => Int -> Type -> m (TelView, Boundary) Source #
(TelV Γ b, [(i,t_i,u_i)]) <- telViewUpToPathBoundary n a
Input: Δ ⊢ a
Output: ΔΓ ⊢ b
ΔΓ ⊢ i : I
ΔΓ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : b
telViewUpToPathBoundaryP :: PureTCM m => Int -> Type -> m (TelView, Boundary) Source #
(TelV Γ b, [(i,t_i,u_i)]) <- telViewUpToPathBoundaryP n a
Input: Δ ⊢ a
Output: Δ.Γ ⊢ b
Δ.Γ ⊢ T is the codomain of the PathP at variable i
Δ.Γ ⊢ i : I
Δ.Γ ⊢ [ (i=0) -> t_i; (i=1) -> u_i ] : T
Useful to reconstruct IApplyP patterns after teleNamedArgs Γ.
teleElims :: DeBruijn a => Telescope -> Boundary' (a, a) -> [Elim' a] Source #
teleElimsB args bs = es
Input: Δ.Γ ⊢ args : Γ
Δ.Γ ⊢ T is the codomain of the PathP at variable i
Δ.Γ ⊢ i : I
Δ.Γ ⊢ bs = [ (i=0) -> t_i; (i=1) -> u_i ] : T
Output: Δ.Γ | PiPath Γ bs A ⊢ es : A
pathViewAsPi'whnf :: HasBuiltins m => m (Type -> Either ((Dom Type, Abs Type), (Term, Term)) Type) Source #
piOrPath :: HasBuiltins m => Type -> m (Either (Dom Type, Abs Type) Type) Source #
returns Left (a,b) in case the type is Pi a b or PathP b _ _
assumes the type is in whnf.
telePatterns' :: DeBruijn a => (forall a. DeBruijn a => Telescope -> [NamedArg a]) -> Telescope -> Boundary -> [NamedArg (Pattern' a)] Source #
ifPi :: MonadReduce m => Term -> (Dom Type -> Abs Type -> m a) -> (Term -> m a) -> m 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 :: MonadReduce m => Type -> (Dom Type -> Abs Type -> m a) -> (Type -> m a) -> m 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 :: MonadReduce m => Term -> (Term -> m a) -> (Dom Type -> Abs Type -> m a) -> m 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 :: MonadReduce m => Type -> (Type -> m a) -> (Dom Type -> Abs Type -> m a) -> m 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.
ifNotPiOrPathType :: (MonadReduce tcm, HasBuiltins tcm) => Type -> (Type -> tcm a) -> (Dom Type -> Abs Type -> tcm a) -> tcm a Source #
class PiApplyM a where Source #
A safe variant of piApply.
Minimal complete definition
Methods
piApplyM' :: (MonadReduce m, HasBuiltins m) => m Empty -> Type -> a -> m Type Source #
piApplyM :: (MonadReduce m, HasBuiltins m) => Type -> a -> m Type Source #
Instances
Instance definitions
data OutputTypeName Source #
getOutputTypeName :: Type -> TCM (Telescope, OutputTypeName) Source #
Strips all hidden and instance Pi's and return the argument telescope and head definition name, if possible.
addTypedInstance :: QName -> Type -> TCM () Source #
Register the definition with the given type as an instance
resolveUnknownInstanceDefs :: TCM () Source #
getInstanceDefs :: TCM InstanceTable Source #
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.