Agda.TypeChecking.Substitute

Application

class Apply t where

Apply something to a bunch of arguments. Preserves blocking tags (application can never resolve blocking).

Minimal complete definition

Nothing

Methods

apply :: t -> Args -> t

applyE :: t -> Elims -> t

Instances

Apply Permutation

Apply ClauseBody

Apply Clause

Apply Sort

Apply Type

Apply Term

Apply CompiledClauses

Apply FunctionInverse

Apply PrimFun

Apply Defn

Apply Projection

Apply Definition

Apply RewriteRule

Apply DisplayTerm

Apply t => Apply [t]

Apply [Occurrence]

Apply [Polarity]

Apply t => Apply (Maybe t)

Apply a => Apply (Ptr a)

DoDrop a => Apply (Drop a)

Apply t => Apply (Blocked t)

Subst a => Apply (Tele a)

Apply a => Apply (Case a)

Apply a => Apply (WithArity a)

(Apply a, Apply b) => Apply (a, b)

Apply v => Apply (Map k v)

(Apply a, Apply b, Apply c) => Apply (a, b, c)

canProject :: QName -> Term -> Maybe (Arg Term)

If $v$ is a record value, canProject f v returns its field f.

conApp :: ConHead -> Args -> Elims -> Term

Eliminate a constructed term.

defApp :: QName -> Elims -> Elims -> Term

defApp f us vs applies Def f us to further arguments vs, eliminating top projection redexes. If us is not empty, we cannot have a projection redex, since the record argument is the first one.

argToDontCare :: Arg c Term -> Term

piApply :: Type -> Args -> Type

The type must contain the right number of pis without have to perform any reduction.

Abstraction

class Abstract t where

(abstract args v) apply args --> v[args].

Methods

abstract :: Telescope -> t -> t

Instances

Abstract Permutation

Abstract ClauseBody

Abstract Clause

Abstract Sort

Abstract Telescope

Abstract Type

Abstract Term

Abstract CompiledClauses

Abstract FunctionInverse

Abstract PrimFun

Abstract Defn

Abstract Projection

Abstract Definition

Abstract RewriteRule

tel ⊢ (Γ ⊢ lhs ↦ rhs : t) becomes tel, Γ ⊢ lhs ↦ rhs : t) we do not need to change lhs, rhs, and t since they live in Γ. See 'Abstract Clause'.

Abstract t => Abstract [t]

Abstract [Occurrence]

Abstract [Polarity]

Abstract t => Abstract (Maybe t)

DoDrop a => Abstract (Drop a)

Abstract a => Abstract (Case a)

Abstract a => Abstract (WithArity a)

Abstract v => Abstract (Map k v)

telVars :: Telescope -> [Arg Pattern]

namedTelVars :: Telescope -> [NamedArg Pattern]

abstractArgs :: Abstract a => Args -> a -> a

Explicit substitutions

idS :: Substitution

wkS :: Int -> Substitution -> Substitution

raiseS :: Int -> Substitution

consS :: Term -> Substitution -> Substitution

singletonS :: Term -> Substitution

liftS :: Int -> Substitution -> Substitution

dropS :: Int -> Substitution -> Substitution

composeS :: Substitution -> Substitution -> Substitution

applySubst (ρ composeS σ) v == applySubst ρ (applySubst σ v)

splitS :: Int -> Substitution -> (Substitution, Substitution)

(++#) :: [Term] -> Substitution -> Substitution infixr 4

prependS :: Empty -> [Maybe Term] -> Substitution -> Substitution

parallelS :: [Term] -> Substitution

compactS :: Empty -> [Maybe Term] -> Substitution

lookupS :: Substitution -> Nat -> Term

Substitution and raisingshiftingweakening

class Subst t where

Apply a substitution.

Methods

applySubst :: Substitution -> t -> t

Instances

Subst Bool

Subst ()

Subst Name

Subst Substitution

Subst Pattern

Subst ClauseBody

Subst Clause

Subst LevelAtom

Subst PlusLevel

Subst Level

Subst Sort

Subst Type

Subst Elim

Subst Term

Subst DisplayTerm

Subst DisplayForm

Subst Constraint

Subst AsBinding

Subst DotPatternInst

Subst ProblemRest

Subst Equality

Subst SizeConstraint

Subst SizeMeta

Subst a => Subst [a]

Subst a => Subst (Maybe a)

Subst a => Subst (Ptr a)

Subst t => Subst (Blocked t)

Subst a => Subst (Tele a)

Subst a => Subst (Abs a)

Subst a => Subst (Dom a)

Subst a => Subst (Arg a)

Subst (Problem' p)

Subst a => Subst (HomHet a)

(Subst a, Subst b) => Subst (a, b)

Subst (SizeExpr' NamedRigid SizeMeta)

Only for raise.

Subst a => Subst (Named name a)

(Subst a, Subst b, Subst c) => Subst (a, b, c)

(Subst a, Subst b, Subst c, Subst d) => Subst (a, b, c, d)

raise :: Subst t => Nat -> t -> t

raiseFrom :: Subst t => Nat -> Nat -> t -> t

subst :: Subst t => Term -> t -> t

strengthen :: Subst t => Empty -> t -> t

substUnder :: Subst t => Nat -> Term -> t -> t

Telescopes

type TelView = TelV Type

data TelV a

Constructors

TelV

Fields

theTel :: Tele (Dom a)

theCore :: a

Instances

Functor TelV

(Eq a, Subst a) => Eq (TelV a)

(Ord a, Subst a) => Ord (TelV a)

Show a => Show (TelV a)

Typeable (* -> *) TelV

type ListTel' a = [Dom (a, Type)]

type ListTel = ListTel' ArgName

telFromList' :: (a -> ArgName) -> ListTel' a -> Telescope

telFromList :: ListTel -> Telescope

telToList :: Telescope -> ListTel

telToArgs :: Telescope -> [Arg ArgName]

bindsToTel' :: (Name -> a) -> [Name] -> Dom Type -> ListTel' a

Turn a typed binding (x1 .. xn : A) into a telescope.

bindsToTel :: [Name] -> Dom Type -> ListTel

telView' :: Type -> TelView

mkPi :: Dom (ArgName, Type) -> Type -> Type

mkPi dom t = telePi (telFromList [dom]) t

mkLam :: Arg ArgName -> Term -> Term

telePi' :: (Abs Type -> Abs Type) -> Telescope -> Type -> Type

telePi :: Telescope -> Type -> Type

Uses free variable analysis to introduce noAbs bindings.

telePi_ :: Telescope -> Type -> Type

Everything will be a Abs.

teleLam :: Telescope -> Term -> Term

class TeleNoAbs a where

Performs void (noAbs) abstraction over telescope.

Methods

teleNoAbs :: a -> Term -> Term

Instances

TeleNoAbs Telescope

TeleNoAbs ListTel

dLub :: Sort -> Abs Sort -> Sort

Dependent least upper bound, to assign a level to expressions like forall i -> Set i.

dLub s1 i.s2 = omega if i appears in the rigid variables of s2.

Functions on abstractions

absApp :: Subst t => Abs t -> Term -> t

Instantiate an abstraction. Strict in the term.

lazyAbsApp :: Subst t => Abs t -> Term -> t

Instantiate an abstraction. Lazy in the term, which allow it to be IMPOSSIBLE in the case where the variable shouldn't be used but we cannot use noabsApp. Used in Apply.

noabsApp :: Subst t => Empty -> Abs t -> t

Instantiate an abstraction that doesn't use its argument.

absBody :: Subst t => Abs t -> t

mkAbs :: (Subst a, Free a) => ArgName -> a -> Abs a

reAbs :: (Subst a, Free a) => Abs a -> Abs a

underAbs :: Subst a => (a -> b -> b) -> a -> Abs b -> Abs b

underAbs k a b applies k to a and the content of abstraction b and puts the abstraction back. a is raised if abstraction was proper such that at point of application of k and the content of b are at the same context. Precondition: a and b are at the same context at call time.

underLambdas :: Subst a => Int -> (a -> Term -> Term) -> a -> Term -> Term

underLambdas n k a b drops n initial Lams from b, performs operation k on a and the body of b, and puts the Lams back. a is raised correctly according to the number of abstractions.

class GetBody a where

Methods to retrieve the clauseBody.

Methods

getBody :: a -> Maybe Term

Returns the properly raised clause Body, and Nothing if NoBody.

getBodyUnraised :: a -> Maybe Term

Just grabs the body, without raising the de Bruijn indices. This is useful if you want to consider the body in context clauseTel.

Instances

GetBody ClauseBody

GetBody Clause

Syntactic equality and order

Level stuff

sLub :: Sort -> Sort -> Sort

lvlView :: Term -> Level

levelMax :: [PlusLevel] -> Level

sortTm :: Sort -> Term

levelSort :: Level -> Sort

levelTm :: Level -> Term

unLevelAtom :: LevelAtom -> Term

Boring instances

data Substitution

Substitutions.

Constructors

IdS

EmptyS

Wk !Int Substitution

Term :# Substitution infixr 4

Strengthen Empty Substitution

Lift !Int Substitution

Instances

Eq Substitution

Ord Substitution

Show Substitution

KillRange Substitution

Sized Substitution

Subst Substitution