Bound.Scope.Simple

Scope provides a single traditional de Bruijn level and is often used inside of the definition of binders.

Documentation

newtype Scope b f a

Scope b f a is an f expression with bound variables in b, and free variables in a

This implements traditional de Bruijn indices, while Scope implements generalized de Bruijn indices.

These traditional indices can be used to test the performance gain of generalized indices.

While this type Scope is identical to EitherT this module focuses on a drop-in replacement for Scope.

Another use case is for syntaxes not stable under substitution, therefore with only a Functor instance and no Monad instance.

Constructors

Scope

Fields

• unscope :: f (Var b a)

Instances

MonadTrans (Scope b)

Defined in Bound.Scope.Simple

Methods

lift :: Monad m => m a -> Scope b m a

Bound (Scope b)

Defined in Bound.Scope.Simple

Methods

(>>>=) :: Monad f => Scope b f a -> (a -> f c) -> Scope b f c

MFunctor (Scope b :: (Type -> Type) -> Type -> Type)

Defined in Bound.Scope.Simple

Methods

hoist :: Monad m => (forall a. m a -> n a) -> Scope b m b0 -> Scope b n b0

Functor f => Generic1 (Scope b f :: Type -> Type)

Defined in Bound.Scope.Simple

Associated Types

type Rep1 (Scope b f) :: k -> Type

Methods

from1 :: Scope b f a -> Rep1 (Scope b f) a

to1 :: Rep1 (Scope b f) a -> Scope b f a

Monad f => Monad (Scope b f)

The monad permits substitution on free variables, while preserving bound variables

Defined in Bound.Scope.Simple

Methods

(>>=) :: Scope b f a -> (a -> Scope b f b0) -> Scope b f b0

(>>) :: Scope b f a -> Scope b f b0 -> Scope b f b0

return :: a -> Scope b f a

fail :: String -> Scope b f a

Functor f => Functor (Scope b f)

Defined in Bound.Scope.Simple

Methods

fmap :: (a -> b0) -> Scope b f a -> Scope b f b0

(<$) :: a -> Scope b f b0 -> Scope b f a

Monad f => Applicative (Scope b f)

Defined in Bound.Scope.Simple

Methods

pure :: a -> Scope b f a

(<*>) :: Scope b f (a -> b0) -> Scope b f a -> Scope b f b0

liftA2 :: (a -> b0 -> c) -> Scope b f a -> Scope b f b0 -> Scope b f c

(*>) :: Scope b f a -> Scope b f b0 -> Scope b f b0

(<*) :: Scope b f a -> Scope b f b0 -> Scope b f a

Foldable f => Foldable (Scope b f)

toList is provides a list (with duplicates) of the free variables

Defined in Bound.Scope.Simple

Methods

fold :: Monoid m => Scope b f m -> m

foldMap :: Monoid m => (a -> m) -> Scope b f a -> m

foldr :: (a -> b0 -> b0) -> b0 -> Scope b f a -> b0

foldr' :: (a -> b0 -> b0) -> b0 -> Scope b f a -> b0

foldl :: (b0 -> a -> b0) -> b0 -> Scope b f a -> b0

foldl' :: (b0 -> a -> b0) -> b0 -> Scope b f a -> b0

foldr1 :: (a -> a -> a) -> Scope b f a -> a

foldl1 :: (a -> a -> a) -> Scope b f a -> a

toList :: Scope b f a -> [a]

null :: Scope b f a -> Bool

length :: Scope b f a -> Int

elem :: Eq a => a -> Scope b f a -> Bool

maximum :: Ord a => Scope b f a -> a

minimum :: Ord a => Scope b f a -> a

sum :: Num a => Scope b f a -> a

product :: Num a => Scope b f a -> a

Traversable f => Traversable (Scope b f)

Defined in Bound.Scope.Simple

Methods

traverse :: Applicative f0 => (a -> f0 b0) -> Scope b f a -> f0 (Scope b f b0)

sequenceA :: Applicative f0 => Scope b f (f0 a) -> f0 (Scope b f a)

mapM :: Monad m => (a -> m b0) -> Scope b f a -> m (Scope b f b0)

sequence :: Monad m => Scope b f (m a) -> m (Scope b f a)

(Eq b, Eq1 f) => Eq1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

liftEq :: (a -> b0 -> Bool) -> Scope b f a -> Scope b f b0 -> Bool

(Ord b, Ord1 f) => Ord1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

liftCompare :: (a -> b0 -> Ordering) -> Scope b f a -> Scope b f b0 -> Ordering

(Read b, Read1 f) => Read1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Scope b f a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Scope b f a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Scope b f a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Scope b f a]

(Show b, Show1 f) => Show1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Scope b f a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Scope b f a] -> ShowS

(Serial b, Serial1 f) => Serial1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Scope b f a -> m ()

deserializeWith :: MonadGet m => m a -> m (Scope b f a)

(Hashable b, Hashable1 f) => Hashable1 (Scope b f)

Defined in Bound.Scope.Simple

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Scope b f a -> Int

(Eq b, Eq1 f, Eq a) => Eq (Scope b f a)

Defined in Bound.Scope.Simple

Methods

(==) :: Scope b f a -> Scope b f a -> Bool

(/=) :: Scope b f a -> Scope b f a -> Bool

(Typeable b, Typeable f, Data a, Data (f (Var b a))) => Data (Scope b f a)

Defined in Bound.Scope.Simple

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Scope b f a -> c (Scope b f a)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Scope b f a)

toConstr :: Scope b f a -> Constr

dataTypeOf :: Scope b f a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Scope b f a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Scope b f a))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Scope b f a -> Scope b f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Scope b f a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Scope b f a -> r

gmapQ :: (forall d. Data d => d -> u) -> Scope b f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Scope b f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Scope b f a -> m (Scope b f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Scope b f a -> m (Scope b f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Scope b f a -> m (Scope b f a)

(Ord b, Ord1 f, Ord a) => Ord (Scope b f a)

Defined in Bound.Scope.Simple

Methods

compare :: Scope b f a -> Scope b f a -> Ordering

(<) :: Scope b f a -> Scope b f a -> Bool

(<=) :: Scope b f a -> Scope b f a -> Bool

(>) :: Scope b f a -> Scope b f a -> Bool

(>=) :: Scope b f a -> Scope b f a -> Bool

max :: Scope b f a -> Scope b f a -> Scope b f a

min :: Scope b f a -> Scope b f a -> Scope b f a

(Read b, Read1 f, Read a) => Read (Scope b f a)

Defined in Bound.Scope.Simple

Methods

readsPrec :: Int -> ReadS (Scope b f a)

readList :: ReadS [Scope b f a]

readPrec :: ReadPrec (Scope b f a)

readListPrec :: ReadPrec [Scope b f a]

(Show b, Show1 f, Show a) => Show (Scope b f a)

Defined in Bound.Scope.Simple

Methods

showsPrec :: Int -> Scope b f a -> ShowS

show :: Scope b f a -> String

showList :: [Scope b f a] -> ShowS

Generic (Scope b f a)

Defined in Bound.Scope.Simple

Associated Types

type Rep (Scope b f a) :: Type -> Type

Methods

from :: Scope b f a -> Rep (Scope b f a) x

to :: Rep (Scope b f a) x -> Scope b f a

(Binary b, Serial1 f, Binary a) => Binary (Scope b f a)

Defined in Bound.Scope.Simple

Methods

put :: Scope b f a -> Put

get :: Get (Scope b f a)

putList :: [Scope b f a] -> Put

(Serial b, Serial1 f, Serial a) => Serial (Scope b f a)

Defined in Bound.Scope.Simple

Methods

serialize :: MonadPut m => Scope b f a -> m ()

deserialize :: MonadGet m => m (Scope b f a)

(Serialize b, Serial1 f, Serialize a) => Serialize (Scope b f a)

Defined in Bound.Scope.Simple

Methods

put :: Putter (Scope b f a)

get :: Get (Scope b f a)

NFData (f (Var b a)) => NFData (Scope b f a)

Defined in Bound.Scope.Simple

Methods

rnf :: Scope b f a -> ()

(Hashable b, Hashable1 f, Hashable a) => Hashable (Scope b f a)

Defined in Bound.Scope.Simple

Methods

hashWithSalt :: Int -> Scope b f a -> Int

hash :: Scope b f a -> Int

type Rep1 (Scope b f :: Type -> Type)

Defined in Bound.Scope.Simple

type Rep1 (Scope b f :: Type -> Type) = D1 (MetaData "Scope" "Bound.Scope.Simple" "bound-2.0.1-AtZsY3yZaEKLBfeR1JA5NI" True) (C1 (MetaCons "Scope" PrefixI True) (S1 (MetaSel (Just "unscope") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (f :.: Rec1 (Var b))))

type Rep (Scope b f a)

Defined in Bound.Scope.Simple

type Rep (Scope b f a) = D1 (MetaData "Scope" "Bound.Scope.Simple" "bound-2.0.1-AtZsY3yZaEKLBfeR1JA5NI" True) (C1 (MetaCons "Scope" PrefixI True) (S1 (MetaSel (Just "unscope") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (Var b a)))))

Abstraction

abstract :: Functor f => (a -> Maybe b) -> f a -> Scope b f a

Capture some free variables in an expression to yield a Scope with bound variables in b

>>> :m + Data.List
>>> abstract (`elemIndex` "bar") "barry"
Scope [B 0,B 1,B 2,B 2,F 'y']

abstract1 :: (Functor f, Eq a) => a -> f a -> Scope () f a

Abstract over a single variable

>>> abstract1 'x' "xyz"
Scope [B (),F 'y',F 'z']

Instantiation

instantiate :: Monad f => (b -> f a) -> Scope b f a -> f a

Enter a scope, instantiating all bound variables

>>> :m + Data.List
>>> instantiate (\x -> [toEnum (97 + x)]) $ abstract (`elemIndex` "bar") "barry"
"abccy"

instantiate1 :: Monad f => f a -> Scope n f a -> f a

Enter a Scope that binds one variable, instantiating it

>>> instantiate1 "x" $ Scope [B (),F 'y',F 'z']
"xyz"

Alternative names for 'unscope'/'Scope'

fromScope :: Scope b f a -> f (Var b a)

fromScope is just another name for unscope and is exported to mimick fromScope. In particular no Monad constraint is required.

toScope :: f (Var b a) -> Scope b f a

toScope is just another name for Scope and is exported to mimick toScope. In particular no Monad constraint is required.

Bound variable manipulation

splat :: Monad f => (a -> f c) -> (b -> f c) -> Scope b f a -> f c

Perform substitution on both bound and free variables in a Scope.

bindings :: Foldable f => Scope b f a -> [b]

Return a list of occurences of the variables bound by this Scope.

mapBound :: Functor f => (b -> b') -> Scope b f a -> Scope b' f a

Perform a change of variables on bound variables.

mapScope :: Functor f => (b -> d) -> (a -> c) -> Scope b f a -> Scope d f c

Perform a change of variables, reassigning both bound and free variables.

liftMBound :: Monad m => (b -> b') -> Scope b m a -> Scope b' m a

Perform a change of variables on bound variables given only a Monad instance

liftMScope :: Monad m => (b -> d) -> (a -> c) -> Scope b m a -> Scope d m c

A version of mapScope that can be used when you only have the Monad instance

foldMapBound :: (Foldable f, Monoid r) => (b -> r) -> Scope b f a -> r

Obtain a result by collecting information from both bound and free variables

foldMapScope :: (Foldable f, Monoid r) => (b -> r) -> (a -> r) -> Scope b f a -> r

Obtain a result by collecting information from both bound and free variables

traverseBound_ :: (Applicative g, Foldable f) => (b -> g d) -> Scope b f a -> g ()

traverse_ the bound variables in a Scope.

traverseScope_ :: (Applicative g, Foldable f) => (b -> g d) -> (a -> g c) -> Scope b f a -> g ()

traverse both the variables bound by this scope and any free variables.

mapMBound_ :: (Monad g, Foldable f) => (b -> g d) -> Scope b f a -> g ()

mapM_ over the variables bound by this scope

mapMScope_ :: (Monad m, Foldable f) => (b -> m d) -> (a -> m c) -> Scope b f a -> m ()

A traverseScope_ that can be used when you only have a Monad instance

traverseBound :: (Applicative g, Traversable f) => (b -> g c) -> Scope b f a -> g (Scope c f a)

Traverse both bound and free variables

traverseScope :: (Applicative g, Traversable f) => (b -> g d) -> (a -> g c) -> Scope b f a -> g (Scope d f c)

Traverse both bound and free variables

mapMBound :: (Monad m, Traversable f) => (b -> m c) -> Scope b f a -> m (Scope c f a)

mapM over both bound and free variables

mapMScope :: (Monad m, Traversable f) => (b -> m d) -> (a -> m c) -> Scope b f a -> m (Scope d f c)

A traverseScope that can be used when you only have a Monad instance

serializeScope :: (Serial1 f, MonadPut m) => (b -> m ()) -> (v -> m ()) -> Scope b f v -> m ()

deserializeScope :: (Serial1 f, MonadGet m) => m b -> m v -> m (Scope b f v)

hoistScope :: (f (Var b a) -> g (Var b a)) -> Scope b f a -> Scope b g a

bitraverseScope :: (Bitraversable t, Applicative f) => (k -> f k') -> (a -> f a') -> Scope b (t k) a -> f (Scope b (t k') a')

This allows you to bitraverse a Scope.

bitransverseScope :: Applicative f => (forall a a'. (a -> f a') -> t a -> f (u a')) -> forall a a'. (a -> f a') -> Scope b t a -> f (Scope b u a')

transverseScope :: Functor f => (forall r. g r -> f (h r)) -> Scope b g a -> f (Scope b h a)

This is a higher-order analogue of traverse.

instantiateVars :: Monad t => [a] -> Scope Int t a -> t a

instantiate bound variables using a list of new variables