Safe Haskell	Safe
Language	Haskell2010

DDF.DBI

Documentation

class Monoid r m where Source #

Minimal complete definition

zero, plus

Methods

zero :: r h m Source #

plus :: r h (m -> m -> m) Source #

Instances

Lang repr => ProdCon (Monoid * repr) l r Source #
Methods prodCon :: (Monoid * repr l, Monoid * repr r) :- Monoid * repr (l, r) Source #

class DBI r where Source #

Minimal complete definition

z, s, abs, app

Methods

z :: r (a, h) a Source #

s :: r h b -> r (a, h) b Source #

abs :: r (a, h) b -> r h (a -> b) Source #

app :: r h (a -> b) -> r h a -> r h b Source #

hoas :: (r (a, h) a -> r (a, h) b) -> r h (a -> b) Source #

We use a variant of HOAS so it can be compile to DBI, which is more compositional (No Negative Occurence). It require explicit lifting of variables. Use lam to do automatic lifting of variables.

com :: r h ((b -> c) -> (a -> b) -> a -> c) Source #

flip :: r h ((a -> b -> c) -> b -> a -> c) Source #

id :: r h (a -> a) Source #

const :: r h (a -> b -> a) Source #

scomb :: r h ((a -> b -> c) -> (a -> b) -> a -> c) Source #

dup :: r h ((a -> a -> b) -> a -> b) Source #

let_ :: r h (a -> (a -> b) -> b) Source #

Instances

DBI Eval Source #
Methods z :: Eval (a, h) a Source # s :: Eval h b -> Eval (a, h) b Source # abs :: Eval (a, h) b -> Eval h (a -> b) Source # app :: Eval h (a -> b) -> Eval h a -> Eval h b Source # hoas :: (Eval (a, h) a -> Eval (a, h) b) -> Eval h (a -> b) Source # com :: Eval h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: Eval h ((a -> b -> c) -> b -> a -> c) Source # id :: Eval h (a -> a) Source # const :: Eval h (a -> b -> a) Source # scomb :: Eval h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: Eval h ((a -> a -> b) -> a -> b) Source # let_ :: Eval h (a -> (a -> b) -> b) Source #
DBI Show Source #
Methods z :: Show (a, h) a Source # s :: Show h b -> Show (a, h) b Source # abs :: Show (a, h) b -> Show h (a -> b) Source # app :: Show h (a -> b) -> Show h a -> Show h b Source # hoas :: (Show (a, h) a -> Show (a, h) b) -> Show h (a -> b) Source # com :: Show h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: Show h ((a -> b -> c) -> b -> a -> c) Source # id :: Show h (a -> a) Source # const :: Show h (a -> b -> a) Source # scomb :: Show h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: Show h ((a -> a -> b) -> a -> b) Source # let_ :: Show h (a -> (a -> b) -> b) Source #
DBI Size Source #
Methods z :: Size (a, h) a Source # s :: Size h b -> Size (a, h) b Source # abs :: Size (a, h) b -> Size h (a -> b) Source # app :: Size h (a -> b) -> Size h a -> Size h b Source # hoas :: (Size (a, h) a -> Size (a, h) b) -> Size h (a -> b) Source # com :: Size h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: Size h ((a -> b -> c) -> b -> a -> c) Source # id :: Size h (a -> a) Source # const :: Size h (a -> b -> a) Source # scomb :: Size h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: Size h ((a -> a -> b) -> a -> b) Source # let_ :: Size h (a -> (a -> b) -> b) Source #
DBI r => DBI (P r) Source #
Methods z :: P r (a, h) a Source # s :: P r h b -> P r (a, h) b Source # abs :: P r (a, h) b -> P r h (a -> b) Source # app :: P r h (a -> b) -> P r h a -> P r h b Source # hoas :: (P r (a, h) a -> P r (a, h) b) -> P r h (a -> b) Source # com :: P r h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: P r h ((a -> b -> c) -> b -> a -> c) Source # id :: P r h (a -> a) Source # const :: P r h (a -> b -> a) Source # scomb :: P r h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: P r h ((a -> a -> b) -> a -> b) Source # let_ :: P r h (a -> (a -> b) -> b) Source #
SubL c DBI => DBI (Term c) Source #
Methods z :: Term c (a, h) a Source # s :: Term c h b -> Term c (a, h) b Source # abs :: Term c (a, h) b -> Term c h (a -> b) Source # app :: Term c h (a -> b) -> Term c h a -> Term c h b Source # hoas :: (Term c (a, h) a -> Term c (a, h) b) -> Term c h (a -> b) Source # com :: Term c h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: Term c h ((a -> b -> c) -> b -> a -> c) Source # id :: Term c h (a -> a) Source # const :: Term c h (a -> b -> a) Source # scomb :: Term c h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: Term c h ((a -> a -> b) -> a -> b) Source # let_ :: Term c h (a -> (a -> b) -> b) Source #
DBI repr => DBI (UnHOAS repr) Source #
Methods z :: UnHOAS repr (a, h) a Source # s :: UnHOAS repr h b -> UnHOAS repr (a, h) b Source # abs :: UnHOAS repr (a, h) b -> UnHOAS repr h (a -> b) Source # app :: UnHOAS repr h (a -> b) -> UnHOAS repr h a -> UnHOAS repr h b Source # hoas :: (UnHOAS repr (a, h) a -> UnHOAS repr (a, h) b) -> UnHOAS repr h (a -> b) Source # com :: UnHOAS repr h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: UnHOAS repr h ((a -> b -> c) -> b -> a -> c) Source # id :: UnHOAS repr h (a -> a) Source # const :: UnHOAS repr h (a -> b -> a) Source # scomb :: UnHOAS repr h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: UnHOAS repr h ((a -> a -> b) -> a -> b) Source # let_ :: UnHOAS repr h (a -> (a -> b) -> b) Source #
Prod r => DBI (UnLiftEnv r) Source #
Methods z :: UnLiftEnv r (a, h) a Source # s :: UnLiftEnv r h b -> UnLiftEnv r (a, h) b Source # abs :: UnLiftEnv r (a, h) b -> UnLiftEnv r h (a -> b) Source # app :: UnLiftEnv r h (a -> b) -> UnLiftEnv r h a -> UnLiftEnv r h b Source # hoas :: (UnLiftEnv r (a, h) a -> UnLiftEnv r (a, h) b) -> UnLiftEnv r h (a -> b) Source # com :: UnLiftEnv r h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: UnLiftEnv r h ((a -> b -> c) -> b -> a -> c) Source # id :: UnLiftEnv r h (a -> a) Source # const :: UnLiftEnv r h (a -> b -> a) Source # scomb :: UnLiftEnv r h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: UnLiftEnv r h ((a -> a -> b) -> a -> b) Source # let_ :: UnLiftEnv r h (a -> (a -> b) -> b) Source #
Prod r => DBI (ImpW r) Source #
Methods z :: ImpW r (a, h) a Source # s :: ImpW r h b -> ImpW r (a, h) b Source # abs :: ImpW r (a, h) b -> ImpW r h (a -> b) Source # app :: ImpW r h (a -> b) -> ImpW r h a -> ImpW r h b Source # hoas :: (ImpW r (a, h) a -> ImpW r (a, h) b) -> ImpW r h (a -> b) Source # com :: ImpW r h ((b -> c) -> (a -> b) -> a -> c) Source # flip :: ImpW r h ((a -> b -> c) -> b -> a -> c) Source # id :: ImpW r h (a -> a) Source # const :: ImpW r h (a -> b -> a) Source # scomb :: ImpW r h ((a -> b -> c) -> (a -> b) -> a -> c) Source # dup :: ImpW r h ((a -> a -> b) -> a -> b) Source # let_ :: ImpW r h (a -> (a -> b) -> b) Source #
type SubLC c DBI Source #
type SubLC c DBI = ()

class LiftEnv r where Source #

Minimal complete definition

liftEnv

Methods

liftEnv :: r () a -> r h a Source #

const1 :: DBI r => r h a -> r h (b -> a) Source #

map2 :: Functor r f => r h (a -> b) -> r h (f a) -> r h (f b) Source #

return :: Applicative r a => r h (x -> a x) Source #

bind2 :: Monad r m => r h (m a) -> r h (a -> m b) -> r h (m b) Source #

map1 :: Functor r f => r h (a -> b) -> r h (f a -> f b) Source #

join1 :: Monad r m => r h (m (m a)) -> r h (m a) Source #

bimap2 :: (BiFunctor * r p, DBI r) => r h (a -> b) -> r h (c -> d) -> r h (p a c -> p b d) Source #

bimap3 :: (BiFunctor * r p, DBI r) => r h (a -> b) -> r h (c -> d) -> r h (p a c) -> r h (p b d) Source #

flip1 :: DBI r => r h (a -> b -> c) -> r h (b -> a -> c) Source #

flip2 :: DBI r => r h (a1 -> a -> c) -> r h a -> r h (a1 -> c) Source #

let_2 :: DBI r => r h a -> r h (a -> b) -> r h b Source #

class DBI r => Functor r f where Source #

Minimal complete definition

map

Methods

map :: r h ((a -> b) -> f a -> f b) Source #

Instances

Functor Eval IO Source #
Methods map :: Eval h ((a -> b) -> IO a -> IO b) Source #
Functor Show x Source #
Methods map :: Show h ((a -> b) -> x a -> x b) Source #
Functor Size x Source #
Methods map :: Size h ((a -> b) -> x a -> x b) Source #
SubL c IO => Functor (Term c) IO Source #
Methods map :: Term c h ((a -> b) -> IO a -> IO b) Source #
Functor r x => Functor (UnHOAS r) x Source #
Methods map :: UnHOAS r h ((a -> b) -> x a -> x b) Source #
(Prod r, Functor r m) => Functor (UnLiftEnv r) m Source #
Methods map :: UnLiftEnv r h ((a -> b) -> m a -> m b) Source #
(Prod r, Functor r x) => Functor (ImpW r) x Source #
Methods map :: ImpW r h ((a -> b) -> x a -> x b) Source #

class Functor r a => Applicative r a where Source #

Minimal complete definition

pure, ap

Methods

pure :: r h (x -> a x) Source #

ap :: r h (a (x -> y) -> a x -> a y) Source #

Instances

Applicative Eval IO Source #
Methods pure :: Eval h (x -> IO x) Source # ap :: Eval h (IO (x -> y) -> IO x -> IO y) Source #
Applicative Show x Source #
Methods pure :: Show h (x -> x x) Source # ap :: Show h (x (x -> y) -> x x -> x y) Source #
Applicative Size x Source #
Methods pure :: Size h (x -> x x) Source # ap :: Size h (x (x -> y) -> x x -> x y) Source #
SubL c IO => Applicative (Term c) IO Source #
Methods pure :: Term c h (x -> IO x) Source # ap :: Term c h (IO (x -> y) -> IO x -> IO y) Source #
Applicative r x => Applicative (UnHOAS r) x Source #
Methods pure :: UnHOAS r h (x -> x x) Source # ap :: UnHOAS r h (x (x -> y) -> x x -> x y) Source #
(Prod r, Applicative r m) => Applicative (UnLiftEnv r) m Source #
Methods pure :: UnLiftEnv r h (x -> m x) Source # ap :: UnLiftEnv r h (m (x -> y) -> m x -> m y) Source #
(Prod r, Applicative r x) => Applicative (ImpW r) x Source #
Methods pure :: ImpW r h (x -> x x) Source # ap :: ImpW r h (x (x -> y) -> x x -> x y) Source #

class Applicative r m => Monad r m where Source #

Minimal complete definition

join | bind

Methods

bind :: r h (m a -> (a -> m b) -> m b) Source #

join :: r h (m (m a) -> m a) Source #

Instances

Monad Eval IO Source #
Methods bind :: Eval h (IO a -> (a -> IO b) -> IO b) Source # join :: Eval h (IO (IO a) -> IO a) Source #
Monad Show x Source #
Methods bind :: Show h (x a -> (a -> x b) -> x b) Source # join :: Show h (x (x a) -> x a) Source #
Monad Size x Source #
Methods bind :: Size h (x a -> (a -> x b) -> x b) Source # join :: Size h (x (x a) -> x a) Source #
SubL c IO => Monad (Term c) IO Source #
Methods bind :: Term c h (IO a -> (a -> IO b) -> IO b) Source # join :: Term c h (IO (IO a) -> IO a) Source #
Monad r x => Monad (UnHOAS r) x Source #
Methods bind :: UnHOAS r h (x a -> (a -> x b) -> x b) Source # join :: UnHOAS r h (x (x a) -> x a) Source #
(Prod r, Monad r m) => Monad (UnLiftEnv r) m Source #
Methods bind :: UnLiftEnv r h (m a -> (a -> m b) -> m b) Source # join :: UnLiftEnv r h (m (m a) -> m a) Source #
(Prod r, Monad r x) => Monad (ImpW r) x Source #
Methods bind :: ImpW r h (x a -> (a -> x b) -> x b) Source # join :: ImpW r h (x (x a) -> x a) Source #

class BiFunctor r p where Source #

Minimal complete definition

bimap

Methods

bimap :: r h ((a -> b) -> (c -> d) -> p a c -> p b d) Source #

com2 :: DBI r => r h (b -> c) -> r h (a -> b) -> r h (a -> c) Source #

class NT repr l r where Source #

Minimal complete definition

conv

Methods

conv :: repr l t -> repr r t Source #

Instances

NT k k1 repr x x Source #
Methods conv :: x l t -> x r t Source #
NTS k k1 repr l r => NT k k1 repr l r Source #
Methods conv :: r l t -> r r t Source #

class NTS repr l r where Source #

Minimal complete definition

convS

Methods

convS :: repr l t -> repr r t Source #

Instances

(DBI repr, NT * * repr l r) => NTS * * repr l (a, r) Source #
Methods convS :: (a, r) l t -> (a, r) r t Source #

lam :: forall repr a b h. DBI repr => ((forall k. NT repr (a, h) k => repr k a) -> repr (a, h) b) -> repr h (a -> b) Source #

lam2 :: forall repr a b c h. DBI repr => ((forall k. NT repr (a, h) k => repr k a) -> (forall k. NT repr (b, (a, h)) k => repr k b) -> repr (b, (a, h)) c) -> repr h (a -> b -> c) Source #

lam3 :: (NT * * repr (a, (b1, (a1, h))) k, NT * * repr (b1, (a1, h)) k1, NT * * repr (a1, h) k2, DBI repr) => (repr k2 a1 -> repr k1 b1 -> repr k a -> repr (a, (b1, (a1, h))) b) -> repr h (a1 -> b1 -> a -> b) Source #

lam4 :: (NT * * repr (a, (a1, (b1, (a2, h)))) k, NT * * repr (a2, h) k3, NT * * repr (b1, (a2, h)) k2, NT * * repr (a1, (b1, (a2, h))) k1, DBI repr) => (repr k3 a2 -> repr k2 b1 -> repr k1 a1 -> repr k a -> repr (a, (a1, (b1, (a2, h)))) b) -> repr h (a2 -> b1 -> a1 -> a -> b) Source #

app2 :: DBI r => r h (a1 -> a -> b) -> r h a1 -> r h a -> r h b Source #

app3 :: DBI r => r h (a2 -> a1 -> a -> b) -> r h a2 -> r h a1 -> r h a -> r h b Source #

app4 :: DBI r => r h (a3 -> a2 -> a1 -> a -> b) -> r h a3 -> r h a2 -> r h a1 -> r h a -> r h b Source #

app5 :: DBI r => r h (a4 -> a3 -> a2 -> a1 -> a -> b) -> r h a4 -> r h a3 -> r h a2 -> r h a1 -> r h a -> r h b Source #

plus2 :: (Monoid * r b, DBI r) => r h b -> r h b -> r h b Source #

noEnv :: repr () x -> repr () x Source #

scomb2 :: DBI r => r h (a -> b -> c) -> r h (a -> b) -> r h (a -> c) Source #

plus1 :: (Monoid * r a, DBI r) => r h a -> r h (a -> a) Source #

dup1 :: DBI r => r h (a -> a -> b) -> r h (a -> b) Source #

module DDF.ImportMeta