DBI

Documentation

class DBI repr where

Minimal complete definition

z, s, lam, app, mkProd, zro, fst, lit, plus, minus, mult, divide, fix, left, right, sumMatch, unit, exfalso, nothing, just, optionMatch, ioRet, ioBind, ioMap, nil, cons, listMatch, writer, runWriter

Methods

z :: repr (a, h) a

s :: repr h b -> repr (a, h) b

lam :: repr (a, h) b -> repr h (a -> b)

app :: repr h (a -> b) -> repr h a -> repr h b

mkProd :: repr h (a -> b -> (a, b))

zro :: repr h ((a, b) -> a)

fst :: repr h ((a, b) -> b)

lit :: Double -> repr h Double

litZro :: repr h Double

litOne :: repr h Double

plus :: repr h (Double -> Double -> Double)

minus :: repr h (Double -> Double -> Double)

mult :: repr h (Double -> Double -> Double)

divide :: repr h (Double -> Double -> Double)

hoas :: (repr (a, h) a -> repr (a, h) b) -> repr h (a -> b)

fix :: repr h ((a -> a) -> a)

left :: repr h (a -> Either a b)

right :: repr h (b -> Either a b)

sumMatch :: repr h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: repr h ()

exfalso :: repr h (Void -> a)

nothing :: repr h (Maybe a)

just :: repr h (a -> Maybe a)

optionMatch :: repr h (b -> (a -> b) -> Maybe a -> b)

ioRet :: repr h (a -> IO a)

ioBind :: repr h (IO a -> (a -> IO b) -> IO b)

ioMap :: repr h ((a -> b) -> IO a -> IO b)

nil :: repr h [a]

cons :: repr h (a -> [a] -> [a])

listMatch :: repr h (b -> (a -> [a] -> b) -> [a] -> b)

com :: repr h ((b -> c) -> (a -> b) -> a -> c)

append :: repr h ([a] -> [a] -> [a])

writer :: repr h ((a, w) -> Writer w a)

runWriter :: repr h (Writer w a -> (a, w))

swap :: repr h ((l, r) -> (r, l))

flip :: repr h ((a -> b -> c) -> b -> a -> c)

id :: repr h (a -> a)

const :: repr h (a -> b -> a)

Instances

DBI Eval

Methods

z :: Eval (a, h) a

s :: Eval h b -> Eval (a, h) b

lam :: Eval (a, h) b -> Eval h (a -> b)

app :: Eval h (a -> b) -> Eval h a -> Eval h b

mkProd :: Eval h (a -> b -> (a, b))

zro :: Eval h ((a, b) -> a)

fst :: Eval h ((a, b) -> b)

lit :: Double -> Eval h Double

litZro :: Eval h Double

litOne :: Eval h Double

plus :: Eval h (Double -> Double -> Double)

minus :: Eval h (Double -> Double -> Double)

mult :: Eval h (Double -> Double -> Double)

divide :: Eval h (Double -> Double -> Double)

hoas :: (Eval (a, h) a -> Eval (a, h) b) -> Eval h (a -> b)

fix :: Eval h ((a -> a) -> a)

left :: Eval h (a -> Either a b)

right :: Eval h (b -> Either a b)

sumMatch :: Eval h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: Eval h ()

exfalso :: Eval h (Void -> a)

nothing :: Eval h (Maybe a)

just :: Eval h (a -> Maybe a)

optionMatch :: Eval h (b -> (a -> b) -> Maybe a -> b)

ioRet :: Eval h (a -> IO a)

ioBind :: Eval h (IO a -> (a -> IO b) -> IO b)

ioMap :: Eval h ((a -> b) -> IO a -> IO b)

nil :: Eval h [a]

cons :: Eval h (a -> [a] -> [a])

listMatch :: Eval h (b -> (a -> [a] -> b) -> [a] -> b)

com :: Eval h ((b -> c) -> (a -> b) -> a -> c)

append :: Eval h ([a] -> [a] -> [a])

writer :: Eval h ((a, w) -> Writer w a)

runWriter :: Eval h (Writer w a -> (a, w))

swap :: Eval h ((l, r) -> (r, l))

flip :: Eval h ((a -> b -> c) -> b -> a -> c)

id :: Eval h (a -> a)

const :: Eval h (a -> b -> a)

DBI repr => DBI (WDiff repr)

Methods

z :: WDiff repr (a, h) a

s :: WDiff repr h b -> WDiff repr (a, h) b

lam :: WDiff repr (a, h) b -> WDiff repr h (a -> b)

app :: WDiff repr h (a -> b) -> WDiff repr h a -> WDiff repr h b

mkProd :: WDiff repr h (a -> b -> (a, b))

zro :: WDiff repr h ((a, b) -> a)

fst :: WDiff repr h ((a, b) -> b)

lit :: Double -> WDiff repr h Double

litZro :: WDiff repr h Double

litOne :: WDiff repr h Double

plus :: WDiff repr h (Double -> Double -> Double)

minus :: WDiff repr h (Double -> Double -> Double)

mult :: WDiff repr h (Double -> Double -> Double)

divide :: WDiff repr h (Double -> Double -> Double)

hoas :: (WDiff repr (a, h) a -> WDiff repr (a, h) b) -> WDiff repr h (a -> b)

fix :: WDiff repr h ((a -> a) -> a)

left :: WDiff repr h (a -> Either a b)

right :: WDiff repr h (b -> Either a b)

sumMatch :: WDiff repr h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: WDiff repr h ()

exfalso :: WDiff repr h (Void -> a)

nothing :: WDiff repr h (Maybe a)

just :: WDiff repr h (a -> Maybe a)

optionMatch :: WDiff repr h (b -> (a -> b) -> Maybe a -> b)

ioRet :: WDiff repr h (a -> IO a)

ioBind :: WDiff repr h (IO a -> (a -> IO b) -> IO b)

ioMap :: WDiff repr h ((a -> b) -> IO a -> IO b)

nil :: WDiff repr h [a]

cons :: WDiff repr h (a -> [a] -> [a])

listMatch :: WDiff repr h (b -> (a -> [a] -> b) -> [a] -> b)

com :: WDiff repr h ((b -> c) -> (a -> b) -> a -> c)

append :: WDiff repr h ([a] -> [a] -> [a])

writer :: WDiff repr h ((a, w) -> Writer w a)

runWriter :: WDiff repr h (Writer w a -> (a, w))

swap :: WDiff repr h ((l, r) -> (r, l))

flip :: WDiff repr h ((a -> b -> c) -> b -> a -> c)

id :: WDiff repr h (a -> a)

const :: WDiff repr h (a -> b -> a)

DBI (Show * *)

Methods

z :: Show * * (a, h) a

s :: Show * * h b -> Show * * (a, h) b

lam :: Show * * (a, h) b -> Show * * h (a -> b)

app :: Show * * h (a -> b) -> Show * * h a -> Show * * h b

mkProd :: Show * * h (a -> b -> (a, b))

zro :: Show * * h ((a, b) -> a)

fst :: Show * * h ((a, b) -> b)

lit :: Double -> Show * * h Double

litZro :: Show * * h Double

litOne :: Show * * h Double

plus :: Show * * h (Double -> Double -> Double)

minus :: Show * * h (Double -> Double -> Double)

mult :: Show * * h (Double -> Double -> Double)

divide :: Show * * h (Double -> Double -> Double)

hoas :: (Show * * (a, h) a -> Show * * (a, h) b) -> Show * * h (a -> b)

fix :: Show * * h ((a -> a) -> a)

left :: Show * * h (a -> Either a b)

right :: Show * * h (b -> Either a b)

sumMatch :: Show * * h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: Show * * h ()

exfalso :: Show * * h (Void -> a)

nothing :: Show * * h (Maybe a)

just :: Show * * h (a -> Maybe a)

optionMatch :: Show * * h (b -> (a -> b) -> Maybe a -> b)

ioRet :: Show * * h (a -> IO a)

ioBind :: Show * * h (IO a -> (a -> IO b) -> IO b)

ioMap :: Show * * h ((a -> b) -> IO a -> IO b)

nil :: Show * * h [a]

cons :: Show * * h (a -> [a] -> [a])

listMatch :: Show * * h (b -> (a -> [a] -> b) -> [a] -> b)

com :: Show * * h ((b -> c) -> (a -> b) -> a -> c)

append :: Show * * h ([a] -> [a] -> [a])

writer :: Show * * h ((a, w) -> Writer w a)

runWriter :: Show * * h (Writer w a -> (a, w))

swap :: Show * * h ((l, r) -> (r, l))

flip :: Show * * h ((a -> b -> c) -> b -> a -> c)

id :: Show * * h (a -> a)

const :: Show * * h (a -> b -> a)

const1 :: DBI repr => repr h a -> repr h (b -> a)

cons2 :: DBI repr => repr h a -> repr h [a] -> repr h [a]

listMatch2 :: DBI repr => repr h a1 -> repr h (a -> [a] -> a1) -> repr h ([a] -> a1)

fix2 :: DBI repr => repr h ((a -> b) -> a -> b) -> repr h a -> repr h b

class DBI r => Monoid r m where

Minimal complete definition

mzero, mappend

Methods

mzero :: r h m

mappend :: r h (m -> m -> m)

Instances

DBI r => Monoid r [a]

Methods

mzero :: r h [a]

mappend :: r h ([a] -> [a] -> [a])

class DBI r => Functor r f where

Minimal complete definition

map

Methods

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

Instances

DBI r => Functor r Maybe

Methods

map :: r h ((a -> b) -> Maybe a -> Maybe b)

DBI r => Functor r IO

Methods

map :: r h ((a -> b) -> IO a -> IO b)

DBI r => Functor r (Writer w)

Methods

map :: r h ((a -> b) -> Writer w a -> Writer w b)

class Functor r a => Applicative r a where

Minimal complete definition

pure, ap

Methods

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

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

Instances

DBI r => Applicative r Maybe

Methods

pure :: r h (x -> Maybe x)

ap :: r h (Maybe (x -> y) -> Maybe x -> Maybe y)

DBI r => Applicative r IO

Methods

pure :: r h (x -> IO x)

ap :: r h (IO (x -> y) -> IO x -> IO y)

(DBI r, Monoid r w) => Applicative r (Writer w)

Methods

pure :: r h (x -> Writer w x)

ap :: r h (Writer w (x -> y) -> Writer w x -> Writer w y)

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

class Applicative r m => Monad r m where

Minimal complete definition

join | bind

Methods

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

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

Instances

DBI r => Monad r Maybe

Methods

bind :: r h (Maybe a -> (a -> Maybe b) -> Maybe b)

join :: r h (Maybe (Maybe a) -> Maybe a)

DBI r => Monad r IO

Methods

bind :: r h (IO a -> (a -> IO b) -> IO b)

join :: r h (IO (IO a) -> IO a)

(DBI r, Monoid r w) => Monad r (Writer w)

Methods

bind :: r h (Writer w a -> (a -> Writer w b) -> Writer w b)

join :: r h (Writer w (Writer w a) -> Writer w a)

bind2 :: Monad repr m => repr h (m a) -> repr h (a -> m b) -> repr h (m b)

map1 :: Functor repr f => repr h (a -> b) -> repr h (f a -> f b)

join1 :: Monad repr m => repr h (m (m a)) -> repr h (m a)

bimap2 :: BiFunctor repr p => repr h (a -> b) -> repr h (c -> d) -> repr h (p a c -> p b d)

flip1 :: DBI repr => repr h (a -> b -> c) -> repr h (b -> a -> c)

flip2 :: DBI repr => repr h (a1 -> a -> c) -> repr h a -> repr h (a1 -> c)

class DBI r => BiFunctor r p where

Minimal complete definition

bimap

Methods

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

Instances

DBI r => BiFunctor r (,)

Methods

bimap :: r h ((a -> b) -> (c -> d) -> (a, c) -> (b, d))

writer1 :: DBI repr => repr h (a, w) -> repr h (Writer w a)

runWriter1 :: DBI repr => repr h (Writer w a) -> repr h (a, w)

mappend2 :: Monoid repr b => repr h b -> repr h b -> repr h b

ioBind2 :: DBI repr => repr h (IO a) -> repr h (a -> IO b) -> repr h (IO b)

app3 :: DBI repr => repr h (a2 -> a1 -> a -> b) -> repr h a2 -> repr h a1 -> repr h a -> repr h b

optionMatch3 :: DBI repr => repr h b -> repr h (a -> b) -> repr h (Maybe a) -> repr h b

optionMatch2 :: DBI repr => repr h a1 -> repr h (a -> a1) -> repr h (Maybe a -> a1)

com2 :: DBI repr => repr h (b -> c) -> repr h (a -> b) -> repr h (a -> c)

newtype Eval h x

Constructors

Eval

Fields

• runEval :: h -> x

Instances

DBI Eval

Methods

z :: Eval (a, h) a

s :: Eval h b -> Eval (a, h) b

lam :: Eval (a, h) b -> Eval h (a -> b)

app :: Eval h (a -> b) -> Eval h a -> Eval h b

mkProd :: Eval h (a -> b -> (a, b))

zro :: Eval h ((a, b) -> a)

fst :: Eval h ((a, b) -> b)

lit :: Double -> Eval h Double

litZro :: Eval h Double

litOne :: Eval h Double

plus :: Eval h (Double -> Double -> Double)

minus :: Eval h (Double -> Double -> Double)

mult :: Eval h (Double -> Double -> Double)

divide :: Eval h (Double -> Double -> Double)

hoas :: (Eval (a, h) a -> Eval (a, h) b) -> Eval h (a -> b)

fix :: Eval h ((a -> a) -> a)

left :: Eval h (a -> Either a b)

right :: Eval h (b -> Either a b)

sumMatch :: Eval h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: Eval h ()

exfalso :: Eval h (Void -> a)

nothing :: Eval h (Maybe a)

just :: Eval h (a -> Maybe a)

optionMatch :: Eval h (b -> (a -> b) -> Maybe a -> b)

ioRet :: Eval h (a -> IO a)

ioBind :: Eval h (IO a -> (a -> IO b) -> IO b)

ioMap :: Eval h ((a -> b) -> IO a -> IO b)

nil :: Eval h [a]

cons :: Eval h (a -> [a] -> [a])

listMatch :: Eval h (b -> (a -> [a] -> b) -> [a] -> b)

com :: Eval h ((b -> c) -> (a -> b) -> a -> c)

append :: Eval h ([a] -> [a] -> [a])

writer :: Eval h ((a, w) -> Writer w a)

runWriter :: Eval h (Writer w a -> (a, w))

swap :: Eval h ((l, r) -> (r, l))

flip :: Eval h ((a -> b -> c) -> b -> a -> c)

id :: Eval h (a -> a)

const :: Eval h (a -> b -> a)

comb :: x -> Eval h x

data AST

Constructors

Leaf String

App String AST [AST]

Lam String [String] AST

Instances

Show AST

Methods

showsPrec :: Int -> AST -> ShowS

show :: AST -> String

showList :: [AST] -> ShowS

appAST :: AST -> AST -> AST

lamAST :: String -> AST -> AST

newtype Show h a

Constructors

Show

Fields

• runShow :: [String] -> Int -> AST

Instances

DBI (Show * *)

Methods

z :: Show * * (a, h) a

s :: Show * * h b -> Show * * (a, h) b

lam :: Show * * (a, h) b -> Show * * h (a -> b)

app :: Show * * h (a -> b) -> Show * * h a -> Show * * h b

mkProd :: Show * * h (a -> b -> (a, b))

zro :: Show * * h ((a, b) -> a)

fst :: Show * * h ((a, b) -> b)

lit :: Double -> Show * * h Double

litZro :: Show * * h Double

litOne :: Show * * h Double

plus :: Show * * h (Double -> Double -> Double)

minus :: Show * * h (Double -> Double -> Double)

mult :: Show * * h (Double -> Double -> Double)

divide :: Show * * h (Double -> Double -> Double)

hoas :: (Show * * (a, h) a -> Show * * (a, h) b) -> Show * * h (a -> b)

fix :: Show * * h ((a -> a) -> a)

left :: Show * * h (a -> Either a b)

right :: Show * * h (b -> Either a b)

sumMatch :: Show * * h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: Show * * h ()

exfalso :: Show * * h (Void -> a)

nothing :: Show * * h (Maybe a)

just :: Show * * h (a -> Maybe a)

optionMatch :: Show * * h (b -> (a -> b) -> Maybe a -> b)

ioRet :: Show * * h (a -> IO a)

ioBind :: Show * * h (IO a -> (a -> IO b) -> IO b)

ioMap :: Show * * h ((a -> b) -> IO a -> IO b)

nil :: Show * * h [a]

cons :: Show * * h (a -> [a] -> [a])

listMatch :: Show * * h (b -> (a -> [a] -> b) -> [a] -> b)

com :: Show * * h ((b -> c) -> (a -> b) -> a -> c)

append :: Show * * h ([a] -> [a] -> [a])

writer :: Show * * h ((a, w) -> Writer w a)

runWriter :: Show * * h (Writer w a -> (a, w))

swap :: Show * * h ((l, r) -> (r, l))

flip :: Show * * h ((a -> b -> c) -> b -> a -> c)

id :: Show * * h (a -> a)

const :: Show * * h (a -> b -> a)

name :: String -> Show k k1 h a

class NT repr l r where

Minimal complete definition

conv

Methods

conv :: repr l t -> repr r t

Instances

NT k k1 repr x x

Methods

conv :: x l t -> x r t

(DBI repr, NT * * repr l r) => NT * * repr l (a, r)

Methods

conv :: (a, r) l t -> (a, r) r t

hlam :: 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)

type family Diff x

Instances

type Diff Double

type Diff Double = (Double, Double)

type Diff ()

type Diff () = ()

type Diff Void

type Diff Void = Void

type Diff [a]

type Diff [a] = [Diff a]

type Diff (Maybe a)

type Diff (Maybe a) = Maybe (Diff a)

type Diff (IO a)

type Diff (IO a) = IO (Diff a)

type Diff (a -> b)

type Diff (a -> b) = Diff a -> Diff b

type Diff (Either a b)

type Diff (Either a b) = Either (Diff a) (Diff b)

type Diff (a, b)

type Diff (a, b) = (Diff a, Diff b)

type Diff (Writer w a)

type Diff (Writer w a) = Writer (Diff w) (Diff a)

newtype WDiff repr h x

Constructors

WDiff

Fields

• runWDiff :: repr (Diff h) (Diff x)

Instances

DBI repr => DBI (WDiff repr)

Methods

z :: WDiff repr (a, h) a

s :: WDiff repr h b -> WDiff repr (a, h) b

lam :: WDiff repr (a, h) b -> WDiff repr h (a -> b)

app :: WDiff repr h (a -> b) -> WDiff repr h a -> WDiff repr h b

mkProd :: WDiff repr h (a -> b -> (a, b))

zro :: WDiff repr h ((a, b) -> a)

fst :: WDiff repr h ((a, b) -> b)

lit :: Double -> WDiff repr h Double

litZro :: WDiff repr h Double

litOne :: WDiff repr h Double

plus :: WDiff repr h (Double -> Double -> Double)

minus :: WDiff repr h (Double -> Double -> Double)

mult :: WDiff repr h (Double -> Double -> Double)

divide :: WDiff repr h (Double -> Double -> Double)

hoas :: (WDiff repr (a, h) a -> WDiff repr (a, h) b) -> WDiff repr h (a -> b)

fix :: WDiff repr h ((a -> a) -> a)

left :: WDiff repr h (a -> Either a b)

right :: WDiff repr h (b -> Either a b)

sumMatch :: WDiff repr h ((a -> c) -> (b -> c) -> Either a b -> c)

unit :: WDiff repr h ()

exfalso :: WDiff repr h (Void -> a)

nothing :: WDiff repr h (Maybe a)

just :: WDiff repr h (a -> Maybe a)

optionMatch :: WDiff repr h (b -> (a -> b) -> Maybe a -> b)

ioRet :: WDiff repr h (a -> IO a)

ioBind :: WDiff repr h (IO a -> (a -> IO b) -> IO b)

ioMap :: WDiff repr h ((a -> b) -> IO a -> IO b)

nil :: WDiff repr h [a]

cons :: WDiff repr h (a -> [a] -> [a])

listMatch :: WDiff repr h (b -> (a -> [a] -> b) -> [a] -> b)

com :: WDiff repr h ((b -> c) -> (a -> b) -> a -> c)

append :: WDiff repr h ([a] -> [a] -> [a])

writer :: WDiff repr h ((a, w) -> Writer w a)

runWriter :: WDiff repr h (Writer w a -> (a, w))

swap :: WDiff repr h ((l, r) -> (r, l))

flip :: WDiff repr h ((a -> b -> c) -> b -> a -> c)

id :: WDiff repr h (a -> a)

const :: WDiff repr h (a -> b -> a)

app2 :: DBI repr => repr h (a1 -> a -> b) -> repr h a1 -> repr h a -> repr h b

mkProd1 :: DBI repr => repr h a -> repr h (b -> (a, b))

mkProd2 :: DBI repr => repr h a1 -> repr h a -> repr h (a1, a)

plus2 :: DBI repr => repr h Double -> repr h Double -> repr h Double

zro1 :: DBI repr => repr h (b1, b) -> repr h b1

fst1 :: DBI repr => repr h (a, b) -> repr h b

minus2 :: DBI repr => repr h Double -> repr h Double -> repr h Double

mult2 :: DBI repr => repr h Double -> repr h Double -> repr h Double

divide2 :: DBI repr => repr h Double -> repr h Double -> repr h Double

scomb :: DBI repr => repr h ((a1 -> a -> b) -> (a1 -> a) -> a1 -> b)

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