Language.Hakaru.Syntax.IClasses

A collection of classes generalizing standard classes in order to support indexed types.

TODO: DeriveDataTypeable for all our newtypes?

Showing indexed types

class Show1 a where

Uniform variant of Show for k-indexed types. This differs from transformers:Show1 in being polykinded, like it ought to be.

Alas, I don't think there's any way to derive instances the way we can derive for Show.

Minimal complete definition

showsPrec1 | show1

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Instances

Show1 Hakaru Literal

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru Value

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Symbol (Sing Symbol)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 k (Sing k) => Show1 k (Variable k)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 HakaruCon (Sing HakaruCon)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 HakaruFun (Sing HakaruFun)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru (Sing Hakaru)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru (Pattern vars)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru ast => Show1 Hakaru (Datum ast)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show2 Hakaru [Hakaru] abt => Show1 Hakaru (LC_ abt)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show2 Hakaru [Hakaru] abt => Show1 Hakaru (Term abt)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Untyped (Sing Untyped)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show a => Show1 k (Lift1 k a)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show2 Hakaru [Hakaru] abt => Show1 Hakaru (Branch a abt)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru (PDatumFun x vars)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru (PDatumStruct xs vars)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru (PDatumCode xss vars)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru ast => Show1 Hakaru (DatumFun x ast)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru ast => Show1 Hakaru (DatumStruct xs ast)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 Hakaru ast => Show1 Hakaru (DatumCode xss ast)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 Hakaru ast, Show2 Hakaru [Hakaru] abt) => Show1 Hakaru (MatchResult ast abt)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k a, Show1 k b) => Show1 k (Pair1 k a b)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k (Sing k), Show1 k (syn (MemoizedABT k syn))) => Show1 k (MemoizedABT k syn xs)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k (Sing k), Show1 k (syn (TrivialABT k syn))) => Show1 k (TrivialABT k syn xs)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k (Sing k), Show1 k rec) => Show1 k (View k rec xs)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show a => Show1 k (Lift2 k k1 a i)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k (Sing k), Show1 k (syn (MetaABT k meta syn)), Show meta) => Show1 k (MetaABT k meta syn xs)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show2 k k1 a, Show2 k k1 b) => Show1 k (Pair2 k k1 a b i)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 [[HakaruFun]] (Sing [[HakaruFun]])

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show2 Hakaru [Hakaru] abt => Show1 [([Hakaru], Hakaru)] (SArgs abt)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 [HakaruFun] (Sing [HakaruFun])

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Show1 k a => Show1 [k] (List1 k a)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

shows1 :: Show1 a => a i -> ShowS

showList1 :: Show1 a => [a i] -> ShowS

class Show2 a where

Minimal complete definition

showsPrec2 | show2

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Instances

Show a => Show2 k2 k1 (Lift2 k2 k1 a)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show2 k2 k1 a, Show2 k2 k1 b) => Show2 k2 k1 (Pair2 k2 k1 a b)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Show2 Hakaru [Hakaru] Pattern

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Show2 Hakaru [Hakaru] (PDatumFun x)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Show2 Hakaru [Hakaru] (PDatumStruct xs)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Show2 Hakaru [Hakaru] (PDatumCode xss)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show1 k (Sing k), Show1 k (syn (MemoizedABT k syn))) => Show2 k [k] (MemoizedABT k syn)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show1 k (Sing k), Show1 k (syn (TrivialABT k syn))) => Show2 k [k] (TrivialABT k syn)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show1 k (Sing k), Show1 k rec) => Show2 k [k] (View k rec)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show1 k (Sing k), Show1 k (syn (MetaABT k meta syn)), Show meta) => Show2 k [k] (MetaABT k meta syn)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

shows2 :: Show2 a => a i j -> ShowS

showList2 :: Show2 a => [a i j] -> ShowS

Some more-generic helper functions for showing things

showListWith :: (a -> ShowS) -> [a] -> ShowS

showTuple :: [ShowS] -> ShowS

some helpers for implementing the instances

showParen_0 :: Show a => Int -> String -> a -> ShowS

showParen_1 :: Show1 a => Int -> String -> a i -> ShowS

showParen_2 :: Show2 a => Int -> String -> a i j -> ShowS

showParen_01 :: (Show b, Show1 a) => Int -> String -> b -> a i -> ShowS

showParen_02 :: (Show b, Show2 a) => Int -> String -> b -> a i j -> ShowS

showParen_11 :: (Show1 a, Show1 b) => Int -> String -> a i -> b j -> ShowS

showParen_12 :: (Show1 a, Show2 b) => Int -> String -> a i -> b j l -> ShowS

showParen_22 :: (Show2 a, Show2 b) => Int -> String -> a i1 j1 -> b i2 j2 -> ShowS

showParen_010 :: (Show a, Show1 b, Show c) => Int -> String -> a -> b i -> c -> ShowS

showParen_011 :: (Show a, Show1 b, Show1 c) => Int -> String -> a -> b i -> c j -> ShowS

showParen_111 :: (Show1 a, Show1 b, Show1 c) => Int -> String -> a i -> b j -> c k -> ShowS

Equality

class Eq1 a where

Uniform variant of Eq for homogeneous k-indexed types. N.B., we keep this separate from the JmEq1 class because for some types we may be able to decide eq1 while not being able to decide jmEq1 (e.g., if using phantom types rather than GADTs). N.B., this function returns value/term equality! That is, the following four laws must hold relating the Eq1 class to the Eq class:

1. if eq1 x y == True, then x and y have the same type index and (x == y) == True
2. if eq1 x y == False where x and y have the same type index, then (x == y) == False
3. if (x == y) == True, then eq1 x y == True
4. if (x == y) == False, then eq1 x y == False

Alas, I don't think there's any way to derive instances the way we can derive for Eq.

Minimal complete definition

eq1

Methods

eq1 :: a i -> a i -> Bool

Instances

Eq1 Hakaru HContinuous

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HDiscrete

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HIntegrable

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HRadical

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HFractional

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HRing

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru HSemiring

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru NaryOp

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru Literal

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru Value

Methods

eq1 :: a i -> a i -> Bool

Eq1 Symbol (Sing Symbol)

Methods

eq1 :: a i -> a i -> Bool

Eq1 k (Variable k)

Methods

eq1 :: a i -> a i -> Bool

Eq1 HakaruCon (Sing HakaruCon)

Methods

eq1 :: a i -> a i -> Bool

Eq1 HakaruFun (Sing HakaruFun)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (Sing Hakaru)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (Coercion a)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (PrimCoercion a)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (Pattern vars)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru ast => Eq1 Hakaru (Datum ast)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (MeasureOp typs)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (ArrayOp args)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (PrimOp args)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Untyped (Sing Untyped)

Methods

eq1 :: a i -> a i -> Bool

Eq a => Eq1 k (Lift1 k a)

Methods

eq1 :: a i -> a i -> Bool

Eq2 Hakaru [Hakaru] abt => Eq1 Hakaru (Reducer abt xs)

Methods

eq1 :: a i -> a i -> Bool

Eq2 Hakaru [Hakaru] abt => Eq1 Hakaru (Branch a abt)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (PDatumFun x vars)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (PDatumStruct xs vars)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru (PDatumCode xss vars)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru ast => Eq1 Hakaru (DatumFun x ast)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru ast => Eq1 Hakaru (DatumStruct xs ast)

Methods

eq1 :: a i -> a i -> Bool

Eq1 Hakaru ast => Eq1 Hakaru (DatumCode xss ast)

Methods

eq1 :: a i -> a i -> Bool

Eq a => Eq1 k (Lift2 k k1 a i)

Methods

eq1 :: a i -> a i -> Bool

Eq1 [[HakaruFun]] (Sing [[HakaruFun]])

Methods

eq1 :: a i -> a i -> Bool

Eq2 Hakaru [Hakaru] abt => Eq1 [([Hakaru], Hakaru)] (SArgs abt)

Methods

eq1 :: a i -> a i -> Bool

Eq1 [HakaruFun] (Sing [HakaruFun])

Methods

eq1 :: a i -> a i -> Bool

Eq1 k a => Eq1 [k] (List1 k a)

Methods

eq1 :: a i -> a i -> Bool

class Eq2 a where

Minimal complete definition

eq2

Methods

eq2 :: a i j -> a i j -> Bool

Instances

Eq2 Hakaru Hakaru Coercion

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru Hakaru PrimCoercion

Methods

eq2 :: a i j -> a i j -> Bool

Eq a => Eq2 k2 k1 (Lift2 k2 k1 a)

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] Pattern

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] MeasureOp

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] ArrayOp

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] PrimOp

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] (PDatumFun x)

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] (PDatumStruct xs)

Methods

eq2 :: a i j -> a i j -> Bool

Eq2 Hakaru [Hakaru] (PDatumCode xss)

Methods

eq2 :: a i j -> a i j -> Bool

data TypeEq :: k -> k -> * where

Concrete proofs of type equality. In order to make use of a proof p :: TypeEq a b, you must pattern-match on the Refl constructor in order to show GHC that the types a and b are equal.

Constructors

Refl :: TypeEq a a

Instances

Category k (TypeEq k)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

symmetry :: TypeEq a b -> TypeEq b a

Type equality is symmetric.

transitivity :: TypeEq a b -> TypeEq b c -> TypeEq a c

Type equality is transitive. N.B., this is has a more general type than (.)

congruence :: TypeEq a b -> TypeEq (f a) (f b)

Type constructors are extensional.

class Eq1 a => JmEq1 a where

Uniform variant of Eq for heterogeneous k-indexed types. N.B., this function returns value/term equality! That is, the following four laws must hold relating the JmEq1 class to the Eq1 class:

1. if jmEq1 x y == Just Refl, then x and y have the same type index and eq1 x y == True
2. if jmEq1 x y == Nothing where x and y have the same type index, then eq1 x y == False
3. if eq1 x y == True, then jmEq1 x y == Just Refl
4. if eq1 x y == False, then jmEq1 x y == Nothing

Alas, I don't think there's any way to derive instances the way we can derive for Eq.

Minimal complete definition

jmEq1

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq i j)

Instances

JmEq1 Hakaru HContinuous

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HContinuous i j)

JmEq1 Hakaru HDiscrete

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HDiscrete i j)

JmEq1 Hakaru HIntegrable

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HIntegrable i j)

JmEq1 Hakaru HRadical

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HRadical i j)

JmEq1 Hakaru HFractional

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HFractional i j)

JmEq1 Hakaru HRing

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HRing i j)

JmEq1 Hakaru HSemiring

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq HSemiring i j)

JmEq1 Hakaru NaryOp

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq NaryOp i j)

JmEq1 Hakaru Literal

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq Literal i j)

JmEq1 Symbol (Sing Symbol)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing Symbol) i j)

JmEq1 HakaruCon (Sing HakaruCon)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing HakaruCon) i j)

JmEq1 HakaruFun (Sing HakaruFun)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing HakaruFun) i j)

JmEq1 Hakaru (Sing Hakaru)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing Hakaru) i j)

JmEq1 Hakaru (PrimCoercion a)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (PrimCoercion a) i j)

Eq1 Hakaru ast => JmEq1 Hakaru (Datum ast)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Datum ast) i j)

JmEq1 Untyped (Sing Untyped)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing Untyped) i j)

JmEq2 Hakaru [Hakaru] abt => JmEq1 Hakaru (Reducer abt xs)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Reducer abt xs) i j)

JmEq1 [[HakaruFun]] (Sing [[HakaruFun]])

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing [[HakaruFun]]) i j)

JmEq1 [HakaruFun] (Sing [HakaruFun])

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (Sing [HakaruFun]) i j)

JmEq1 k a => JmEq1 [k] (List1 k a)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (List1 k a) i j)

class Eq2 a => JmEq2 a where

Minimal complete definition

jmEq2

Methods

jmEq2 :: a i1 j1 -> a i2 j2 -> Maybe (TypeEq i1 i2, TypeEq j1 j2)

Instances

JmEq2 Hakaru Hakaru PrimCoercion

Methods

jmEq2 :: a i1 j1 -> a i2 j2 -> Maybe (TypeEq k1 i1 i2, TypeEq PrimCoercion j1 j2)

JmEq2 Hakaru [Hakaru] MeasureOp

Methods

jmEq2 :: a i1 j1 -> a i2 j2 -> Maybe (TypeEq k1 i1 i2, TypeEq MeasureOp j1 j2)

JmEq2 Hakaru [Hakaru] ArrayOp

Methods

jmEq2 :: a i1 j1 -> a i2 j2 -> Maybe (TypeEq k1 i1 i2, TypeEq ArrayOp j1 j2)

JmEq2 Hakaru [Hakaru] PrimOp

Methods

jmEq2 :: a i1 j1 -> a i2 j2 -> Maybe (TypeEq k1 i1 i2, TypeEq PrimOp j1 j2)

Generalized abstract nonsense

class Functor11 f where

A functor on the category of k-indexed types (i.e., from k-indexed types to k-indexed types). We unify the two indices, because that seems the most helpful for what we're doing; we could, of course, offer a different variant that maps k1-indexed types to k2-indexed types...

Alas, I don't think there's any way to derive instances the way we can derive for Functor.

Minimal complete definition

fmap11

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

Instances

Functor11 Hakaru Hakaru Datum

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

Functor11 Hakaru Hakaru (DatumFun x)

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

Functor11 Hakaru Hakaru (DatumStruct xs)

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

Functor11 Hakaru Hakaru (DatumCode xss)

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

Functor11 [k1] k1 (List1 k1)

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

newtype Fix11 f i

Constructors

Fix11

Fields

• unFix11 :: f (Fix11 f) i

cata11 :: forall f a j. Functor11 f => (forall i. f a i -> a i) -> Fix11 f j -> a j

ana11 :: forall f a j. Functor11 f => (forall i. a i -> f a i) -> a j -> Fix11 f j

hylo11 :: forall f a b j. Functor11 f => (forall i. a i -> f a i) -> (forall i. f b i -> b i) -> a j -> b j

class Functor12 f where

Minimal complete definition

fmap12

Methods

fmap12 :: (forall i. a i -> b i) -> f a j l -> f b j l

Instances

Functor12 k3 [k3] k3 (View k3)

Methods

fmap12 :: (forall i. a i -> b i) -> f a j l -> f b j l

class Functor21 f where

A functor from (k1,k2)-indexed types to k3-indexed types.

Minimal complete definition

fmap21

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Instances

Functor21 Hakaru Hakaru [Hakaru] Term

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Functor21 Hakaru Hakaru [Hakaru] Head

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Functor21 Untyped Untyped [Untyped] Term

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Functor21 Hakaru Hakaru [Hakaru] (Branch a)

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Functor21 Untyped Untyped [Untyped] (Reducer xs)

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

Functor21 [([Hakaru], Hakaru)] Hakaru [Hakaru] SArgs

Methods

fmap21 :: (forall h i. a h i -> b h i) -> f a j -> f b j

class Functor22 f where

A functor from (k1,k2)-indexed types to (k3,k4)-indexed types.

Minimal complete definition

fmap22

Methods

fmap22 :: (forall h i. a h i -> b h i) -> f a j l -> f b j l

Instances

Functor22 Hakaru [Hakaru] Hakaru [Hakaru] Reducer

Methods

fmap22 :: (forall h i. a h i -> b h i) -> f a j l -> f b j l

class Functor11 f => Foldable11 f where

A foldable functor on the category of k-indexed types.

Alas, I don't think there's any way to derive instances the way we can derive for Foldable.

Minimal complete definition

fold11 | foldMap11

Methods

fold11 :: Monoid m => f (Lift1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Instances

Foldable11 Hakaru Hakaru Datum

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Foldable11 Hakaru Hakaru (DatumFun x)

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Foldable11 Hakaru Hakaru (DatumStruct xs)

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Foldable11 Hakaru Hakaru (DatumCode xss)

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Foldable11 [k1] k1 (List1 k1)

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

newtype Lift1 a i

Any unindexed type can be lifted to be (trivially) k-indexed.

Constructors

Lift1

Fields

• unLift1 :: a

Instances

Eq a => Eq1 k (Lift1 k a)

Methods

eq1 :: a i -> a i -> Bool

Show a => Show1 k (Lift1 k a)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Eq a => Eq (Lift1 k a i)

Methods

(==) :: Lift1 k a i -> Lift1 k a i -> Bool

(/=) :: Lift1 k a i -> Lift1 k a i -> Bool

Ord a => Ord (Lift1 k a i)

Methods

compare :: Lift1 k a i -> Lift1 k a i -> Ordering

(<) :: Lift1 k a i -> Lift1 k a i -> Bool

(<=) :: Lift1 k a i -> Lift1 k a i -> Bool

(>) :: Lift1 k a i -> Lift1 k a i -> Bool

(>=) :: Lift1 k a i -> Lift1 k a i -> Bool

max :: Lift1 k a i -> Lift1 k a i -> Lift1 k a i

min :: Lift1 k a i -> Lift1 k a i -> Lift1 k a i

Read a => Read (Lift1 k a i)

Methods

readsPrec :: Int -> ReadS (Lift1 k a i)

readList :: ReadS [Lift1 k a i]

readPrec :: ReadPrec (Lift1 k a i)

readListPrec :: ReadPrec [Lift1 k a i]

Show a => Show (Lift1 k a i)

Methods

showsPrec :: Int -> Lift1 k a i -> ShowS

show :: Lift1 k a i -> String

showList :: [Lift1 k a i] -> ShowS

class Functor12 f => Foldable12 f where

Minimal complete definition

fold12 | foldMap12

Methods

fold12 :: Monoid m => f (Lift1 m) j l -> m

foldMap12 :: Monoid m => (forall i. a i -> m) -> f a j l -> m

Instances

Foldable12 k3 [k3] k3 (View k3)

Methods

fold12 :: Monoid m => f (Lift1 k1 m) j l -> m

foldMap12 :: Monoid m => (forall i. a i -> m) -> f a j l -> m

class Functor21 f => Foldable21 f where

Minimal complete definition

fold21 | foldMap21

Methods

fold21 :: Monoid m => f (Lift2 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Instances

Foldable21 Hakaru Hakaru [Hakaru] Term

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Foldable21 Hakaru Hakaru [Hakaru] Head

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Foldable21 Untyped Untyped [Untyped] Term

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Foldable21 Hakaru Hakaru [Hakaru] (Branch a)

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Foldable21 Untyped Untyped [Untyped] (Reducer xs)

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

Foldable21 [([Hakaru], Hakaru)] Hakaru [Hakaru] SArgs

Methods

fold21 :: Monoid m => f (Lift2 k2 k1 m) j -> m

foldMap21 :: Monoid m => (forall h i. a h i -> m) -> f a j -> m

newtype Lift2 a i j

Any unindexed type can be lifted to be (trivially) (k1,k2)-indexed.

Constructors

Lift2

Fields

• unLift2 :: a

Instances

Eq a => Eq2 k2 k1 (Lift2 k2 k1 a)

Methods

eq2 :: a i j -> a i j -> Bool

Show a => Show2 k2 k1 (Lift2 k2 k1 a)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

Eq a => Eq1 k (Lift2 k k1 a i)

Methods

eq1 :: a i -> a i -> Bool

Show a => Show1 k (Lift2 k k1 a i)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Eq a => Eq (Lift2 k2 k1 a i j)

Methods

(==) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

(/=) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

Ord a => Ord (Lift2 k2 k1 a i j)

Methods

compare :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Ordering

(<) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

(<=) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

(>) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

(>=) :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Bool

max :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j

min :: Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j -> Lift2 k2 k1 a i j

Read a => Read (Lift2 k2 k1 a i j)

Methods

readsPrec :: Int -> ReadS (Lift2 k2 k1 a i j)

readList :: ReadS [Lift2 k2 k1 a i j]

readPrec :: ReadPrec (Lift2 k2 k1 a i j)

readListPrec :: ReadPrec [Lift2 k2 k1 a i j]

Show a => Show (Lift2 k2 k1 a i j)

Methods

showsPrec :: Int -> Lift2 k2 k1 a i j -> ShowS

show :: Lift2 k2 k1 a i j -> String

showList :: [Lift2 k2 k1 a i j] -> ShowS

class Functor22 f => Foldable22 f where

Minimal complete definition

fold22 | foldMap22

Methods

fold22 :: Monoid m => f (Lift2 m) j l -> m

foldMap22 :: Monoid m => (forall h i. a h i -> m) -> f a j l -> m

Instances

Foldable22 Hakaru [Hakaru] Hakaru [Hakaru] Reducer

Methods

fold22 :: Monoid m => f (Lift2 k2 k1 m) j l -> m

foldMap22 :: Monoid m => (forall h i. a h i -> m) -> f a j l -> m

class Foldable11 t => Traversable11 t where

Minimal complete definition

traverse11

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Instances

Traversable11 Hakaru Hakaru Datum

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Traversable11 Hakaru Hakaru (DatumFun x)

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Traversable11 Hakaru Hakaru (DatumStruct xs)

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Traversable11 Hakaru Hakaru (DatumCode xss)

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Traversable11 [k1] k1 (List1 k1)

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

class Foldable12 t => Traversable12 t where

Minimal complete definition

traverse12

Methods

traverse12 :: Applicative f => (forall i. a i -> f (b i)) -> t a j l -> f (t b j l)

Instances

Traversable12 k3 [k3] k3 (View k3)

Methods

traverse12 :: Applicative f => (forall i. a i -> f (b i)) -> t a j l -> f (t b j l)

class Foldable21 t => Traversable21 t where

Minimal complete definition

traverse21

Methods

traverse21 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j -> f (t b j)

Instances

Traversable21 Hakaru Hakaru [Hakaru] Term

Methods

traverse21 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j -> f (t b j)

Traversable21 Hakaru Hakaru [Hakaru] Head

Methods

traverse21 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j -> f (t b j)

Traversable21 Hakaru Hakaru [Hakaru] (Branch a)

Methods

traverse21 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j -> f (t b j)

Traversable21 [([Hakaru], Hakaru)] Hakaru [Hakaru] SArgs

Methods

traverse21 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j -> f (t b j)

class Foldable22 t => Traversable22 t where

Minimal complete definition

traverse22

Methods

traverse22 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j l -> f (t b j l)

Instances

Traversable22 Hakaru [Hakaru] Hakaru [Hakaru] Reducer

Methods

traverse22 :: Applicative f => (forall h i. a h i -> f (b h i)) -> t a j l -> f (t b j l)

Helper types

data Some1 a

Existentially quantify over a single index. TODO: replace SomeVariable with (Some1 Variable)

Constructors

Some1 !(a i)

Instances

JmEq1 k a => Eq (Some1 k a)

Methods

(==) :: Some1 k a -> Some1 k a -> Bool

(/=) :: Some1 k a -> Some1 k a -> Bool

Show1 k a => Show (Some1 k a)

Methods

showsPrec :: Int -> Some1 k a -> ShowS

show :: Some1 k a -> String

showList :: [Some1 k a] -> ShowS

data Some2 a

Existentially quantify over two indices.

Constructors

Some2 !(a i j)

Instances

JmEq2 k2 k1 a => Eq (Some2 k2 k1 a)

Methods

(==) :: Some2 k2 k1 a -> Some2 k2 k1 a -> Bool

(/=) :: Some2 k2 k1 a -> Some2 k2 k1 a -> Bool

Show2 k2 k1 a => Show (Some2 k2 k1 a)

Methods

showsPrec :: Int -> Some2 k2 k1 a -> ShowS

show :: Some2 k2 k1 a -> String

showList :: [Some2 k2 k1 a] -> ShowS

data Pair1 a b i

A lazy pairing of identically k-indexed values.

Constructors

Pair1 (a i) (b i)

Instances

(Show1 k a, Show1 k b) => Show1 k (Pair1 k a b)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show1 k a, Show1 k b) => Show (Pair1 k a b i)

Methods

showsPrec :: Int -> Pair1 k a b i -> ShowS

show :: Pair1 k a b i -> String

showList :: [Pair1 k a b i] -> ShowS

fst1 :: Pair1 a b i -> a i

snd1 :: Pair1 a b i -> b i

data Pair2 a b i j

A lazy pairing of identically (k1,k2)-indexed values.

Constructors

Pair2 (a i j) (b i j)

Instances

(Show2 k2 k1 a, Show2 k2 k1 b) => Show2 k2 k1 (Pair2 k2 k1 a b)

Methods

showsPrec2 :: Int -> a i j -> ShowS

show2 :: a i j -> String

(Show2 k k1 a, Show2 k k1 b) => Show1 k (Pair2 k k1 a b i)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

(Show2 k2 k1 a, Show2 k2 k1 b) => Show (Pair2 k2 k1 a b i j)

Methods

showsPrec :: Int -> Pair2 k2 k1 a b i j -> ShowS

show :: Pair2 k2 k1 a b i j -> String

showList :: [Pair2 k2 k1 a b i j] -> ShowS

fst2 :: Pair2 a b i j -> a i j

snd2 :: Pair2 a b i j -> b i j

List types

type family (xs :: [k]) ++ (ys :: [k]) :: [k] where ...

Equations

'[] ++ ys = ys

(x ': xs) ++ ys = x ': (xs ++ ys)

eqAppendIdentity :: proxy xs -> TypeEq xs (xs ++ '[])

The empty list is (also) a right-identity for (++). Because we define (++) by induction on the first argument, this identity doesn't come for free but rather must be proven.

eqAppendAssoc :: proxy1 xs -> proxy2 ys -> proxy3 zs -> TypeEq ((xs ++ ys) ++ zs) (xs ++ (ys ++ zs))

(++) is associative. This identity doesn't come for free but rather must be proven.

data List1 :: (k -> *) -> [k] -> * where

A lazy list of k-indexed elements, itself indexed by the list of indices

Constructors

Nil1 :: List1 a '[]

Cons1 :: a x -> List1 a xs -> List1 a (x ': xs) infixr 5

Instances

Traversable11 [k1] k1 (List1 k1)

Methods

traverse11 :: Applicative f => (forall i. a i -> f (b i)) -> t a j -> f (t b j)

Foldable11 [k1] k1 (List1 k1)

Methods

fold11 :: Monoid m => f (Lift1 k1 m) i -> m

foldMap11 :: Monoid m => (forall i. a i -> m) -> f a j -> m

Functor11 [k1] k1 (List1 k1)

Methods

fmap11 :: (forall i. a i -> b i) -> f a j -> f b j

JmEq1 k a => JmEq1 [k] (List1 k a)

Methods

jmEq1 :: a i -> a j -> Maybe (TypeEq (List1 k a) i j)

Eq1 k a => Eq1 [k] (List1 k a)

Methods

eq1 :: a i -> a i -> Bool

Show1 k a => Show1 [k] (List1 k a)

Methods

showsPrec1 :: Int -> a i -> ShowS

show1 :: a i -> String

Eq1 k a => Eq (List1 k a xs)

Methods

(==) :: List1 k a xs -> List1 k a xs -> Bool

(/=) :: List1 k a xs -> List1 k a xs -> Bool

Show1 k a => Show (List1 k a xs)

Methods

showsPrec :: Int -> List1 k a xs -> ShowS

show :: List1 k a xs -> String

showList :: [List1 k a xs] -> ShowS

append1 :: List1 a xs -> List1 a ys -> List1 a (xs ++ ys)

newtype DList1 a xs

A difference-list variant of List1.

Constructors

DList1

Fields

• unDList1 :: forall ys. List1 a ys -> List1 a (xs ++ ys)

toList1 :: DList1 a xs -> List1 a xs

fromList1 :: List1 a xs -> DList1 a xs

dnil1 :: DList1 a '[]

dcons1 :: a x -> DList1 a xs -> DList1 a (x ': xs)

dsnoc1 :: DList1 a xs -> a x -> DList1 a (xs ++ '[x])

dsingleton1 :: a x -> DList1 a '[x]

dappend1 :: DList1 a xs -> DList1 a ys -> DList1 a (xs ++ ys)