LAoP.Utils.Internal

Natural data type

newtype Natural (start :: Nat) (end :: Nat)

Wrapper around Ints that have a restrictive semantic associated. A value of type Natural n m can only be instanciated with some Int i that's n <= i <= m.

Constructors

Nat Int

Instances

(KnownNat n, KnownNat m) => Bounded (Natural n m)

Defined in LAoP.Utils.Internal

Methods

minBound :: Natural n m

maxBound :: Natural n m

(KnownNat n, KnownNat m) => Enum (Natural n m)

Defined in LAoP.Utils.Internal

Methods

succ :: Natural n m -> Natural n m

pred :: Natural n m -> Natural n m

toEnum :: Int -> Natural n m

fromEnum :: Natural n m -> Int

enumFrom :: Natural n m -> [Natural n m]

enumFromThen :: Natural n m -> Natural n m -> [Natural n m]

enumFromTo :: Natural n m -> Natural n m -> [Natural n m]

enumFromThenTo :: Natural n m -> Natural n m -> Natural n m -> [Natural n m]

Eq (Natural start end)

Defined in LAoP.Utils.Internal

Methods

(==) :: Natural start end -> Natural start end -> Bool

(/=) :: Natural start end -> Natural start end -> Bool

(KnownNat n, KnownNat m) => Num (Natural n m)

Throws a runtime error if any of the operations overflows or underflows.

Defined in LAoP.Utils.Internal

Methods

(+) :: Natural n m -> Natural n m -> Natural n m

(-) :: Natural n m -> Natural n m -> Natural n m

(*) :: Natural n m -> Natural n m -> Natural n m

negate :: Natural n m -> Natural n m

abs :: Natural n m -> Natural n m

signum :: Natural n m -> Natural n m

fromInteger :: Integer -> Natural n m

Ord (Natural start end)

Defined in LAoP.Utils.Internal

Methods

compare :: Natural start end -> Natural start end -> Ordering

(<) :: Natural start end -> Natural start end -> Bool

(<=) :: Natural start end -> Natural start end -> Bool

(>) :: Natural start end -> Natural start end -> Bool

(>=) :: Natural start end -> Natural start end -> Bool

max :: Natural start end -> Natural start end -> Natural start end

min :: Natural start end -> Natural start end -> Natural start end

Read (Natural start end)

Defined in LAoP.Utils.Internal

Methods

readsPrec :: Int -> ReadS (Natural start end)

readList :: ReadS [Natural start end]

readPrec :: ReadPrec (Natural start end)

readListPrec :: ReadPrec [Natural start end]

Show (Natural start end)

Defined in LAoP.Utils.Internal

Methods

showsPrec :: Int -> Natural start end -> ShowS

show :: Natural start end -> String

showList :: [Natural start end] -> ShowS

Generic (Natural start end)

Defined in LAoP.Utils.Internal

Associated Types

type Rep (Natural start end) :: Type -> Type

Methods

from :: Natural start end -> Rep (Natural start end) x

to :: Rep (Natural start end) x -> Natural start end

NFData (Natural start end)

Defined in LAoP.Utils.Internal

Methods

rnf :: Natural start end -> ()

type Rep (Natural start end)

Defined in LAoP.Utils.Internal

type Rep (Natural start end) = D1 ('MetaData "Natural" "LAoP.Utils.Internal" "laop-0.1.1.1-inplace" 'True) (C1 ('MetaCons "Nat" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int)))

nat :: forall n m. (KnownNat n, KnownNat m) => Int -> Natural n m

Natural constructor function. Throws a runtime error if the Int value is greater than the corresponding m or lower than n in the Natural n m type.

Coerce auxiliar functions to help promote Int typed functions to

coerceNat :: (Int -> Int -> Int) -> Natural a a' -> Natural b b' -> Natural c c'

Auxiliary function that promotes binary Int functions to Natural binary functions.

coerceNat2 :: ((Int, Int) -> Int -> Int) -> (Natural a a', Natural b b') -> Natural c c' -> Natural d d'

Auxiliary function that promotes ternary (binary) Int functions to Natural functions.

coerceNat3 :: (Int -> Int -> a) -> Natural b b' -> Natural c c' -> a

Auxiliary function that promotes ternary (binary) Int functions to Natural functions.

List data type

newtype List a

Powerset data type.

This data type is a newtype wrapper around '[]'. This exists in order to implement an Enum and Bounded instance that cannot be harmful for the outside.

Constructors

L [a]

Instances

(Enum a, Bounded a) => Bounded (List a)

Defined in LAoP.Utils.Internal

Methods

minBound :: List a

maxBound :: List a

(Bounded a, Enum a, Eq a) => Enum (List a)

Defined in LAoP.Utils.Internal

Methods

succ :: List a -> List a

pred :: List a -> List a

toEnum :: Int -> List a

fromEnum :: List a -> Int

enumFrom :: List a -> [List a]

enumFromThen :: List a -> List a -> [List a]

enumFromTo :: List a -> List a -> [List a]

enumFromThenTo :: List a -> List a -> List a -> [List a]

Eq a => Eq (List a)

Defined in LAoP.Utils.Internal

Methods

(==) :: List a -> List a -> Bool

(/=) :: List a -> List a -> Bool

Read a => Read (List a)

Defined in LAoP.Utils.Internal

Methods

readsPrec :: Int -> ReadS (List a)

readList :: ReadS [List a]

readPrec :: ReadPrec (List a)

readListPrec :: ReadPrec [List a]

Show a => Show (List a)

Defined in LAoP.Utils.Internal

Methods

showsPrec :: Int -> List a -> ShowS

show :: List a -> String

showList :: [List a] -> ShowS

Category type class

class Category k where

Constrained category instance

Associated Types

type Object k o :: Constraint

type Object k o = ()

Methods

id :: Object k a => k a a

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

Instances

Category Relation

It is possible to implement a constrained version of the category type class.

Defined in LAoP.Relation.Internal

Associated Types

type Object Relation o

Methods

id :: Object Relation a => Relation a a

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

Num e => Category (Matrix e)

It is possible to implement a constrained version of the category type class.

Defined in LAoP.Matrix.Internal

Associated Types

type Object (Matrix e) o

Methods

id :: Object (Matrix e) a => Matrix e a a

(.) :: Matrix e b c -> Matrix e a b -> Matrix e a c

Num e => Category (Matrix e)

It is possible to implement a constrained version of the category type class.

Defined in LAoP.Matrix.Type

Associated Types

type Object (Matrix e) o

Methods

id :: Object (Matrix e) a => Matrix e a a

(.) :: Matrix e b c -> Matrix e a b -> Matrix e a c

Category ((->) :: Type -> Type -> Type)

Defined in LAoP.Utils.Internal

Associated Types

type Object (->) o

Methods

id :: Object (->) a => a -> a

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

Orphan instances

(Bounded a, Bounded b) => Bounded (Either a b)

Methods

minBound :: Either a b

maxBound :: Either a b

(Enum a, Bounded a, Enum b, Bounded b) => Enum (Either a b)

Methods

succ :: Either a b -> Either a b

pred :: Either a b -> Either a b

toEnum :: Int -> Either a b

fromEnum :: Either a b -> Int

enumFrom :: Either a b -> [Either a b]

enumFromThen :: Either a b -> Either a b -> [Either a b]

enumFromTo :: Either a b -> Either a b -> [Either a b]

enumFromThenTo :: Either a b -> Either a b -> Either a b -> [Either a b]

(Enum a, Enum b, Bounded b) => Enum (a, b)

Optimized Enum instance for tuples that comply with the given constraints.

Methods

succ :: (a, b) -> (a, b)

pred :: (a, b) -> (a, b)

toEnum :: Int -> (a, b)

fromEnum :: (a, b) -> Int

enumFrom :: (a, b) -> [(a, b)]

enumFromThen :: (a, b) -> (a, b) -> [(a, b)]

enumFromTo :: (a, b) -> (a, b) -> [(a, b)]

enumFromThenTo :: (a, b) -> (a, b) -> (a, b) -> [(a, b)]