Safe Haskell	None
Language	Haskell2010

LAoP.Utils.Internal

Contents

Natural data type
Coerce auxiliar functions to help promote Int typed functions to
List data type
Orphan instances

Synopsis

newtype Natural (start :: Nat) (end :: Nat) = Nat Int
nat :: forall n m. (KnownNat n, KnownNat m) => Int -> Natural n m
coerceNat :: (Int -> Int -> Int) -> Natural a a' -> Natural b b' -> Natural c c'
coerceNat2 :: ((Int, Int) -> Int -> Int) -> (Natural a a', Natural b b') -> Natural c c' -> Natural d d'
coerceNat3 :: (Int -> Int -> a) -> Natural b b' -> Natural c c' -> a
newtype List a = L [a]

`Natural` data type

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

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) Source #
Instance details Defined in LAoP.Utils.Internal Methods minBound :: Natural n m # maxBound :: Natural n m #
(KnownNat n, KnownNat m) => Enum (Natural n m) Source #
Instance details 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) Source #
Instance details 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) Source #	Throws a runtime error if any of the operations overflows or underflows.
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in LAoP.Utils.Internal Methods rnf :: Natural start end -> () #
type Rep (Natural start end) Source #
Instance details Defined in LAoP.Utils.Internal type Rep (Natural start end) = D1 (MetaData "Natural" "LAoP.Utils.Internal" "laop-0.1.0.4-Bw4Lqoa8fX9DTvULz34n1s" 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 Source #

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' Source #

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' Source #

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

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

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

`List` data type

newtype List a Source #

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) Source #
Instance details Defined in LAoP.Utils.Internal Methods minBound :: List a # maxBound :: List a #
(Bounded a, Enum a, Eq a) => Enum (List a) Source #
Instance details 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) Source #
Instance details Defined in LAoP.Utils.Internal Methods (==) :: List a -> List a -> Bool # (/=) :: List a -> List a -> Bool #
Read a => Read (List a) Source #
Instance details 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) Source #
Instance details Defined in LAoP.Utils.Internal Methods showsPrec :: Int -> List a -> ShowS # show :: List a -> String # showList :: [List a] -> ShowS #

Orphan instances

(Bounded a, Bounded b) => Bounded (Either a b) Source #
Instance details Methods minBound :: Either a b # maxBound :: Either a b #
(Enum a, Bounded a, Enum b, Bounded b) => Enum (Either a b) Source #
Instance details 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) Source #	Optimized `Enum` instance for tuples that comply with the given constraints.
Instance details 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)] #

Natural data type

Coerce auxiliar functions to help promote Int typed functions to

List data type

Orphan instances

`Natural` data type

Coerce auxiliar functions to help promote `Int` typed functions to

`List` data type