Data.Finite

Documentation

data Finite n

Finite number type. Finite n is inhabited by exactly n values. Invariants:

getFinite x < natVal x

getFinite x >= 0

packFinite :: KnownNat n => Integer -> Maybe (Finite n)

Convert an Integer into a Finite, returning Nothing if the input is out of bounds.

packFiniteProxy :: KnownNat n => proxy n -> Integer -> Maybe (Finite n)

Same as packFinite but with a proxy argument to avoid type signatures.

finite :: KnownNat n => Integer -> Finite n

Convert an Integer into a Finite, throwing an error if the input is out of bounds.

finiteProxy :: KnownNat n => proxy n -> Integer -> Finite n

Same as finite but with a proxy argument to avoid type signatures.

getFinite :: Finite n -> Integer

Convert a Finite into the corresponding Integer.

equals :: Finite n -> Finite m -> Bool infix 4

Test two different types of finite numbers for equality.

cmp :: Finite n -> Finite m -> Ordering

Compare two different types of finite numbers.

natToFinite :: (KnownNat n, KnownNat m, (n + 1) <= m) => proxy n -> Finite m

Convert a type-level literal into a Finite.

weaken :: Finite n -> Finite (n + 1)

Add one inhabitant in the end.

strengthen :: KnownNat n => Finite (n + 1) -> Maybe (Finite n)

Remove one inhabitant from the end. Returns Nothing if the input was the removed inhabitant.

shift :: Finite n -> Finite (n + 1)

Add one inhabitant in the beginning, shifting everything up by one.

unshift :: Finite (n + 1) -> Maybe (Finite n)

Remove one inhabitant from the beginning, shifting everything down by one. Returns Nothing if the input was the removed inhabitant.

weakenN :: n <= m => Finite n -> Finite m

Add multiple inhabitants in the end.

strengthenN :: (KnownNat n, n <= m) => Finite m -> Maybe (Finite n)

Remove multiple inhabitants from the end. Returns Nothing if the input was one of the removed inhabitants.

shiftN :: (KnownNat n, KnownNat m, n <= m) => Finite n -> Finite m

Add multiple inhabitant in the beginning, shifting everything up by the amount of inhabitants added.

unshiftN :: (KnownNat n, KnownNat m, n <= m) => Finite m -> Maybe (Finite n)

Remove multiple inhabitants from the beginning, shifting everything down by the amount of inhabitants removed. Returns Nothing if the input was one of the removed inhabitants.

weakenProxy :: proxy k -> Finite n -> Finite (n + k)

strengthenProxy :: KnownNat n => proxy k -> Finite (n + k) -> Maybe (Finite n)

shiftProxy :: KnownNat k => proxy k -> Finite n -> Finite (n + k)

unshiftProxy :: KnownNat k => proxy k -> Finite (n + k) -> Maybe (Finite n)

add :: Finite n -> Finite m -> Finite (n + m)

Add two Finites.

sub :: Finite n -> Finite m -> Either (Finite m) (Finite n)

Subtract two Finites. Returns Left for negative results, and Right for positive results. Note that this function never returns Left 0.

multiply :: Finite n -> Finite m -> Finite (n * m)

Multiply two Finites.

combineSum :: KnownNat n => Either (Finite n) (Finite m) -> Finite (n + m)

Left-biased (left values come first) disjoint union of finite sets.

combineProduct :: KnownNat n => (Finite n, Finite m) -> Finite (n * m)

fst-biased (fst is the inner, and snd is the outer iteratee) product of finite sets.

separateSum :: KnownNat n => Finite (n + m) -> Either (Finite n) (Finite m)

Take a Left-biased disjoint union apart.

separateProduct :: KnownNat n => Finite (n * m) -> (Finite n, Finite m)

Take a fst-biased product apart.

isValidFinite :: KnownNat n => Finite n -> Bool

Verifies that a given Finite is valid. Should always return True unles you bring the Data.Finite.Internal.Finite constructor into the scope, or use unsafeCoerce or other nasty hacks