hamusic-0.1.2.1: Library to handle abstract music Source code Contents Index

Music.Analysis.PF Portability portable Stability experimental Maintainer silva.samuel@alumni.uminho.pt

Contents Product Combinators Renamings Coproduct Renamings Combinators Exponentiation Combinators Others Natural isomorphisms More funtions Algebras and Co-Algebras Algebras and Co-Algebras

Description

This module implements Point-Free library

Synopsis

split :: (a -> b) -> (a -> c) -> a -> (b, c) (><) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) (!) :: a -> () p1 :: (a, b) -> a p2 :: (a, b) -> b i1 :: a -> Either a b i2 :: b -> Either a b (-|-) :: (a -> b) -> (c -> d) -> Either a c -> Either b d cond :: (b -> Bool) -> (b -> c) -> (b -> c) -> b -> c ap :: (a -> b, a) -> b expn :: (b -> c) -> (a -> b) -> a -> c grd :: (a -> Bool) -> a -> Either a a swap :: (a, b) -> (b, a) assocr :: ((a, b), c) -> (a, (b, c)) assocl :: (a, (b, c)) -> ((a, b), c) distr :: (a, Either b c) -> Either (a, b) (a, c) undistr :: Either (a, b) (a, c) -> (a, Either b c) flatr :: (a, (b, c)) -> (a, b, c) flatl :: ((a, b), c) -> (a, b, c) unflatr :: (a, b, c) -> (a, (b, c)) unflatl :: (a, b, c) -> ((a, b), c) pwnil :: a -> (a, ()) coswap :: Either a b -> Either b a coassocr :: Either (Either a b) c -> Either a (Either b c) maybe2either :: Maybe a -> Either () a either2maybe :: Either () a -> Maybe a e2m :: Either () a -> Maybe a m2e :: Maybe a -> Either () a outL :: [a] -> Maybe (a, [a]) cataL :: (Maybe (a, c) -> c) -> [a] -> c inL :: Maybe (a, [a]) -> [a] anaL :: (c -> Maybe (a, c)) -> c -> [a] hyloL :: (Maybe (c, b) -> b) -> (a -> Maybe (c, a)) -> a -> b mapL :: (a -> b) -> [a] -> [b] concatL :: [[a]] -> [a] reverseL :: [a] -> [a] outL1 :: [a] -> Maybe (Either a (a, [a])) cataL1 :: (Maybe (Either a (a, c)) -> c) -> [a] -> c inL1 :: Maybe (Either a (a, [a])) -> [a] anaL1 :: (c -> Maybe (Either a (a, c))) -> c -> [a] hyloL1 :: (Maybe (Either d (c, b)) -> b) -> (a -> Maybe (Either d (c, a))) -> a -> b

Product

Combinators

split :: (a -> b) -> (a -> c) -> a -> (b, c) Source

split

(><) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) Source

product

(!) :: a -> () Source

the 0-adic split

Renamings

p1 :: (a, b) -> a Source

fst

p2 :: (a, b) -> b Source

snd

Coproduct

Renamings

i1 :: a -> Either a b Source

Left

i2 :: b -> Either a b Source

Right

Combinators

(-|-) :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source

sum

cond :: (b -> Bool) -> (b -> c) -> (b -> c) -> b -> c Source

McCarthy's conditional:

Exponentiation

Combinators

ap :: (a -> b, a) -> b Source

ap

expn :: (b -> c) -> (a -> b) -> a -> c Source

expn

Others

grd :: (a -> Bool) -> a -> Either a a Source

guard

Natural isomorphisms

swap :: (a, b) -> (b, a) Source

swap

assocr :: ((a, b), c) -> (a, (b, c)) Source

assoc right

assocl :: (a, (b, c)) -> ((a, b), c) Source

assoc left

distr :: (a, Either b c) -> Either (a, b) (a, c) Source

dist right

undistr :: Either (a, b) (a, c) -> (a, Either b c) Source

undist right

flatr :: (a, (b, c)) -> (a, b, c) Source

flat right

flatl :: ((a, b), c) -> (a, b, c) Source

flat left

unflatr :: (a, b, c) -> (a, (b, c)) Source

unflat right

unflatl :: (a, b, c) -> ((a, b), c) Source

unflat left

pwnil :: a -> (a, ()) Source

pair with nil

coswap :: Either a b -> Either b a Source

coswap

coassocr :: Either (Either a b) c -> Either a (Either b c) Source

coassoc right

More funtions

maybe2either :: Maybe a -> Either () a Source

maybe 2 Either

either2maybe :: Either () a -> Maybe a Source

either 2 maybe

e2m :: Either () a -> Maybe a Source

Binding to either2maybe

m2e :: Maybe a -> Either () a Source

Binding to maybe2either

Algebras and Co-Algebras

outL :: [a] -> Maybe (a, [a]) Source

out

cataL :: (Maybe (a, c) -> c) -> [a] -> c Source

catamorphism

inL :: Maybe (a, [a]) -> [a] Source

in

anaL :: (c -> Maybe (a, c)) -> c -> [a] Source

anamorphism

hyloL :: (Maybe (c, b) -> b) -> (a -> Maybe (c, a)) -> a -> b Source

hylomorphism

mapL :: (a -> b) -> [a] -> [b] Source

mapping

concatL :: [[a]] -> [a] Source

concat

reverseL :: [a] -> [a] Source

reverse

Algebras and Co-Algebras

outL1 :: [a] -> Maybe (Either a (a, [a])) Source

out

cataL1 :: (Maybe (Either a (a, c)) -> c) -> [a] -> c Source

catamorphism

inL1 :: Maybe (Either a (a, [a])) -> [a] Source

in

anaL1 :: (c -> Maybe (Either a (a, c))) -> c -> [a] Source

anamorphism

hyloL1 :: (Maybe (Either d (c, b)) -> b) -> (a -> Maybe (Either d (c, a))) -> a -> b Source

hylomorphism

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