Copyright	(c) Alexandre Moine 2019
Maintainer	alexandre@moine.me
Stability	experimental
Safe Haskell	None
Language	Haskell2010

Tungsten.Structure.Graph

Contents

Algebraic graphs as fixed-points
Classical operations on graphs
Operations on graphs
Conversions

Description

This module defines a type isomorphic to algebraic graphs (from A. Mokhov, see the algebraic-graphs package), in terms of Fix from Tungsten.Fix.

A good consumer is a function that can be fused with a good producer. A good producer is a function that can be fused with a good consumer.

Synopsis

data GraphF a b
- = EmptyF
- | VertexF a
- | OverlayF b b
- | ConnectF b b
newtype Graph a = Graph (Fix (GraphF a))
empty :: Graph a
vertex :: a -> Graph a
overlay :: Graph a -> Graph a -> Graph a
connect :: Graph a -> Graph a -> Graph a
foldg :: b -> (a -> b) -> (b -> b -> b) -> (b -> b -> b) -> Graph a -> b
transpose :: Graph a -> Graph a
hasVertex :: Eq a => a -> Graph a -> Bool
vertices :: [a] -> Graph a
edges :: [(a, a)] -> Graph a

Algebraic graphs as fixed-points

data GraphF a b Source #

The "factored-out" recursive type for algebraic graphs.

Constructors

EmptyF
VertexF a
OverlayF b b
ConnectF b b

Instances

Show2 GraphF Source #
Instance details Defined in Tungsten.Structure.Graph Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> GraphF a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [GraphF a b] -> ShowS #
Functor (GraphF a) Source #
Instance details Defined in Tungsten.Structure.Graph Methods fmap :: (a0 -> b) -> GraphF a a0 -> GraphF a b # (<$) :: a0 -> GraphF a b -> GraphF a a0 #
Show a => Show1 (GraphF a) Source #
Instance details Defined in Tungsten.Structure.Graph Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> GraphF a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [GraphF a a0] -> ShowS #
(Eq a, Eq b) => Eq (GraphF a b) Source #
Instance details Defined in Tungsten.Structure.Graph Methods (==) :: GraphF a b -> GraphF a b -> Bool # (/=) :: GraphF a b -> GraphF a b -> Bool #
(Ord a, Ord b) => Ord (GraphF a b) Source #
Instance details Defined in Tungsten.Structure.Graph Methods compare :: GraphF a b -> GraphF a b -> Ordering # (<) :: GraphF a b -> GraphF a b -> Bool # (<=) :: GraphF a b -> GraphF a b -> Bool # (>) :: GraphF a b -> GraphF a b -> Bool # (>=) :: GraphF a b -> GraphF a b -> Bool # max :: GraphF a b -> GraphF a b -> GraphF a b # min :: GraphF a b -> GraphF a b -> GraphF a b #
(Read a, Read b) => Read (GraphF a b) Source #
Instance details Defined in Tungsten.Structure.Graph Methods readsPrec :: Int -> ReadS (GraphF a b) # readList :: ReadS [GraphF a b] # readPrec :: ReadPrec (GraphF a b) # readListPrec :: ReadPrec [GraphF a b] #
(Show a, Show b) => Show (GraphF a b) Source #
Instance details Defined in Tungsten.Structure.Graph Methods showsPrec :: Int -> GraphF a b -> ShowS # show :: GraphF a b -> String # showList :: [GraphF a b] -> ShowS #

newtype Graph a Source #

Constructors

Graph (Fix (GraphF a))

Instances

Monad Graph Source #
Instance details Defined in Tungsten.Structure.Graph Methods (>>=) :: Graph a -> (a -> Graph b) -> Graph b # (>>) :: Graph a -> Graph b -> Graph b # return :: a -> Graph a # fail :: String -> Graph a #
Functor Graph Source #
Instance details Defined in Tungsten.Structure.Graph Methods fmap :: (a -> b) -> Graph a -> Graph b # (<$) :: a -> Graph b -> Graph a #
Applicative Graph Source #
Instance details Defined in Tungsten.Structure.Graph Methods pure :: a -> Graph a # (<>) :: Graph (a -> b) -> Graph a -> Graph b # liftA2 :: (a -> b -> c) -> Graph a -> Graph b -> Graph c # (>) :: Graph a -> Graph b -> Graph b # (<*) :: Graph a -> Graph b -> Graph a #
Show a => Show (Graph a) Source #
Instance details Defined in Tungsten.Structure.Graph Methods showsPrec :: Int -> Graph a -> ShowS # show :: Graph a -> String # showList :: [Graph a] -> ShowS #