How do you represent a graph in Haskell?

Question

It\'s easy enough to represent a tree or list in haskell using algebraic data types. But how would you go about typographically representing a graph? It seems that you need

Answer 1

As Ben mentioned, cyclic data in Haskell is constructed by a mechanism called "tying the knot". In practice, it means that we write mutually recursive declarations using let or where clauses, which works because the mutually recursive parts are lazily evaluated.

Here's an example graph type:

import Data.Maybe (fromJust)

data Node a = Node
    { label    :: a
    , adjacent :: [Node a]
    }

data Graph a = Graph [Node a]

As you can see, we use actual Node references instead of indirection. Here's how to implement a function that constructs the graph from a list of label associations.

mkGraph :: Eq a => [(a, [a])] -> Graph a
mkGraph links = Graph $ map snd nodeLookupList where

    mkNode (lbl, adj) = (lbl, Node lbl $ map lookupNode adj)

    nodeLookupList = map mkNode links

    lookupNode lbl = fromJust $ lookup lbl nodeLookupList

We take in a list of (nodeLabel, [adjacentLabel]) pairs and construct the actual Node values via an intermediate lookup-list (which does the actual knot-tying). The trick is that nodeLookupList (which has the type [(a, Node a)]) is constructed using mkNode, which in turn refers back to the nodeLookupList to find the adjacent nodes.