topsort :: [(*,*)] -> [*] topsort rel = tsort (carrier rel) rel tsort c r = , if c= = error "inconsistent data for tsort", if m= = a : tsort (c--[a]) [(u,v)|(u,v)<-r; u~=a], otherwise where a = hd m m = (c -- ran r) ||remarks on the above || - it is an invariant that c contains the carrier of relation r || - m is the set of elements of c with no predecessor in r dom r = mkset [u|(u,v)<-r] ||domain of a relation ran r = mkset [v|(u,v)<-r] ||range of a relation carrier r = union (dom r) (ran r) union x y = mkset (x++y)
Miranda script for topological sort
topsort takes a list of pairs representing a partial order - where the presence of (u,v) in the list means that u precedes v in the ordering - and returns a total ordering consistent with the information given - that is if (u,v) is in the input data, then u will come before v in the output list.
The error case will arise if the input data contains a cycle - i.e. if there is an element that directly or indirectly precedes itself.
A set is here represented as a list without duplicates. The standard function mkset removes duplicates from a list. The carrier of a relation is the set of all the elements related by it.