(* gsearch *)
(*
Assume you are given a set of edges
*)
val E = [("a","b"),("a","c"),("a","d"),
         ("b","e"),
         ("c","f"),
         ("d","e"),
         ("e","f"),
         ("e","g")];

(*
Therefore E represents the set of edges in a digraph.

(1) Write a predicate 

          fun pathp s g E = ...

    that takes as arguments a starting node s, and a
    goal node g, and a set of edges E and delivers a result true
    if there is a path from s to g in E (deliver false otherwise)

(2) Write a function 

          fun path s g E = ...

    that delivers the list of edges, in order, that if traversed
    take us from s to g in E

(3) assume we then update E, such that *)

val E2 = E @ [("e","d")];

(* Do your functions till operate when we use E2 in place of E? 

(4) Enhance E such that it is a list of triples of the form
    (v1,v2,c12) where v1 is a vertex, v2 is a vertex, and 
    c12 is the cost of going from v1 to v2.
    Enhance function path such that it delivers the minimum cost
    path from s to g in E.
*)


(* Hint: do not assume that the lecturer knows how to do any of the above *)