I am trying to define some vertex labels in Isabelle HOL and have a problem with the successor definition:
record ('v,'w) graph =
nodes :: "('v×'w) set"
edges :: "(('v×'w) × ('v×'w)) set"
definition succ :: "('v,'w) graph ⇒'v ⇒ ('v,'w) set"
where "succ G v ≡ {(v',w). ((v,w),(v',w))∈edges G}"
It says "Bad number of arguments for type constructor: "Set.set"", does anyone know how to fix this?
succ shall probably return a set of vertex-label pairs 'v × 'w, so want to write
definition succ :: "('v,'w) graph ⇒'v ⇒ ('v × 'w) set"