Isabelle 标记图定义

Question

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?

Answer 1

succ可能会返回一组顶点标签对'v × 'w ，所以想写

definition succ :: "('v,'w) graph ⇒'v ⇒ ('v × 'w) set"