GAME SEMANTICS FOR FIRST-ORDER LOGIC
We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of first-order classical logic. We present some relations with Krivine's classical realizability and applications to type isomorphisms.
game semantics first-order logic classical logic lambda-mu-calculus realizability type isomorphisms intuitionistic logic lambda-calculus full completeness control category