We present a new denotational model for the untyped -calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [9] and Nickau [17], but the traditional distinction between \question" and \answer" moves is removed. We rst construct models D and DREC as global sections of a reexive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible -algebras but are neither extensional nor universal. We then introduce a new representation of innocent strategies in an economical form. We show a strong connexion between the economical form of the denotation of a term in the game models and a variable-free form of the Nakajima tree of the term. Using this we show that the denable elements of DREC are precisely what we call eectively almost-everywhere copycat (EAC) strategies. The category A EAC with these strategies as morphisms gives rise to a -model D...

We present a new denotation model for the untyped λ-calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [HO94] and Nickau [Nic96], but the traditional distinction between "question" and "answer" moves is removed. We first construct models D and DREC as global sections of a reflexive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible -algebras but are neither extensional nor universal. We then introduce a new representation of innocent strategies in an economical form. We show a stong connexion between the economical form of the denotation of a term in the game models and a variable-free form of the Nakajima tree of the term. Using this we show that the denable elements of DREC are precisely what we call effectively almost-everywhere copycat (EAC) strategies. The category A EAC with these strategies as morphisms gives rise to a ...

We present a new denotation model for the untyped -calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [HO94] and Nickau [Nic96], but the traditional distinction between \question" and \answer" moves is removed. We rst construct models D and DREC as global sections of a reexive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible -algebras but are neither extensional nor universal. We then introduce a new representation of innocent strategies in an economical form. We show a stong connexion between the economical form of the denotation of a term in the game models and a variable-free form of the Nakajima tree of the term. Using this we show that the denable elements of DREC are precisely what we call eectively almost-everywhere copycat (EAC) strategies. The category A EAC with these strategies as morphisms gives rise to a ...

We define an extension of lambda calculus which is fully abstract for Scott's D_infinity-models. We do so by constructing an infinitary lambda calculus which not only has the confluence property, but also is normalising: every term has its infinity eta-Böhm tree as unique normal form. The extension incorporates...