Games characterizing Levy-Longo trees

We present a simple strongly universal innocent game model for Levy-Longo trees, i.e. every point in the model is the denotation of a unique Levy-Longo tree. The observational quotient of the model then gives a universal, and hence fully abstract, model of the pure Lazy Lambda Calculus.

[1]  Gordon D. Plotkin,et al.  Call-by-Name, Call-by-Value and the lambda-Calculus , 1975, Theor. Comput. Sci..

[2]  C.-H. Luke Ong,et al.  Full Abstraction in the Lazy Lambda Calculus , 1993, Inf. Comput..

[3]  Samson Abramsky,et al.  Games for Recursive Types , 1994, Theory and Formal Methods.

[4]  Vincent Danos,et al.  The Anatomy of Innocence , 2001, CSL.

[5]  Harold T. Hodes,et al.  The | lambda-Calculus. , 1988 .

[6]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[7]  Pietro Di Gianantonio,et al.  Game Semantics for Untyped λβη-Calculus , 1999 .

[8]  A. Edalat,et al.  Advances in theory and formal methods of computing : proceedings of the third Imperial College workshop, Christ Church, Oxford, 1-3 April 1996 , 1996 .

[9]  Pietro Di Gianantonio Game Semantics for the Pure Lazy lambda-calculus , 2001, TLCA.

[10]  C.-H. Luke Ong,et al.  Innocent game models of untyped lambda-calculus , 2002, Theor. Comput. Sci..

[11]  C.-H. Luke Ong,et al.  On Full Abstraction for PCF: I, II, and III , 2000, Inf. Comput..

[12]  Takanori Adachi Powerposets(Lambda Calculus and Computer Science Theory) , 1984 .

[13]  Furio Honsell,et al.  Game Semantics for Untyped lambda beta eta-Calculus , 1999, TLCA.

[14]  Jean-Jacques Lévy,et al.  An algebraic interpretation of the lambda beta - calculus and a labeled lambda - calculus , 1975, Lambda-Calculus and Computer Science Theory.

[15]  C.-H. Luke Ong,et al.  A Universal Innocent Game Model for the Böhm Tree Lambda Theory , 1999, CSL.

[16]  Giuseppe Longo,et al.  Set-theoretical models of λ-calculus: theories, expansions, isomorphisms , 1983, Ann. Pure Appl. Log..

[17]  Samson Abramsky,et al.  Games and full abstraction for the lazy /spl lambda/-calculus , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[18]  Guy McCusker,et al.  Full Abstraction By Translation , 1996 .