Must Preorder in Non-Deterministic Untyped Lambda-Calculus

This paper studies the interplay between functional application and nondeterministic choice in the context of untyped λ-calculus. We introduce an operational semantics which is based on the idea of must preorder, coming from the theory of process algebras. To characterize this relation, we build a model using the classical inverse limit construction, and we prove it fully abstract using a generalization of Bohm trees.

[1]  Gérard Boudol,et al.  A lambda-calculus for parallel functions , 1990 .

[2]  Egidio Astesiano,et al.  Distributive Semantics for Nondeterministic Typed lambda-Calculi , 1984, Theor. Comput. Sci..

[3]  M. Hyland.  A Syntactic Characterization of the Equality in Some Models for the Lambda Calculus , 1976 .

[4]  Christopher P. Wadsworth,et al.  The Relation Between Computational and Denotational Properties for Scott's Dinfty-Models of the Lambda-Calculus , 1976, SIAM J. Comput..

[5]  Mariangiola Dezani-Ciancaglini,et al.  (Semi)-separability of Finite Sets of Terms in Scott's D_infty-Models of the lambda-Calculus , 1978, ICALP.

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

[7]  Radha Jagadeesan,et al.  A Domain-Theoretic Model for a Higher-Order Process Calculus , 1990, ICALP.

[8]  James H. Morris,et al.  Lambda-calculus models of programming languages. , 1969 .

[9]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..

[10]  Rocco De Nicola,et al.  Testing Equivalence for Processes , 1983, ICALP.

[11]  Gordon D. Plotkin,et al.  A Powerdomain Construction , 1976, SIAM J. Comput..

[12]  G. Longo,et al.  Lambda-Calculus Models and Extensionality , 1980, Math. Log. Q..

[13]  Bent Thomsen,et al.  A calculus of higher order communicating systems , 1989, POPL '89.

[14]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[15]  Matthew Hennessy,et al.  The Semantics of Call-By-Value and Call-By-Name in a Nondeterministic Environment , 1980, SIAM J. Comput..

[16]  Matthew Hennessy,et al.  Full Abstraction for a Simple Parallel Programming Language , 1979, MFCS.

[17]  Matthew Hennessy,et al.  A Mathematical Semantics for a Nondeterministic Typed lambda-Calculus , 1980, Theor. Comput. Sci..

[18]  Robin Milner.  Functions as Processes , 1990, ICALP.

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