Filter Models for a Parallel and Non Deterministic Lambda-Calculus

The distinction between the conjunctive nature of non-determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λ-calculus is extended with both a non-deterministic choice and a parallel operator; a notion of reduction is introduced, extending β-reduction of the classical calculus.

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

[2]  Martín Abadi A Semantics for Static Type Inference in a Nondeterministic Language , 1994, Inf. Comput..

[3]  Mariangiola Dezani-Ciancaglini,et al.  Intersection and Union Types , 1991, TACS.

[4]  M.Dezani Mdezani,et al.  Intersection and Union Types , 1991 .

[5]  J. Roger Hindley,et al.  The Completeness Theorem for Typing lambda-Terms , 1983, Theor. Comput. Sci..

[6]  Ugo de'Liguoro,et al.  Must Preorder in Non-Deterministic Untyped Lambda-Calculus , 1992, CAAP.

[7]  Gordon D. Plotkin,et al.  A Semantics for Static Type Inference , 1994, Inf. Comput..

[8]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

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

[10]  Mariangiola Dezani-Ciancaglini,et al.  A filter lambda model and the completeness of type assignment , 1983, Journal of Symbolic Logic.

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

[12]  C.-H. Luke Ong,et al.  Non-determinism in a functional setting , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

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

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

[15]  Davide Sangiorgi,et al.  The lazy lambda calculus in a concurrency scenario , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[16]  Samson Abramsky,et al.  Domain Theory in Logical Form , 1991, LICS.

[17]  J. Krivine Lambda-calcul : types et modèles , 1990 .