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Page 2268 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally  ...  defined subsorts), exception handling, and an operational semantics based on term rewriting.  ... 

Full abstraction, totality and PCF

GORDON PLOTKIN
1999 Mathematical Structures in Computer Science  
Some apparently rather difficult open problems arise, essentially concerning whether the sequential and parallel versions of PCF have the same expressive power, in the sense of total equivalence.  ...  Define (using evident abbreviations) the PCF terms: and (f b t) and ¬(f f f) then t else f and N = λb o .λf o→o→o . if (f tb) and (f b t) and ¬(f f f) then (b or ¬b) else f.  ...  Acknowledgments I would like to thank Samson Abramsky for reawakening my interest in totality and domain theory, and Ulrich Berger, John Longley and Dag Normann for interesting and informative discussions  ... 
doi:10.1017/s0960129598002692 fatcat:kg4f66ts25budmwdb6hqsgr57q

Axioms for Definability and Full Completeness [article]

Samson Abramsky
2014 arXiv   pre-print
These axioms have been distilled from recent results on definability and full abstraction of game semantics for a number of programming languages.  ...  Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness  ...  I am grateful to Guy McCusker and the two anonymous referees for their comments on the preliminary version of this paper.  ... 
arXiv:1401.4735v2 fatcat:kti4sxivinbqteeoxdcghmjvzm

Extensional Collapse Situations I: non-termination and unrecoverable errors [article]

Antonio Bucciarelli
2011 arXiv   pre-print
The proofs are carried out by exhibiting suitable applied λ-calculi, and by exploiting the fundamental lemma of logical relations.  ...  We show that the models so defined form a lattice when ordered by the extensional collapse situation relation, introduced in order to compare models with respect to the amount of "intensional information  ...  Thanks to an anonymous referee of a previous version of this work, for suggesting that pre-logical relations are the proper framework to deal with extensional collapse situations.  ... 
arXiv:1101.4465v1 fatcat:kjnwhlevhfb5xkejlaq2kj4dqi

Page 8491 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
, Definability of total objects in PCF and related calculi (4-5); Peter Selinger, Categorical semantics of control (6-7); Thorsten Altenkirch, Representations of first order function types as terminal  ...  , Second-order pre-logical relations and representation inde- pendence (298-314); Ugo de’Liguoro, Characterizing convergent terms in object calculi via intersection types (315-328); Ralph Matthes, Parigot  ... 

Program Logics for Homogeneous Meta-programming [chapter]

Martin Berger, Laurence Tratt
2010 Lecture Notes in Computer Science  
We also demonstrate that our logics are relatively complete in the sense of Cook, enable the inductive derivation of characteristic formulae, and exactly capture the observational properties induced by  ...  A meta-program is a program that generates or manipulates another program; in homogeneous meta-programming, a program may generate new parts of, or manipulate, itself.  ...  The reduction relation → is unchanged from PCF for the PCF-fragment of PCF DP , and adapted to PCF DP as follows. First we define define reduction contexts, by extending those for PCF as follows.  ... 
doi:10.1007/978-3-642-17511-4_5 fatcat:enz6xvuksvhtlkum47jmefagom

Relative Completeness for Logics of Functional Programs

Bernhard Reus, Thomas Streicher, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
In both cases we need to extend traditional LCF in order to capture a sufficient amount of domain theory.  ...  We establish relative completeness for two models: for the Scott model we use the theory of Baire Space as data theory, and for the effective Scott model we take first-order arithmetic.  ...  We would like to thank Martin Berger for discussions on the completeness results of [9] and the anonymous referees for their suggestions and comments.  ... 
doi:10.4230/lipics.csl.2011.470 dblp:conf/csl/ReusS11 fatcat:vx33aaxktnfq3lw7visuubmoc4

Initial Semantics for Reduction Rules [article]

Benedikt Ahrens
2018 arXiv   pre-print
We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and  ...  In the second work we characterize untyped syntax with reduction rules as initial object in a category of models.  ...  The data thus defined constitutes a relative monad PCFEM on the functor ∆ T PCF (IDelta TY). We omit the details.  ... 
arXiv:1212.5668v2 fatcat:7b5ptjcofzc6bb6r2kaapdwja4

Page 7470 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
In fact, as is shown elsewhere, Martin-Lof’s inconsistent type theory, Type : Type, is definable in it.  ...  Recent developments in areas related to concurrent program specification and verification, as well as database and information systems specification, justify the inter- est of this extension.  ... 

Game semantics and linear CPS interpretation

J. Laird
2005 Theoretical Computer Science  
We show that this embedding corresponds precisely to linear CPS interpretation in its action on a games model of call-by-value PCF, yielding a proof of full abstraction for the associated translation.  ...  This consists of a category of games with a coherence condition on moves-yielding a fully complete model of an affine-type theory-and a syntax-independent and full embedding of a category of Hyland-Ong  ...  Acknowledgements I would like to thank the referees for a correction and several helpful comments.  ... 
doi:10.1016/j.tcs.2004.10.022 fatcat:blaorxezvrggjnlxesdtxmggim

Aspects of categorical recursion theory [article]

Pieter Hofstra, Philip Scott
2020 arXiv   pre-print
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek  ...  Conclusion We hope that we have shown in this -admittedly biased-overview of categorical recursion theory how various of Lambek's seminal ideas have initiated and inspired numerous strands of research  ...  We also hope to have conveyed to the reader that there are still many interesting unanswered questions and relatively unexplored facets of categorical recursion theory that deserve further investigation  ... 
arXiv:2001.05778v1 fatcat:orhmpipltngtdcnkuq2y7rvqaa

A stable programming language

Luca Paolini
2006 Information and Computation  
This fact is related to the existence of stable parallel functions and of stable functions that are not monotone with respect to the extensional order, which cannot be defined by programs of PCF .  ...  The operational description of the extended language is presented in an effective way, although the evaluation of one of the new operators cannot be formalized in a PCF-like rewrite system.  ...  I am also grateful to the anonymous referees for all the mistakes and the typos they pointed out in a preliminary version of this paper and for all the suggestions they put forward.  ... 
doi:10.1016/j.ic.2005.11.002 fatcat:h65f4javvbfvbcj4j5hlniw6pu

Strong normalization for applied lambda calculi

Ulrich Berger, Martín Escardó
2005 Logical Methods in Computer Science  
We consider the untyped lambda calculus with constructors and recursively defined constants.  ...  From this we derive a general normalisation theorem for applied typed lambda-calculi: If all constants have a total value, then all typeable terms are strongly normalising.  ...  Introduction Extensions of typed λ-calculi by data types and recursively defined higher-order functions, often called applied λ-calculi, play an important role in logic and computer science.  ... 
doi:10.2168/lmcs-1(2:3)2005 fatcat:62yvbhp6ong2pncufiltflnocm

Reasoning with hypothetical judgments and open terms in hybrid

Amy P. Felty, Alberto Momigliano
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
In this paper, we add new capabilities for reasoning by induction on encodings of object-level inference rules.  ...  We illustrate the approach using PCF, a simple programming language that serves as the core of a variety of functional languages.  ...  Acknowledgments The first author's research is supported in part by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.1145/1599410.1599422 dblp:conf/ppdp/FeltyM09 fatcat:2atmaaaunzb4fbcf5dypebsqh4

Equational theories for inductive types

Ralph Loader
1997 Annals of Pure and Applied Logic  
The characterisation may be cast as a full abstraction result; in other words we show that the equations between terms valid in this model coincides with a certain syntactically defined equivalence relation  ...  Along the way we give other characterisations of this equivalence; from below, from above, and from a domain model; a version of the Kreisel-Lacombe-Shoenfield theorem allows us to transfer the result  ...  In the case of calculi such as pcf, the observables are the termination or non-termination of programs.  ... 
doi:10.1016/s0168-0072(96)00021-8 fatcat:ctkcdeu4ljdbzd3ew24fxegcee
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