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Kripke Logical Relations and PCF

P.W. Ohearn, J.G. Riecke
1995 Information and Computation  
Sieber has described a model of PCF consisting of continuous functions that are invariant under certain ( nitary) logical relations, and shown that it is fully abstract for closed terms of up to third-order  ...  We show that one may achieve full abstraction at all types using a form of \Kripke logical relations" introduced by Jung and Tiuryn to characterize -de nability.  ...  , and Ramesh Subrahmanyam for their encouragement.  ... 
doi:10.1006/inco.1995.1103 fatcat:s45erba4hzaori6mqilf6aokei

Matching typed and untyped realizability

John Longley
1999 Electronical Notes in Theoretical Computer Science  
We g i v e some examples of this situation for a variety of extensions of PCF.  ...  Realizability i n terpretations of logics are given by s a ying what it means for computational objects of some kind to realize logical formulae.  ...  This research w as funded by the EPSRC Research G r a n t GR/L89532 \Notions of computability for general datatypes".  ... 
doi:10.1016/s1571-0661(04)00105-7 fatcat:6zp5v23rfjhkdow3vy7yyhaojy

Full abstraction, totality and PCF

1999 Mathematical Structures in Computer Science  
Inspired by a question of Riecke, we consider the interaction of totality and full abstraction, asking whether full abstraction holds for Scott's model of cpos and continuous functions if one restricts  ...  Analysing further, we consider sequential and parallel versions of PCF and several models: Scott's model of continuous functions, Milner's fully abstract model of PCF and their effective submodels.  ...  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

Intelligent control via new efficient logics

Stanislav N. Vassilyev, Artem V. Davydov, Alexander K. Zherlov
2008 IFAC Proceedings Volumes  
A new efficient logic apparatus for intelligent control is proposed.  ...  Problems related to automation of action planning, including those bound up with the mode of cooperative mission performance, are considered.  ...  The common concepts of logic satisfiability, validity, inconsistency, equivalence, free and bound occurrences of variables, etc. for a PCF F are understood likewise for (F) * .  ... 
doi:10.3182/20080706-5-kr-1001.02322 fatcat:ygpw63r7ebcshfbyqm2vefdlje

Totality, definability and boolean circuits [chapter]

Antonio Bucciarelli, Ivano Salvo
1998 Lecture Notes in Computer Science  
The elements of an equivalence class of the totality equivalence relation (totality class) can be seen as different algorithms for computing a given set-theoretic boolean function.  ...  A relation ~C_ [-J~CSPT D~ x D~ is logical at a if either ~r is ground or ~ -ch --+ ~2 and for all f,g E D~, f ~ g ill for all x,y E D~, (x f(z) ~ Moreover ~ is logical up to a if for all 7-structurally  ...  a partial equivalence relation on the Scott's type frame; we show that it is exactly the totality logical relation.  ... 
doi:10.1007/bfb0055104 fatcat:dunvdphxfbfg3krdftdhb7ocoy

Program Logics for Sequential Higher-Order Control [chapter]

Martin Berger
2010 Lecture Notes in Computer Science  
We introduce a Hoare logic for call-by-value higher-order functional languages with control operators such as callcc.  ...  The more heavyweight logical apparatus for higher-order control is required only where control is manipulated explicitly, leading to more concise proofs and specifications.  ...  Reasoning about PCF-terms using the logic for PCF + is moderately more laborious than using a logic tailor-made for PCF like [16] .  ... 
doi:10.1007/978-3-642-11623-0_11 fatcat:rpsyqznddjbblggxv4gsbctc3a

Parametric Polymorphism and Operational Equivalence (Preliminary Version)

Andrew M. Pitts
1998 Electronical Notes in Theoretical Computer Science  
An operationally-based approach to Reynolds' notion of relational parametricity is developed for an extension of Plotkin's PCF with 8-types and lazy lists.  ...  The resulting logical relation is shown to be a useful tool for proving properties of polymorphic types up to a notion of operational equivalence based on Morris-style contextual equivalence. c 1998 Published  ...  congruence (de ned in Theorem 3.2) in terms of a binary`logical relation' incorporating a notion of relational parametricity analogous to that introduced by Reynolds 33 ] for the This`action' of PCF  ... 
doi:10.1016/s1571-0661(05)80685-1 fatcat:mtk3jpsuqbdhlpf43mwybkv3m4

Embedding a logical theory of constructions in Agda

Ana Bove, Peter Dybjer, Andrés Sicard-Ramírez
2008 Proceedings of the 3rd workshop on Programming languages meets program verification - PLPV '09  
To illustrate our approach we specify an LTC-style logic for PCF, and show how to prove the termination and correctness of a general recursive algorithm for computing the greatest common divisor of two  ...  We show how to embed an external programming logic, Aczel's Logical Theory of Constructions (LTC) inside Agda.  ...  LTC for PCF We use LTC as a generic name for a family of related logical systems which have been used by Aczel (1977 Aczel ( , 1980 Aczel ( , 1989 and Smith (1984) for the purpose of interpreting Martin-Löf  ... 
doi:10.1145/1481848.1481857 dblp:conf/plpv/BoveDS09 fatcat:uckoavielzedbhmedjqw7os6ua

Page 4082 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
“Our model for classical PCF is different from Ong’s model of Parigot’s lambda-mu calculus.  ...  98¢:03044 98¢:03044 03B40 Herbelin, Hugo (F-PARIS7-LI; Paris) Games and weak-head reduction for classical PCF.  ... 

A Model of PCF in Guarded Type Theory

Marco Paviotti, Rasmus Ejlers Møgelberg, Lars Birkedal
2015 Electronical Notes in Theoretical Computer Science  
The model construction is related to Escardo's metric model for PCF, but here everything is carried out entirely in type theory with guarded recursion, including the formulation of the operational semantics  ...  Previous work has shown how guarded recursion is useful for constructing logics for reasoning about programming languages with advanced features, as well as for constructing and reasoning about elements  ...  Acknowledgement We thank Aleš Bizjak for fruitful discussions.  ... 
doi:10.1016/j.entcs.2015.12.020 fatcat:xzirbdlpkbbunjbh7kmleu7bzq

Sequentiality and Piecewise-affinity in Segments of Real-PCF

Amin Farjudian
2004 Electronical Notes in Theoretical Computer Science  
Real PCF (RPCF) was proposed by Martín Escardó [8] as a language for Real number computation.  ...  I like to thank him for his invaluable help throughout all the stages of preparing the paper.  ...  Also my thanks go to Martín Escardó for his comments and suggestions, especially on Corollary 2.10, page 31.  ... 
doi:10.1016/j.entcs.2004.08.002 fatcat:kqv3mhh6dzhshimladtzqa436y

Relative Completeness for Logics of Functional Programs

Bernhard Reus, Thomas Streicher, Marc Herbstritt
2011 Annual Conference for Computer Science Logic  
For such a logic, contrary to results for Hoare logic, it does not make sense to ask whether it is complete relative to the full theory of its first-order part, since the first order part does not determine  ...  We prove a relative completeness result for a logic of functional programs extending D. Scott's LCF.  ...  Acknowledgements This research has been supported by the EPSRC Research Grant "Relative Completeness for Logics of Functional Programs" (EPSRC EP/I01456X/1).  ... 
doi:10.4230/lipics.csl.2011.470 dblp:conf/csl/ReusS11 fatcat:vx33aaxktnfq3lw7visuubmoc4

Stable Bistructure Models of PCF

Glynn Winskel
1994 BRICS Report Series  
A main motivation for bidomains came from the full abstraction problem for Plotkin's functional language PCF.  ...  Bistructures form a categorical model of Girard's linear logic consisting of a linear category together with a comonad.  ...  As such it is a relation between the events of E 0 and E 1 . Composition in the category is that of relations. The category is a model of intuitionistic linear logic.  ... 
doi:10.7146/brics.v1i13.21656 fatcat:7fpnjkudije2jncdbvwn4s6cuq

Page 6048 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
convertibility relation).  ...  Logic Comput. 11 (2001), no. 4, 527-544. In this paper, the author provides a model for a A-calculus he calls ah? This calculus allows for subtyping, overloading, and late-binding.  ... 

Definability and Full Abstraction

Pierre-Louis Curien
2007 Electronical Notes in Theoretical Computer Science  
In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.  ...  But let us come back to the semantics of PCF and related languages.  ...  Concluding remarks The full abstraction problem for PCF has triggered a lot of work, and is to be celebrated for its "side effects". • The stable model (reinvented by Girard) gave rise to linear logic  ... 
doi:10.1016/j.entcs.2007.02.011 fatcat:y65s4eku4ja75n3t3pam3wd3py
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