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Kripke Logical Relations and PCF

P.W. Ohearn, J.G. Riecke
1995 Information and Computation  
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.  ...  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  ...  Acknowledgements: We thank Gerard Berry, Achim Jung, Albert Meyer, Gordon Plotkin, Kurt Sieber and Allen Stoughton for helpful discussions and comments, and especially Matthias Felleisen, Martin Odersky  ... 
doi:10.1006/inco.1995.1103 fatcat:s45erba4hzaori6mqilf6aokei

Page 8173 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
relations.  ...  Summary: “Unary PCF is a fragment of the simply typed lambda- calculus PCF. We present a short proof that behavioral equivalence in unary PCF is decidable.  ... 

Page 1419 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
Guo-Qiang Zhang (\~-GA-C; Athens, GA) 97¢:03047 03B40 03G30 68Q55 O’Hearn, Peter W. (1-SRCS-C; Syracuse, NY); Riecke, Jon G. (1-BELL; Murray Hill, NJ) Kripke logical relations and PCF.  ...  We show that one may achieve full abstraction at all types using a form of ‘Kripke logical relations’ introduced by A. Jung and J.  ... 

A Relational Account of Call-by-Value Sequentiality

Jon G. Riecke, Anders B. Sandholm
1997 BRICS Report Series  
The model is built from partial continuous<br />functions, in the style of Plotkin, further constrained to be uniform<br />with respect to a class of logical relations.  ...  The second author thanks Bell Laboratories for offering a very stimulating and pleasant environment during his visit in the summer of 1996. We also thank Thomas Hildebrandt,  ...  We follow the O'Hearn-Riecke construction for PCF [22] and lift the relations to Kripke relations, using a definition found in [13] .  ... 
doi:10.7146/brics.v4i41.18967 fatcat:7taft7bitzgo5awvrpyhanyf2q

A Relational Account of Call-by-Value Sequentiality

Jon G. Riecke, Anders Sandholm
2002 Information and Computation  
The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations.  ...  The second author thanks Bell Laboratories for offering a very stimulating and pleasant environment during his visit in the summer of 1996. We also thank Thomas Hildebrandt,  ...  We follow the O'Hearn-Riecke construction for PCF [22] and lift the relations to Kripke relations, using a definition found in [13] .  ... 
doi:10.1006/inco.2002.2957 fatcat:qbjj523frbe2th5xmsxgg35daa

A Relational Account of Call-by-Value Sequentiality

Jon G. Riecke, Anders B. Sandholm
1999 BRICS Report Series  
The model is built from partial continuous functions,<br />in the style of Plotkin, further constrained to be uniform with respect to<br />a class of logical relations.  ...  The second author thanks Bell Laboratories for offering a very stimulating and pleasant environment during his visit in the summer of 1996. We also thank Thomas Hildebrandt,  ...  We follow the O'Hearn-Riecke construction for PCF [22] and lift the relations to Kripke relations, using a definition found in [13] .  ... 
doi:10.7146/brics.v6i10.20067 fatcat:6jgkkzp565dbtaudgfck3cwjma

A fully abstract model for sequential computation

M MARZ
2000 Electronical Notes in Theoretical Computer Science  
Besides, I thank Dieter Spreen for organising the nice workshop in Remagen-Rolandseck and for giving me the opportunity to present my work.  ...  A family R = (R w ) w∈Obj(C) of w-logical relations on a domain A is called C-Kripke logical relation on A if it is C-Kripke monotone: f ∈ R w , µ : v C → w ⇒ f • µ ∈ R v .  ...  If C is a subcategory of SPIC and A a domain, then the set R of all C-Kripke logical relations on A forms a closure system.  ... 
doi:10.1016/s1571-0661(05)01206-5 fatcat:tu7njgwzzbgixp6kilhq5grpbq

A rough logic based on incomplete information and its application

Akira Nakamura
1996 International Journal of Approximate Reasoning  
Also, del Cerro and Orlowska [2] proposed a deductive system for indiscernibility logic. These logics are strongly related to modal logic. Starting from these  ...  In [7] and [8], Orlowska and Pawlak discussed theoretical foundations of knowledge representation from the point of view of logic.  ...  K'>_K K'>K Thus, we have (8). • It is well-known that modal logics are characterized in terms of Kripke model (W, R, V).  ... 
doi:10.1016/s0888-613x(96)00075-8 fatcat:nzxy4bvqmfaihbrf2pz6rjzxge

Page 6841 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
To be useful in practice, proof-theoretic criteria for observational implementations are provided and a proof technique (called ‘con- text induction’) for the verification of implementation relations is  ...  A theory of programming is presented in which the description of a computation is divided into two parts: logic and timing.  ... 

Denotational Completeness Revisited

Thomas STREICHER
1999 Electronical Notes in Theoretical Computer Science  
We de ne a notion of Kripke logical predicate for models of classical linear logic.  ...  A Kripke logical predicate on a type A will be a set of generalised elements of A satisfying certain closure properties.  ...  In particular I am indebted Thomas Ehrhard who patiently explained to me his work on non{Kripke logical relations on the coherence space model of Linear Logic.  ... 
doi:10.1016/s1571-0661(05)80321-4 fatcat:q4ev44cuhncj7fulsa64loe4nm

Page 4643 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
The resulting Kripke-style frame for orthomodular logic consists of a semigroup with operations instead of relations on the underlying set.  ...  In the paper under review, the author extends these results to the logic obtained by adding negation and the logical constants 0 and | (ie. L and T).  ... 

Lambda Definability with Sums via Grothendieck Logical Relations [chapter]

Marcelo Fiore, Alex Simpson
1999 Lecture Notes in Computer Science  
We introduce a notion of Grothendieck logical relation and use it to characterise the de nability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with  ...  nite products and nite sums.  ...  Kripke logical relations of varying arity had already been used to obtain full abstraction for PCF by O'Hearn and Riecke 8] .  ... 
doi:10.1007/3-540-48959-2_12 fatcat:es7yckuxgfdq7hsat5bieihnsm

History and Developments

Jaap van Oosten
1999 Electronical Notes in Theoretical Computer Science  
of Kripke models).  ...  Of course, it came to be used in the late seventies to interpret versions of Martin-L of's type theory (e.g., 4]), and analogous versions for systems based on PCF have been studied by John Longley.  ... 
doi:10.1016/s1571-0661(04)00106-9 fatcat:j2wdurx6nzaotixrh3r2k76t5a

Page 4083 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
We illustrate this approach through examples involving the sim- ple functional and imperative programming languages PCF and PCF...  ...  Summary: “A multi-valued version of CTL* (mv-CTL”*), where both the propositions and the accessibility relation are multi- valued, taking values in a finite quasi-Boolean algebra, is defined.  ... 

Fully abstract models for effectful λ-calculi via category-theoretic logical relations

Ohad Kammar, Shin-ya Katsumata, Philip Saville
2022 Proceedings of the ACM on Programming Languages (PACMPL)  
The construction, which uses the theory of fibrations, categorical glueing, ⊤⊤-lifting, and ⊤⊤-closure, takes inspiration from O'Hearn & Riecke's fully abstract model for PCF.  ...  We present a construction which, under suitable assumptions, takes a model of Moggi's computational λ-calculus with sum types, effect operations and primitives, and yields a model that is adequate and  ...  Kripke relations form a category Krip M,𝐹 with objects (𝑋, 𝑅) where 𝑋 ∈ M and 𝑅 is a Kripke relation on 𝑋 .  ... 
doi:10.1145/3498705 fatcat:yr2xfwr4lvf45f2lowgd4byxoi
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