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Stable relations and abstract interpretation of higher-order programs

Benoît Montagu, Thomas Jensen
2020 Proceedings of the ACM on Programming Languages (PACMPL)  
Following the principles of abstract interpretation, we use our denotational semantics as a collecting semantics to derive a modular relational analysis for higher-order programs.  ...  The denotation captures the input-output behaviour of higher-order programs, and is proved sound and complete with respect to the operational semantics.  ...  The analyser infers equalities between the inputs and the outputs of higher-order programs.  ... 
doi:10.1145/3409001 fatcat:ndtv5z56p5fqzmqc6ff7gneina

Page 3618 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
It is demonstrated that higher-order lambda calculus-based languages can be compositionally embedded in logic programming languages, preserving their semantics and abstraction facilities.  ...  deduction techniques, and the promotion strategy, can be viewed as particular instances of our abstract strategy.” 95f:68042 68N17 03B15 03B40 Reddy, Uday S. (1-IL-C; Urbana, IL) Higher-order aspects  ... 

Impredicative Concurrent Abstract Predicates [chapter]

Kasper Svendsen, Lars Birkedal
2014 Lecture Notes in Computer Science  
We present impredicative concurrent abstract predicates -iCAP -a program logic for modular reasoning about concurrent, higherorder, reentrant, imperative code.  ...  We demonstrate the utility of impredicative protocols through a series of examples, including the specification and verification, in the logic, of a spin-lock, a reentrant event loop, and a concurrent  ...  [5] presented a logical relations model for verifying effect-based program transformations for a higher-order concurrent imperative language, and Turon et. al.  ... 
doi:10.1007/978-3-642-54833-8_9 fatcat:dypg5jxw6nek5girya4ylhqkte

Page 6500 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
Two such languages, lambda Prolog and its linear logic refinement, Lolli, provide for various forms of abstraction (mod- ules, abstract data types, and higher-order programming) but lack primitives for  ...  A logic programming presentation of all of higher-order linear logic, named Forum, modularly extends these other languages and also allows for abstractions and con- currency in specifications.  ... 

Book reports

1992 Computers and Mathematics with Applications  
Temporal debugging and its visual animation. 2. Abstract view of prolog executions in opium. LI. Non-horu programs. 3. A complete top-down interpreter for first order programs. 4.  ...  F.xtending the Warren abstract machine to polymorphic order-sorted resolution. IX. Non-classical logic, II. 18. Higher-order horn logic programming. 19.  ... 
doi:10.1016/0898-1221(92)90096-z fatcat:4pjyhq2h5zcxzcjs7pzcgpop54

Semantics of templates in a compositional framework for building logics

INGMAR DASSEVILLE, MATTHIAS VAN DER HALLEN, GERDA JANSSENS, MARC DENECKER
2015 Theory and Practice of Logic Programming  
AbstractThere is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros).  ...  We use the framework to build a logic of nested second order definitions suitable to express templates.  ...  Related Work Abstraction techniques have been an important area of research since the dawn of programming (Shaw 1984) .  ... 
doi:10.1017/s1471068415000319 fatcat:zkn2bmdvxrgdtaf2wsv3ps5gui

Page 2188 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
This is an excellent paper on the structure of abstract domains in abstract interpretation. The paper proposes a theoretical study of the operation of powerset in abstract interpretation.  ...  parameterized constants called con- trols, are equivalent to the closed fragments of action calculi and their higher-order/reflexive extensions.  ... 

Page 7800 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
This information may be used in abstract interpretation as a ba- sis for proving the soundness of program analyses.  ...  The approach extends previous results on minimal function graphs to higher-order functions. The semantics captures the in- termediate calls performed during the evaluation of a program.  ... 

Book review

1999 Science of Computer Programming  
Going to higher-order typed -calculi, dependent types in the Edinburgh Logical Framework (LF) and second-order types in Girard's system F are studied in Chapter 11 from the syntactical and semantical points  ...  This also contains a discussion of the problem of full abstraction, together with a ÿrst approach to sequentiality and the description of the fully abstract model for PCF in terms of B ohm trees its relation  ... 
doi:10.1016/s0167-6423(99)00032-5 fatcat:lkbeujvaxbbxjb2pg2cqlbvksq

Page 1028 of Mathematical Reviews Vol. , Issue 93b [page]

1993 Mathematical Reviews  
The A Prolog logic programming language and the related Elf and Isabelle systems provide meta-programs with both function vari- ables and A-abstractions by containing implementations of higher- order unification  ...  As a result of these restrictions, an implementation of L, does not need to implement full higher-order unification.  ... 

Stable Bistructure Models of PCF

Glynn Winskel
1994 BRICS Report Series  
Stable bistructures are a generalisation of event structures to represent spaces of functions at higher types; the partial order of causal dependency is replaced by two orders, one associated with input  ...  However, although the bidomain model incorporates both the Berry stable order and the Scott pointwise order, its PCF theory (those inequalities on terms which hold in the bidomain model) does not include  ...  Event structures and related models can be used to represent d omains in the semantics of programming languages.  ... 
doi:10.7146/brics.v1i13.21656 fatcat:7fpnjkudije2jncdbvwn4s6cuq

Semantically linear programming languages

Luca Paolini, Mauro Piccolo
2008 Proceedings of the 10th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '08  
We give an interpretation of SℓPCF into a model of linear coherence spaces and we show that such semantics is fully abstract with respect to our language.  ...  Furthermore, we discuss the independence of new syntactical operators and we address the universality problem.  ...  Acknowledgments We wish to express our gratitude to Antonio Bucciarelli and Marco Gaboardi for some useful discussions about topics considered in this paper.  ... 
doi:10.1145/1389449.1389462 dblp:conf/ppdp/PaoliniP08 fatcat:xq7u66ai75gv3fneegxuhujcke

Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter [chapter]

Eric Goubault, Matthieu Martel, Sylvie Putot
2002 Lecture Notes in Computer Science  
representation of the abstract value related to the selected identifier in the list.  ...  Notice that the analyzer also finds that the higher-order errors are always negligible.  ... 
doi:10.1007/3-540-45927-8_15 fatcat:oxy6a6y5rfgbrhmuk5uto6bi5q

Page 7327 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
Namely, in the case of PCF (and of PCF extended with por and with 3) a (stan- dard) denotational interpretation 7 is logical fully abstract if and only if it is equational fully abstract and each element  ...  The correctness of the generic analysis is established as a relation be- tween the derivation trees of the original program and the slice.  ... 

Abstraction Refinement via Inductive Learning [chapter]

Alexey Loginov, Thomas Reps, Mooly Sagiv
2005 Lecture Notes in Computer Science  
This paper concerns how to automatically create abstractions for program analysis.  ...  An advantage of an approach based on inductive learning is that it does not require the use of a theorem prover.  ...  Abstract interpretation collects a set of 3-valued structures at each program point.  ... 
doi:10.1007/11513988_50 fatcat:e3ekksspufacpd34dgct4gubmi
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