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Imperative Programs as Proofs via Game Semantics

Martin Churchill, James Laird, Guy McCusker
2011 2011 IEEE 26th Annual Symposium on Logic in Computer Science  
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies.  ...  We can embed intuitionistic firstorder linear logic into this system, as well as an imperative total programming language.  ...  Thus total imperative programs correspond, via the game semantics, to proofs in WS1.  ... 
doi:10.1109/lics.2011.19 dblp:conf/lics/ChurchillLM11 fatcat:redxq676rjfwnlmqn2glx5zj5a

Imperative programs as proofs via game semantics

Martin Churchill, Jim Laird, Guy McCusker
2013 Annals of Pure and Applied Logic  
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies.  ...  The proof system has a tight connection with a simple game model, where games are forests of plays. Formulas are modelled as games, and proofs as history-sensitive winning strategies.  ...  Thus total imperative programs correspond, via the game semantics, to proofs in WS1.  ... 
doi:10.1016/j.apal.2013.05.005 fatcat:iu2drwfiqrdznnt7cundjrxiy4

A Logic of Sequentiality [chapter]

Martin Churchill, James Laird
2010 Lecture Notes in Computer Science  
Game semantics has been used to interpret both proofs and functional programs: an important further development on the programming side has been to model higher-order programs with state by allowing strategies  ...  We describe the semantics of our logic formally by giving a notion of categorical model and an instance based on a simple category of games.  ...  Imperative Objects as Strategies Semantics of a full object-oriented language can be given by interpreting types as games and programs as strategies [22] .  ... 
doi:10.1007/978-3-642-15205-4_19 fatcat:6q55s6nrtvdorjei5tfb6fyqgm

Program Equivalence (Dagstuhl Seminar 18151)

Shuvendu K. Lahiri, Andrzej Murawski, Ofer Strichman, Mattias Ulbrich, Michael Wagner
2018 Dagstuhl Reports  
The field draws researchers from formal verification, semantics and logics. This report documents the program and the outcomes of Dagstuhl Seminar 18151 "Program Equivalence".  ...  Program equivalence is the problem of proving that two programs are equal under some definition of equivalence, e.g., input-output equivalence.  ...  We build an equivalence checker E(P, Q, L, R) that takes as input not only two programs P and Q that we want to prove equivalent, but also the operational semantics L and R of the programming languages  ... 
doi:10.4230/dagrep.8.4.1 dblp:journals/dagstuhl-reports/LahiriMSU18 fatcat:6okakmyai5auths2irdwghogzm

Game Theory Meets Theoretical Computer Science

Samson Abramsky, Marios Mavronicolas
2005 Theoretical Computer Science  
This is posed as a (yet unproven) conjecture. 8. The paper "The First Order Definability of Graphs with Separators via the Ehrenfeucht Game'', by O.  ...  Laurent, studies a notion of sliced proof nets for the polarized fragment of Linear Logic, and a corresponding game semantics.  ... 
doi:10.1016/j.tcs.2005.05.004 fatcat:g75bqy7ipzewlnpw55wtgwyr5m

Constructive Game Logic [chapter]

Brandon Bohrer, André Platzer
2020 Lecture Notes in Computer Science  
Game Logic is an excellent setting to study proofs-aboutprograms via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to  ...  of strategies via proof-terms, and 3. theoretical results including soundness of the proof calculus w.r.t. realizability semantics, progress and preservation of the operational semantics of proofs, and  ...  We gave two understandings of proofs in CGL, as imperative strategies and as functional programs.  ... 
doi:10.1007/978-3-030-44914-8_4 fatcat:by5xt6i2g5gi7ds2kebai5otgu

A Calculus of Coroutines [chapter]

J. Laird
2004 Lecture Notes in Computer Science  
Game semantics is a way of characterizing programming languages and logical calculi intensionally by interpreting proofs or programs as strategies for interacting with the environment; this process of  ...  However, a significant obstacle to the use of domains to reason about programming languages has been a lack of accurate models of imperative and concurrent features of the sort provided by game semantics  ...  Background and context Game semantics is a way of characterizing programming languages and logical calculi intensionally by interpreting proofs or programs as strategies for interacting with the environment  ... 
doi:10.1007/978-3-540-27836-8_74 fatcat:hrcyftg22bcc3mw52qs3vbyr5y

Modeling Imperative Constructs in the Pi-Calculus

Daniel Hirschkoff, Enguerrand Prebet, Davide Sangiorgi
2019 Italian Conference on Theoretical Computer Science  
There also exists a rich literature on game semantics to represent and analyse program execution [7, 1] .  ...  The operational approach, as put forward using the π-calculus, can serve as a complement to the "operational/denotational" point of view promoted by game semantics to reason about high-level languages.  ...  Thus, reasoning via the encoding into π can be seen as a proof technique to establish equivalences between π ref programs.  ... 
dblp:conf/ictcs/HirschkoffPS19 fatcat:ymtkz4lv2jgwfbh6bphz27h2i4

Contents and abstracts of the electronic notes in theoretical computer science vol. 3

1998 Theoretical Computer Science  
This material and the volumes in the series will be available via Elsevier Science's World Wide Web server, which can be accessed at the URL Linearity, Sharing and State: a fully abstract game semantics  ...  We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state.  ...  Perhaps the simplest example of such objects are the program variables of classical imperative languages.  ... 
doi:10.1016/s0304-3975(97)00246-6 fatcat:2skydvbtyvdq3mmxtqwo2hncgi

Game Semantics for Type Soundness

Tim Disney, Cormac Flanagan
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
The key idea of game semantics is that a term can interact with its enclosing context via various events, such as function calls and returns. A trace is a sequence of such interaction events.  ...  This paper uses game semantics to define the meaning of and verify type soundness for a sequence of programming languages, starting with a functional sequential language (the call-by-value simply-typed  ...  Game semantics has also been used as a foundation for language design [27] , [28] . Compositional game semantics also facilitate compositional verification [29] .  ... 
doi:10.1109/lics.2015.20 dblp:conf/lics/DisneyF15 fatcat:ylufv7x6zbgyfjktqvnm4eyobm

Page 1665 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
ISBN 0-387-96957-8 As stated clearly in the introduction, this book has two main con- cerns. One is programming language semantics via the well-known method of predicate transformers.  ...  For the proof we use a modifi- cation of the Ehrenfeucht-Fraissé games, capturing the expressive power of the extended star-free expressions.”  ... 

Alternation as a programming paradigm

Wolfgang Dvořák, Georg Gottlob, Reinhard Pichler, Stefan Woltran
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
In this work, we show how the expressive power of an imperative programming language can be augmented by integrating alternation into it.  ...  Also many problems with a procedural description of the solutions have a very compact declarative description via alternation, among them the evaluation of logic programs.  ...  In case of games, the solution is a winning strategy, in case of Horn logic programming, the solution is a proof tree, etc.  ... 
doi:10.1145/1599410.1599419 dblp:conf/ppdp/DvorakGPW09 fatcat:zmr2zfgvuncytbbydiefpmfzri

Report on BCTCS 2013

Guy McCusker
2014 Bulletin of the European Association for Theoretical Computer Science  
programs in imperative languages.  ...  of imperative program extraction.  ... 
dblp:journals/eatcs/McCusker14 fatcat:6mbueqohg5fxjk2advza4yktr4

Games In The Semantics Of Programming Languages – An Elementary Introduction

Jan Jürjens
2002 Synthese  
This paper gives an introduction to these game-semantical models of programming languages, concentrating on motivating the basic intuitions and putting them into context. Synthese 133: 131-158, 2002.  ...  Mathematical models are an important tool in the development of software technology, including programming languages and algorithms.  ...  2 A 1 A Game Semantics To lead over from Lorenzen Games to games in the semantics of programming languages we can make use of the Curry-Howard-Isomorphism.  ... 
doi:10.1023/a:1020883810034 fatcat:kg3pun6lfnflthteywf7yznpge

Reachability Games and Game Semantics: Comparing Nondeterministic Programs

Andrzej S. Murawski
2008 Logic in Computer Science  
We see our work as a starting point of research that relates game semantics with other game-based theories.  ...  pushdown graphs as well as product constructions.  ...  Introduction Game semantics [3, 20] has emerged as a versatile methodology for giving semantics to programming languages.  ... 
doi:10.1109/lics.2008.24 dblp:conf/lics/Murawski08 fatcat:yyq7wzoqmvemdns2sw3vggm4yy
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