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The Theory of Calculi with Explicit Substitutions Revisited [chapter]

Delia Kesner
Lecture Notes in Computer Science  
Calculi with explicit substitutions (ES) are widely used in different areas of computer science.  ...  Then we use very simple technology to establish a general theory of explicit substitutions for the lambda-calculus which enjoys fundamental properties such as simulation of one-step beta-reduction, confluence  ...  Acknowledgements This work has benefited from fruitful discussions with E. Bonelli, R. David, R. Di Cosmo, J-P. Jouannaud, S. Lengrand, C. Muñoz and V. van Oostrom.  ... 
doi:10.1007/978-3-540-74915-8_20 fatcat:6llmiplxbngw7iairsjxtrd4di

Call-by-Value Solvability, Revisited [chapter]

Beniamino Accattoli, Luca Paolini
2012 Lecture Notes in Computer Science  
In this new setting, we characterise solvable terms as those terms having normal form with respect to a suitable restriction of the rewriting relation.  ...  We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λCBV calculus and from Accattoli and Kesner's substitution calculus λsub  ...  The first author wants to thank Simona Ronchi Della Rocca for inviting him in Turin in march 2011, where this work began.  ... 
doi:10.1007/978-3-642-29822-6_4 fatcat:cflzc2bdovhkthaoeofgfkrbte

Free Variables and Theories: Revisiting Rigid E-unification [chapter]

Peter Backeman, Philipp Rümmer
2015 Lecture Notes in Computer Science  
The efficient integration of theory reasoning in first-order calculi with free variables (such as sequent calculi or tableaux) is a longstanding challenge.  ...  For the case of the theory of equality, an approach that has been extensively studied in the 90s is rigid E -unification, a variant of equational unification in which the assumption is made that every  ...  the theories T considered in Sect. 4, the encoding from Def. 12 can in principle be used to implement sound calculi for first-order logic modulo T with bounded free-variable reasoning.  ... 
doi:10.1007/978-3-319-24246-0_1 fatcat:nmobguv5djhjdlka2sxdjkwaia

Psi-Calculi Revisited: Connectivity and Compositionality [article]

Johannes Åman Pohjola
2020 arXiv   pre-print
Psi-calculi is a parametric framework for process calculi similar to popular pi-calculus extensions such as the explicit fusion calculus, the applied pi-calculus and the spi calculus.  ...  We show how a pi-calculus with preorders that was previously beyond the scope of psi-calculi can be captured, and how to encode mixed choice under very strong quality criteria.  ...  Acknowledgements These ideas have benefited from discussions with many people at Uppsala University, ITU Copenhagen, the University of Oslo and Data61/CSIRO, including Jesper Bengtson, Christian Johansen  ... 
arXiv:1909.06692v4 fatcat:u7oycfxxdjflnc6y4btqn67rd4

Distilling Abstract Machines (Long Version) [article]

Beniamino Accattoli, Pablo Barenbaum, Damiano Mazza
2014 arXiv   pre-print
It is well-known that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES).  ...  Recently, graphical syntaxes and linear logic led to the linear substitution calculus (LSC), a new approach to ES that is halfway between big-step calculi and traditional calculi with ES.  ...  The LSC has a simple meta-theory, and is halfway between traditional calculi with ES-with whom it shares the small-step dynamics-and l-calculus-of which it retains most of the simplicity.  ... 
arXiv:1406.2370v1 fatcat:cpxnmmrqwzaqxa5afy4tllmy3y

Page 4447 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
The restoration of the original contents of the theory is done by appeal to default logic. The overall approach provides us with a family of paraconsistent consequence relations.  ...  mu-calculi.  ... 

Distilling abstract machines

Beniamino Accattoli, Pablo Barenbaum, Damiano Mazza
2014 Proceedings of the 19th ACM SIGPLAN international conference on Functional programming - ICFP '14  
It is well-known that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES).  ...  Recently, graphical syntaxes and linear logic led to the linear substitution calculus (LSC), a new approach to ES that is halfway between big-step calculi and traditional calculi with ES.  ...  In particular, we owe him the intuition that a global analysis of callby-need commutative rules may provide a linear bound.  ... 
doi:10.1145/2628136.2628154 dblp:conf/icfp/AccattoliBM14 fatcat:zkvknxma4jcvnk3w7ipgbv5eh4

Page 5241 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Rose, Combinatory reduction systems with explicit substitu- tion that preserve strong normalisation (169-183); Delia Kesner, Confluence properties of extensional and non-extensional /-calculi with explicit  ...  substitutions (extended abstract) (184-199); Roberto Di Cosmo, On the power of simple diagrams (200-214); S.  ... 

Relating Coalgebraic Notions of Bisimulation [chapter]

Sam Staton
2009 Lecture Notes in Computer Science  
Bisimulation is a crucial notion in the theory of labelled transition systems. We identify four definitions of bisimulation on general coalgebras.  ...  As an extended example, we consider the semantics of name-passing process calculi (such as the pi-calculus), and present a new coalgebraic model for name-passing calculi.  ...  In this paper we revisit work [15, 17, 21, 42] on models of name-passing calculi, such as the π-calculus, where it is appropriate to work in a sheaf topos.  ... 
doi:10.1007/978-3-642-03741-2_14 fatcat:r4rnhkh4mrd33fkw7asspdkdd4

Psi-Calculi Revisited: Connectivity and Compositionality

Johannes Åman Pohjola
2019 Logical Methods in Computer Science  
Psi-calculi is a parametric framework for process calculi similar to popular pi-calculus extensions such as the explicit fusion calculus, the applied pi-calculus and the spi calculus.  ...  We show how a pi-calculus with preorders that was previously beyond the scope of psi-calculi can be captured, and how to encode mixed choice under very strong quality criteria.  ...  Acknowledgements These ideas have benefited from discussions with many people at Uppsala University, ITU Copenhagen, the University of Oslo and Data61/CSIRO, including Jesper Bengtson, Christian Johansen  ... 
doi:10.23638/lmcs-16(4:16)2020 fatcat:qbst7xrttbgbtd52cyqsz344ae

Page 5552 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
It turns out that the system created ranges from the logic with restricted quantifiers of H. J. Biirckert via Re- iter’s default logic to the logic of theory change of P. Gardenfors.”  ...  Summary: “Our principal concern in this paper is to further pave the way towards a semantical version of Milner’s fully abstract model of typed A-calculi.  ... 

Non-idempotent intersection types and strong normalisation

Alexis Bernadet, Stéphane Lengrand, Marc Bezem
2013 Logical Methods in Computer Science  
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure λ-calculus, the calculus with explicit substitutions λS, and the calculus  ...  with explicit substitutions, contractions and weakenings λlxr.  ...  to explicit substitution calculi along the lines of [KL05, KL07, Kes07, Ren11] .  ... 
doi:10.2168/lmcs-9(4:3)2013 fatcat:7ntg4o45znc2llujfoqy6v555u

Contextual Modal Types for Algebraic Effects and Handlers [article]

Nikita Zyuzin, Aleksandar Nanevski
2021 arXiv   pre-print
., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types.  ...  In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types.  ...  Any opinions, findings, and conclusions or recommendations expressed in the material are those of the authors and do not necessarily reflect the views of the funding agencies.  ... 
arXiv:2103.02976v2 fatcat:sffmeshlanhojnn7w6rh4ahn7m

Rewriting logic bibliography by topic: 1990–2011

Narciso Martí-Oliet, Miguel Palomino, Alberto Verdejo
2012 The Journal of Logic and Algebraic Programming  
This bibliography compiles, to the best of our knowledge, all the papers on rewriting logic and its applications which have been written during the more than 20 years that have passed since the introduction  ...  of rewriting logic in 1990.  ...  , inference systems, sequent calculi, explicit substitutions, pure type systems, the open calculus of constructions, and others.  ... 
doi:10.1016/j.jlap.2012.06.001 fatcat:qoyfwnihjfe4bj5drqtk5mlk6a

A Normalisation Result for Higher-Order Calculi with Explicit Substitutions [chapter]

Eduardo Bonelli
2003 Lecture Notes in Computer Science  
Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper P.-A.  ...  This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems  ...  To Delia Kesner, Alejandro Ríos and the referees for providing valuable suggestions.  ... 
doi:10.1007/3-540-36576-1_10 fatcat:qnl5eaowpnchregfagwmvkkvdu
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