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SUBSEXPL: a tool for simulating and comparing explicit substitutions calculi ★

F. L. C. de Moura, M. Ayala-Rincón, F. Kamareddine
2006 Journal of Applied Non-Classical Logics  
Acknowledgements We would like to thank Manuel Maarek and Stéphane Gimenez for the useful help with Ocaml and suggestions to improve the system.  ...  Comparing calculi by the simulation of β-reduction SUBSEXPL has been implemented with the intention of comparing different styles of explicit substitutions with respect to the effort necessary to simulate  ...  We present the system SUBSEXPL used for simulating and comparing explicit substitutions calculi.  ... 
doi:10.3166/jancl.16.119-150 fatcat:uv32uouixrcjzaggh4nod2e5tq

A Flexible Framework for Visualisation of Computational Properties of General Explicit Substitutions Calculi

F.L.C. de Moura, A.V. Barbosa, M. Ayala-Rincón, F. Kamareddine
2011 Electronical Notes in Theoretical Computer Science  
properties of these calculi and to compare the different styles of making explicit the substitution operation in implementations of the λ-calculus in de Bruijn notation.  ...  In addition to dealing the λ-calculus and explicit substitutions calculi in de Bruijn notation, now it is possible to work with the λ-calculus and with several calculi of explicit substitutions using also  ...  Conclusions and Future Work We presented an extension of the SUBSEXPL system which is an OCaml implementation for comparing, simulating and studying λ-calculus and explicit substitutions calculi [24]  ... 
doi:10.1016/j.entcs.2011.03.004 fatcat:iwspr275tvcc7c5bwuyihz5mva

Explicit substitutions calculi with one step Eta-reduction decided explicitly

D. Ventura, M. Ayala-Rincon, F. Kamareddine
2009 Logic Journal of the IGPL  
In this paper constructive Eta rules are proposed for both the λσ-and the λse-calculi of explicit substitutions.  ...  In particular, we show that the explicit definitions of the eta rules coincide with the Eta rule for pure λ-terms and that moreover, their application is decidable in the sense that Eta redices are effectively  ...  Introduction Well-behaved calculi of explicit substitutions are a useful bridge between the formal study of the λ-calculus and its real implementations.  ... 
doi:10.1093/jigpal/jzp027 fatcat:3wsbhxuoqjen7f3msj455ljx2q

Decomposing typed lambda calculus into a couple of categorical programming languages [chapter]

Masahito Hasegawa
1995 Lecture Notes in Computer Science  
We give two categorical programming languages with variable arrows and associated abstraction/reduction mechanisms, which extend the possibility of categorical programming Hag87, CF92] in practice.  ...  This decomposition is a consequence of a semantic analysis on typed lambda calculus due to C. Hermida and B. Jacobs HJ94].  ...  The greater part of this work was done when I was a postgraduate of Kyoto University and Keio University; I am very grateful to supervisors, advisors and colleagues at both universities, especially to  ... 
doi:10.1007/3-540-60164-3_28 fatcat:4ylb4nrc3fcmlkshkqdqedoi4q

Parameterized Cast Calculi and Reusable Meta-theory for Gradually Typed Lambda Calculi [article]

Jeremy G. Siek
2021 arXiv   pre-print
space-efficient implementations.  ...  This article identifies abstractions that capture similarities between many cast calculi in the form of two parameterized cast calculi, one for the purposes of language specification and the other to guide  ...  Like most cast calculi, CC ( ) extends the Simply-Typed Lambda Calculus with the unknown type ? and explicit run-time casts.  ... 
arXiv:2001.11560v2 fatcat:fvykkpvefze5jjsya3wgpqx6aq

More Church-Rosser proofs (in Isabelle/HOL) [chapter]

Tobias Nipkow
1996 Lecture Notes in Computer Science  
For -reduction, both the standard proof and the variation by Takahashi are given and compared.  ...  The proofs of the Church-Rosser theorems for , and reduction in untyped -calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle.  ...  Thanks are due to James McKinna for detailed discussions, to Randy Pollack for his short cut in the abstract con uence proofs 11], and to Konrad Slind for his excellent suggestions for improvements.  ... 
doi:10.1007/3-540-61511-3_125 fatcat:k6rjkyixgzhpvosc5dpqd742li

Higher-Order Rewriting: Framework, Confluence and Termination [chapter]

Jean-Pierre Jouannaud
2005 Lecture Notes in Computer Science  
Mitsuhiro Okada with who I started getting into that subject, and my students Maribel Fernandez, Frederic Blanqui and Daria Walukiewicz who investigated some of these questions within the framework of  ...  Acknowledgments: This paper would not exist without the pionneering work of Klop on higher-order rewriting and the work I have done myself with my coauthors Femke van Raamsdonk and Albert Rubio, my colleague  ...  Typed lambda-calculi are confluent modulo alpha-conversion, and terminating with respect to beta-reductions and either eta-expansion or etareduction, therefore defining normal forms up to the equivalence  ... 
doi:10.1007/11601548_14 fatcat:iwdbwyqmbre2bkbza545hxkjfu

Parameterized cast calculi and reusable meta-theory for gradually typed lambda calculi

2021 Journal of functional programming  
space-efficient implementations.  ...  This article identifies abstractions that capture similarities between many cast calculi in the form of two parameterized cast calculi, one for the purposes of language specification and the other to guide  ...  Like most cast calculi, CC(⇒) extends the Simply Typed Lambda Calculus with the unknown type ? and explicit runtime casts.  ... 
doi:10.1017/s0956796821000241 fatcat:4hgasphgungy7nkkg6tkcnkwuy

Eta-Equivalence in Core Dependent Haskell

Anastasiya Kravchuk-Kirilyuk, Antoine Voizard, Stephanie Weirich, Marc Bezem, Assia Mahboubi
2020 Types for Proofs and Programs  
We extend the core semantics for Dependent Haskell with rules for η-equivalence. This semantics is defined by two related calculi, Systems D and DC.  ...  The second, inspired by the Glasgow Haskell Compiler's core language FC, is the explicitly-typed analogue of System D, suitable for implementation in GHC.  ...  One difficulty with η-reduction in this setting is the problem with confluence for Churchstyle calculi.  ... 
doi:10.4230/lipics.types.2019.7 dblp:conf/types/Kravchuk-Kirilyuk19 fatcat:kjlierzyn5at3ls35xsdzomumm

Explicit Substitutions for Contextual Type Theory

Andreas Abel, Brigitte Pientka
2010 Electronic Proceedings in Theoretical Computer Science  
We first present a dependently typed lambda calculus with explicit substitutions for ordinary variables and explicit meta-substitutions for meta-variables.  ...  We then present a weak head normalization procedure which performs both substitutions lazily and in a single pass thereby combining substitution walks for the two different classes of variables.  ...  To handle eta-equality, we eta-expand the neutral weak head normal form H on the fly when comparing it to a lambda-closure.  ... 
doi:10.4204/eptcs.34.3 fatcat:eyubw2ehtrgsdoqttphyu3qrf4

Observational program calculi and the correctness of translations

Manfred Schmidt-Schauß, David Sabel, Joachim Niehren, Jan Schwinghammer
2015 Theoretical Computer Science  
reduction sequences of the different calculi.  ...  substitutions, which allow to close any program and are a subset of the contexts with specific properties.  ... 
doi:10.1016/j.tcs.2015.02.027 fatcat:3pl4smjufnbploj5gzv7jaj5ma

A Core Model for Choreographic Programming [chapter]

Luís Cruz-Filipe, Fabrizio Montesi
2017 Lecture Notes in Computer Science  
We discuss the design of CC and argue that it constitutes a canonical model for choreographic programming.  ...  Despite strong interest on choreographies, a foundational model that explains which computations can be performed with the hallmark constructs of choreographies is still missing.  ...  Montesi was supported by CRC (Choreographies for Reliable and efficient Communication software), grant no. DFF-4005-00304 from the Danish Council for Independent Research.  ... 
doi:10.1007/978-3-319-57666-4_3 fatcat:evaksyhgijhelhmrdp65r6gjnq

On asynchrony in name-passing calculi

2004 Mathematical Structures in Computer Science  
We prove two coinductive characterisations of barbed congruence in L , and some basic algebraic laws.  ...  The asynchronous -calculus is considered the basis of experimental programming languages (or proposal of programming languages) like Pict, Join, and Blue calculus.  ...  We thank G rard Boudol, Ilaria Castellani, Silvano Dal-Zilio, Matthew Hennessy, Uwe Nestmann, Benjamin Pierce and Nobuko Yoshida for stimulating and insightful discussions.  ... 
doi:10.1017/s0960129504004323 fatcat:w7u6xktqrjh65hzwtivpjhld4m

Explicit substitution calculi with de Bruijn indices and intersection type systems

D. L. Ventura, F. Kamareddine, M. Ayala-Rincon
2014 Logic Journal of the IGPL  
Explicit substitutions calculi with de Bruijn indices and intersection type systems Cλξφ, based on λ dB .  ...  Furthermore, for implementation purposes, many explicit substitution systems are written with de Bruijn indices.  ...  However, both calculi are defined with named variables while in the present work calculi with de Bruijn indices and explicit substitutions with compositions not satisfying PSN are investigated.  ... 
doi:10.1093/jigpal/jzu044 fatcat:lkqsgglyxrflfadytkvlrsupuq

Higher-Order Unification: A structural relation between Huet's method and the one based on explicit substitutions

Flávio L.C. de Moura, Mauricio Ayala-Rincón, Fairouz Kamareddine
2008 Journal of Applied Logic  
We compare two different styles of Higher-Order Unification (HOU): the classical HOU algorithm of Huet for the simply typed λ-calculus and HOU based on the λσ-calculus of explicit substitutions.  ...  For doing so, first, the original Huet algorithm for the simply typed λ-calculus with names is adapted to the language of the λcalculus in de Bruijn's notation, since this is the notation used by the λσ-calculus  ...  Acknowledgements We would like to thank the careful reading, constructive corrections and detailed suggestions of one of the referees.  ... 
doi:10.1016/j.jal.2006.10.001 fatcat:3ym4njp7wnfkbd4dm4virhbh5m
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