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Preface: Theory and Applications of Abstraction, Substitution and Naming

Maribel Fernández, Christian Urban
2011 Journal of automated reasoning  
The first International Workshop on Theory and Applications of Abstraction, Substitution and Naming (TASSN) took place in Edinburgh in 2007, followed by a second workshop in York in 2009, associated to  ...  Formal treatments of abstract syntax have proved harder to develop, especially those addressing properties related to substituting structures for variables, binding of names and fresh name generation.  ...  A presheaf category is presented as a denotational semantics for the calculus of explicit fusions by Bonchi et al. in the article A presheaf environment for the explicit fusion calculus.  ... 
doi:10.1007/s10817-011-9217-2 fatcat:p7pu4z5be5grng44bmhnsueks4

π-calculus in (Co)inductive-type theory

Furio Honsell, Marino Miculan, Ivan Scagnetto
2001 Theoretical Computer Science  
This encoding gives rise to a full-edged proof editor=proof assistant for the -calculus, once we embed it in Coq, an interactive proof-development environment for CC (Co)Ind .  ...  We present a large and we think also signiÿcant case study in computer assisted formal reasoning.  ...  A preliminary version of this paper was presented at the IC-EATCS School Models and Paradigms for Concurrency, held in Udine (Italy), 15-19 September 1997.  ... 
doi:10.1016/s0304-3975(00)00095-5 fatcat:ye26btygmzhjpjcd5cquam44ne

Automating Derivations of Abstract Machines from Reduction Semantics: [chapter]

Filip Sieczkowski, Małgorzata Biernacka, Dariusz Biernacki
2011 Lecture Notes in Computer Science  
We present a generic formalization of the refocusing transformation for functional languages in the Coq proof assistant.  ...  The article is accompanied by a Coq development that contains the formalization of the refocusing method and a number of case studies that serve both as an illustration of the method and as a sanity check  ...  Furthermore, we require that in the C-calculus each closure is either a term with an explicit substitution (i.e., with a list of closures) or a value, and that a closure has only the empty decomposition  ... 
doi:10.1007/978-3-642-24276-2_5 fatcat:7vs2f2krbva4reubcx3ylbvtyu

Focusing and higher-order abstract syntax

Noam Zeilberger
2008 Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '08  
We describe how to translate the language and proof of type safety almost directly into Coq using HOAS, and finally, show how the system's modular design pays off in enabling a very simple extension with  ...  Dually, values are encoded as patterns together with explicit substitutions. This gives us pattern-matching "for free", and lets us reason about a rich type system with minimal syntactic overhead.  ...  Finally, I am grateful to the coq-club mailing list for useful advice on Coq, and particularly to Xavier Leroy for explaining a cool trick for coding mutual induction principles.  ... 
doi:10.1145/1328438.1328482 dblp:conf/popl/Zeilberger08 fatcat:k7z24zxcpnh4hfqt2m33iaj4c4

Focusing and higher-order abstract syntax

Noam Zeilberger
2008 SIGPLAN notices  
We describe how to translate the language and proof of type safety almost directly into Coq using HOAS, and finally, show how the system's modular design pays off in enabling a very simple extension with  ...  Dually, values are encoded as patterns together with explicit substitutions. This gives us pattern-matching "for free", and lets us reason about a rich type system with minimal syntactic overhead.  ...  Finally, I am grateful to the coq-club mailing list for useful advice on Coq, and particularly to Xavier Leroy for explaining a cool trick for coding mutual induction principles.  ... 
doi:10.1145/1328897.1328482 fatcat:xkiaq4eeezaqbb2zsd42vkgu2q

Autosubst: Reasoning with de Bruijn Terms and Parallel Substitutions [chapter]

Steven Schäfer, Tobias Tebbi, Gert Smolka
2015 Lecture Notes in Computer Science  
The approach is implemented in the Coq library Autosubst, which additionally derives substitution operations and proofs of substitution lemmas for custom term types.  ...  Reasoning about syntax with binders plays an essential role in the formalization of the metatheory of programming languages.  ...  The σ -calculus is a calculus of explicit substitutions. Explicit substitutions were intended to analyze reduction and its implementation in a more fine-grained way.  ... 
doi:10.1007/978-3-319-22102-1_24 fatcat:pfok5627gvhstnsmd2nddclina

A Natural Deduction style proof system for propositional μ-calculus and its formalization in inductive type theories [article]

Marino Miculan
1998 arXiv   pre-print
In this paper, we present a formalization of Kozen's propositional modal $\mu$-calculus, in the Calculus of Inductive Constructions.  ...  The encoding can be used in the \Coq system, providing an experimental computer-aided proof environment for the interactive development of error-free proofs in the $\mu$-calculus.  ...  Introduction In this paper, we present a formalization of Kozen's propositional modal µcalculus 10 , often referred to as µK, in the Coq proof assistant 4 .  ... 
arXiv:cs/9809120v1 fatcat:4xvfgdugeffwtjmelzlaijthn4

The Interpretation of Intuitionistic Type Theory in Locally Cartesian Closed Categories – an Intuitionistic Perspective

Alexandre Buisse, Peter Dybjer
2008 Electronical Notes in Theoretical Computer Science  
As an E-categorical substitute for the formal system of Martin-Löf type theory we use E-categories with families (E-cwfs).  ...  (The key part of this interpretation has been typechecked in the Coq system.) The second is a coherence problem which relates groupoid-style E-cwfs with proof-irrelevant ones.  ...  cwfs as a flat record resembles Curien's [5] explicit substitution calculus for dependent types with explicit witnesses of type equalities.  ... 
doi:10.1016/j.entcs.2008.10.003 fatcat:hk46vq3lx5ad7e3ccur2lcud3q

Ambient Calculus and its Logic in the Calculus of Inductive Constructions

Ivan Scagnetto, Marino Miculan
2002 Electronical Notes in Theoretical Computer Science  
The Ambient Calculus has been recently proposed as a model of mobility of agents in a dynamically changing hierarchy of domains.  ...  In this paper, we describe the implementation of the theory and metatheory of Ambient Calculus and its modal logic in the Calculus of Inductive Constructions.  ...  Names of the Ambient Calculus will be represented by variables of Coq of type name; hence, the first constant in our signature Σ A represents the sort of names.  ... 
doi:10.1016/s1571-0661(04)80507-3 fatcat:v4o2ke42yrdlpfr2qjugdtb2ay

Formally verified differential dynamic logic

Brandon Bohrer, Vincent Rahli, Ivana Vukotic, Marcus Völp, André Platzer
2017 Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs - CPP 2017  
Because axioms in a uniform substitution calculus are but individual concrete formulas, there is no need for side conditions: any subtleties have been made explicit in the statement of the axiom.  ...  in Isabelle [33, 34] and Coq [1, 9] , and 2. to obtain verified prover kernels for dL from these mechanizations of the uniform substitution calculus, first embedded in Isabelle and Coq, but in the  ... 
doi:10.1145/3018610.3018616 dblp:conf/cpp/BohrerRVVP17 fatcat:ihx7x24qmfaihiaumfbnmt7wgu

Higher-Order Abstract Syntax with Induction in Isabelle/HOL: Formalizing the π-Calculus and Mechanizing the Theory of Contexts [chapter]

Christine Röckl, Daniel Hirschkoff, Stefan Berghofer
2001 Lecture Notes in Computer Science  
Usually, a substitution is applied to describe that b replaces x in Q.  ...  The paper presents a formalization of the π-calculus in Isabelle/HOL, using well-formedness predicates which both eliminate exotic terms and yield structural induction.  ...  embedding). • Following the classical way, the syntax of the π-calculus is described in terms of a recursive datatype P ::= 0 |āb.P | ab.P | . . . , and substitution functions are introduced explicitely  ... 
doi:10.1007/3-540-45315-6_24 fatcat:q42oxe6uabd2deknr4oy3idkvy

DBGen User Manual [article]

Emmanuel Polonowski
2012 arXiv   pre-print
DBGen is a tool for Coq developers.  ...  It takes as input the definition of a term structure with bindings annotations and generates definitions and properties for lifting and substitution in the De Bruijn setting, up to the substitution lemma  ...  DBGen generate also a named version of the syntax (with strings constants for variable and explicit binding): a '_' is put as a prefix of every names in order to distinguish them from the De Bruijn structure  ... 
arXiv:1212.0253v1 fatcat:yfk7csj3sndbvajrs3a4esomgi

Heterogeneous substitution systems revisited [article]

Benedikt Ahrens, Ralph Matthes
2016 arXiv   pre-print
we develop the proofs of the results of the cited paper and our new ones in UniMath, a recent library of univalent mathematics formalized in the Coq theorem prover.  ...  We extend this work in two directions: we continue the analysis by creating more categorical structure, in particular by organizing substitution systems into a category and studying its properties, and  ...  Thanks to the rest of the UniMath team, for providing a sound base for formalization, and, specifically, to Dan Grayson and Anders Mörtberg for helping maintain the code described in this article.  ... 
arXiv:1601.04299v1 fatcat:7avpaxbofrb47pblvajndvimuy

Touring the MetaCoq Project (Invited Paper)

Matthieu Sozeau
2021 Electronic Proceedings in Theoretical Computer Science  
MetaCoq is a collaborative project that aims to tackle these difficulties to provide the first fully-certified realistic implementation of a type checker for the full calculus underlying the Coq proof  ...  specification of Coq's syntax and type theory, the Polymorphic Cumulative Calculus of (Co)-Inductive Constructions (PCUIC); a monad for the manipulation of raw syntax and interaction with the Coq system  ...  To do so, we need to answer the following questions in a formal, concrete way: • What calculus is implemented by Coq exactly? • Which meta-theoretical properties hold on the implementation?  ... 
doi:10.4204/eptcs.337.2 fatcat:vkzxls6psredfkeo7xwazecbpa

Plug and Play the Theory of Contexts in Higher-Order Abstract Syntax

Alberto Ciaffaglione, Ivan Scagnetto
2004 Electronical Notes in Theoretical Computer Science  
We illustrate the pragmatic aspects of the Theory of Contexts, recently proposed as a general approach for reasoning on languages with binders in Higher-Order Abstract Syntax, through two working examples  ...  : λ-calculus and Abadi and Cardelli's impς-calculus.  ...  This feature is a relevant advantage in respect to first-order techniques, like de Bruijn indexes or explicit names, because encoding and managing α-conversion and substitutions is a non trivial task from  ... 
doi:10.1016/j.entcs.2004.09.022 fatcat:zwqklz5mc5fhxc6qgd7kn2hbi4
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