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Some Domain Theory and Denotational Semantics in Coq [chapter]

Nick Benton, Andrew Kennedy, Carsten Varming
2009 Lecture Notes in Computer Science  
the correspondence between the operational and denotational semantics.  ...  We then define operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case.  ...  Mechanizing domain theory and denotational semantics has an illustrious history.  ... 
doi:10.1007/978-3-642-03359-9_10 fatcat:ettw3j3mw5hmnni2jex66aom3q

GSOS Formalized in Coq

Ken Madlener, Sjaak Smetsers
2013 2013 International Symposium on Theoretical Aspects of Software Engineering  
The present paper formalizes the underlying theory in the theorem prover COQ, and proves the consistency property, also known as the adequacy theorem.  ...  GSOS is a rule format that enjoys the property that the operational semantics and denotational semantics, both derived from the same set of GSOS rules, are consistent.  ...  COQ FORMALIZATION In this section we discuss some details of the COQ formalization, and continue the development of the theory for terms. A.  ... 
doi:10.1109/tase.2013.34 dblp:conf/tase/MadlenerS13 fatcat:muig25u2hvaqzanq4h6sx7hwfi

Mechanizing Matching Logic in Coq [article]

Péter Bereczky, Xiaohong Chen, Dániel Horpácsi, Tamás Bálint Mizsei, Lucas Peña, Jan Tusil
2022 arXiv   pre-print
We formalize the syntax, semantics, and proof system of this representation of matching logic using the Coq proof assistant.  ...  We believe this work provides a previously unexplored avenue for defining and proving matching logic theories and properties.  ...  In particular, we encode first-order logic (FOL) both as a Coq theory and as a matching logic theory (based on [13] ), and we prove some fundamental properties.  ... 
arXiv:2201.05716v3 fatcat:hmo7i3kgrbamjjuxgujwnwlml4

Mechanized Theory of Event Structures: A Case of Parallel Register Machine

Vladimir Gladstein, Dmitrii Mikhailovskii, Evgenii Moiseenko, Anton Trunov
2021 Proceedings of the Institute for System Programming of RAS  
In this work-in-progress report, we present a theory of event structures mechanized in the COQ proof assistant and demonstrate how it can be applied to define certified executable semantics of a simple  ...  The true concurrency models, and in particular event structures, have been introduced in the 1980s as an alternative to operational interleaving semantics of concurrency, and nowadays they are regaining  ...  The programming languages theory and formal semantics research communities are moving to increase the usage of proof assistants like COQ [6] , AGDA [7] , ISABELLE/HOL [8] , AREND [9] , and others,  ... 
doi:10.15514/ispras-2021-33(3)-11 fatcat:l26vlarbcjdura5xtmxwpvkfwe

Type-Theoretic Functional Semantics [chapter]

Yves Bertot, Venanzio Capretta, Kuntal Das Barman
2002 Lecture Notes in Computer Science  
We describe the operational and denotational semantics of a small imperative language in type theory with inductive and recursive definitions.  ...  A second result is a clear understanding of the characterization of the definition domain for general recursive functions, a key aspect in the approach by iteration of Balaa and Bertot.  ...  Our main goal is to develop operational and denotational semantics inside type theory, to implement them in the proof-assistant Coq [12] , and to prove their main properties formally.  ... 
doi:10.1007/3-540-45685-6_7 fatcat:fuuf5rf2hbabtbumwde5vc2ipu

A Formal Quantifier Elimination for Algebraically Closed Fields [chapter]

Cyril Cohen, Assia Mahboubi
2010 Lecture Notes in Computer Science  
We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts.  ...  The algorithm producing the quantifier free formula is programmed in continuation passing style, which leads to both a concise program and an elegant proof of semantic correctness.  ...  Acknowledgments The authors wish to thank Georges Gonthier for numerous comments and improvements. The proofs relating quantifier elimination and  ... 
doi:10.1007/978-3-642-14128-7_17 fatcat:ddgdtdkjlfbv3dq2q7tvfspvdy

A certified type-preserving compiler from lambda calculus to assembly language

Adam Chlipala
2007 Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation - PLDI '07  
The compiler is certified in the sense that it comes with a machine-checked proof of semantics preservation, performed with the Coq proof assistant.  ...  Semantics preservation is proved based on denotational semantics assigned to the intermediate languages.  ...  Acknowledgments Thanks to Manu Sridharan and the anonymous referees for helpful comments on drafts of this paper.  ... 
doi:10.1145/1250734.1250742 dblp:conf/pldi/Chlipala07 fatcat:vligv7peabhupn44dr3sle6v6e

A certified type-preserving compiler from lambda calculus to assembly language

Adam Chlipala
2007 SIGPLAN notices  
The compiler is certified in the sense that it comes with a machine-checked proof of semantics preservation, performed with the Coq proof assistant.  ...  Semantics preservation is proved based on denotational semantics assigned to the intermediate languages.  ...  Acknowledgments Thanks to Manu Sridharan and the anonymous referees for helpful comments on drafts of this paper.  ... 
doi:10.1145/1273442.1250742 fatcat:juukypftbbhg7nvsbzvcgtodwy

A comparative study of two formal semantics of the SIGNAL language

Zhibin Yang, Jean-Paul Bodeveix, Mamoun Filali
2013 Frontiers of Computer Science  
These two semantics have several different definitions respectively, we select appropriate ones and mechanize them in the Coq platform, the Coq expressions of the abstract syntax of SIGNAL and the two  ...  semantics domains, i.e., the trace model and the tagged model, are also given.  ...  Semantics Domains Semantics domains such as the trace model and the tagged model are introduced in this section.  ... 
doi:10.1007/s11704-013-3908-2 fatcat:do6grhfysnas3ga2wlvu4cbzhu

Formalized, Effective Domain Theory in Coq [chapter]

Robert Dockins
2014 Lecture Notes in Computer Science  
I present highlights from a formalized development of domain theory in the theorem prover Coq.  ...  This is the first development of domain theory that is effective, formalized and that supports all the usual constructions on domains.  ...  The goal of this work is ultimately to provide a solid foundation of domain theoretic constructions and theorems that can be used for practical program semantics in Coq.  ... 
doi:10.1007/978-3-319-08970-6_14 fatcat:3lbibth4mvfrhh77g5wxdlt6qq

Natural Language Specifications in Proof Assistants [article]

Colin S. Gordon, Sergey Matskevich
2022 arXiv   pre-print
This paper argues that it is possible to build support for natural language specifications within existing proof assistants, in a way that complements the principles used to establish trust and auditability  ...  in proof assistants themselves.  ...  In traditional semantics in first-order logic, common nouns often denote a kind of predicate to guard quantifications.  ... 
arXiv:2205.07811v1 fatcat:jc4on2o4dfdjfnr2yrcjbdujye

Certified Static Analysis by Abstract Interpretation [chapter]

Frédéric Besson, David Cachera, Thomas Jensen, David Pichardie
2009 Lecture Notes in Computer Science  
A certified static analysis is an analysis whose semantic validity has been formally proved correct with a proof assistant. We propose a tutorial on building a certified static analysis in Coq.  ...  The key idea of abstract interpretation theory is to replace the previous semantic domains by a simpler one, where the computation of the program can be mimicked in a computable way.  ...  in Coq) and post, the operator formally defined by post p (S) = {s 2 | ∃s 1 ∈ S, s 1 -[p]->s 2 } We do not prove here this characterisation in Coq.  ... 
doi:10.1007/978-3-642-03829-7_8 fatcat:eyjfd7uqjbaatn2nei4kiykrti

Formalizing Higher-Order Termination in Coq [article]

Deivid Vale, Niels van der Weide
2021 arXiv   pre-print
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain.  ...  To do so, we use Coq, which is a proof assistant based on dependent type theory.  ...  To do so, we start by formalizing basic theory on rewriting in the proof assistant Coq [1] .  ... 
arXiv:2112.05715v2 fatcat:n5vtlybz45atdiikctf275mfma

Certified Semantics for Relational Programming [article]

Dmitry Rozplokhas, Andrey Vyatkin, Dmitry Boulytchev
2020 arXiv   pre-print
Second, we present operational semantics which models interleaving, the distinctive feature of miniKanren implementation, and prove its soundness and completeness w.r.t. the denotational semantics.  ...  First, we formulate a denotational semantics which corresponds to the minimal Herbrand model for definite logic programs.  ...  To formalize the operational semantics in Coq we first need to define all preliminary notions from unification theory [3] which our semantics uses.  ... 
arXiv:2005.01018v2 fatcat:4y4bhiy3l5ce7klur3iuvdjove

Sets in Coq, Coq in Sets

Bruno; INRIA Saclay-France Barras
2010 Journal of Formalized Reasoning  
On top of these theories we have developped a piece of the usual set theoretical construction of functions, ordinals and fixpoint theory.  ...  One aspect of this work is to axiomatize several set theories: ZF possibly with inaccessible cardinals, and HF, the theory of hereditarily finite sets.  ...  No infinite set is involved so we should be able to build a model of CC in the theory of hereditarily finite sets. Formalizing such a set theory in Coq is the object of the first section.  ... 
doi:10.6092/issn.1972-5787/1695 dblp:journals/jfrea/Barras10 fatcat:w3vjiiyydndsvd7atmoyns5kry
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