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Type soundness proofs with definitional interpreters

Nada Amin, Tiark Rompf
2017 SIGPLAN notices  
proof whereas it is selfsuggesting with a definitional interpreter approach.  ...  Other Related Languages Other calculi related to path-dependent types include the family polymorphism of Ernst [21] , Virtual Conclusions We presented type soundness proofs with definitional interpreters  ... 
doi:10.1145/3093333.3009866 fatcat:gmsh3x2nlrbmtdlwkam4p2lmm4

Type soundness proofs with definitional interpreters

Nada Amin, Tiark Rompf
2017 Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017  
proof whereas it is selfsuggesting with a definitional interpreter approach.  ...  Other Related Languages Other calculi related to path-dependent types include the family polymorphism of Ernst [21] , Virtual Conclusions We presented type soundness proofs with definitional interpreters  ... 
doi:10.1145/3009837.3009866 fatcat:vkj4xuu5kzertc2jn5hdhs6yri

From F to DOT: Type Soundness Proofs with Definitional Interpreters [article]

Tiark Rompf, Nada Amin
2016 arXiv   pre-print
Second, we demonstrate how type soundness can be proved for advanced, polymorphic, type systems with respect to high-level, definitional interpreters, implemented in Coq.  ...  Armed with insights from the definitional interpreter semantics, we also show how equivalent small-step semantics and soundness proofs in Wright-Felleisen-style can be derived for these systems.  ...  to soundness and demonstrate that a proof strategy based on high-level definitional interpreters (Section 5) scales to advanced polymorphic type systems, presenting the first soundness proof for F<: in  ... 
arXiv:1510.05216v2 fatcat:cviag7pfqzhaxiiwziz4p66vza

Compositional soundness proofs of abstract interpreters

Sven Keidel, Casper Bach Poulsen, Sebastian Erdweg
2018 Proceedings of the ACM on Programming Languages  
We were able to prove both analyses sound compositionally with manageable complexity and effort, compared to a conventional soundness proof.  ...  interpretation is a technique for developing static analyses. Yet, proving abstract interpreters sound is challenging for interesting analyses, because of the high proof complexity and proof effort.  ...  We want to thank Robbert Krebbers and Arjen Rouvoet who provided helpful feedback and Jente Hidskes who helped us with the artifact.  ... 
doi:10.1145/3236767 dblp:journals/pacmpl/KeidelPE18 fatcat:otxsbjtkubhy5hsoll3zj2lgke

Constructive Galois connections: taming the Galois connection framework for mechanized metatheory

David Darais, David Van Horn
2016 Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming - ICFP 2016  
basis for gradual typing.  ...  This paper presents constructive Galois connections, a framework for Galois connections that is effective both on paper and in proof assistants; is complete with respect to the set of Galois connections  ...  Acknowledgments We thank Ron Garcia andÉric Tanter for discussions of their work.Éric also helped with our French translation.  ... 
doi:10.1145/2951913.2951934 dblp:conf/icfp/DaraisH16 fatcat:cicsm3zokfg77frcvuq22rcooi

Constructive Galois connections: taming the Galois connection framework for mechanized metatheory

David Darais, David Van Horn
2016 SIGPLAN notices  
basis for gradual typing.  ...  This paper presents constructive Galois connections, a framework for Galois connections that is effective both on paper and in proof assistants; is complete with respect to the set of Galois connections  ...  Acknowledgments We thank Ron Garcia andÉric Tanter for discussions of their work.Éric also helped with our French translation.  ... 
doi:10.1145/3022670.2951934 fatcat:w7ugyervunaabhxkafdan42gpu

Mechanically Verified Calculational Abstract Interpretation [article]

David Darais, David Van Horn
2015 arXiv   pre-print
This paper addresses the problem of deriving correct-by-verified-construction abstract interpreters with the use of a proof assistant.  ...  We identify several technical challenges to overcome with the aim of supporting verified calculational abstract interpretation that is faithful to existing pencil-and-paper proofs, supports calculation  ...  To establish the utility of our theory, we construct a framework for abstract interpretation with Kleisli Galois connections in the dependently typed programming language and proof-assistant, Agda [20  ... 
arXiv:1507.03559v1 fatcat:a2ho4ehqyjaqrprr5nujpaj7ri

Constructive Galois Connections: Taming the Galois Connection Framework for Mechanized Metatheory [article]

David Darais, David Van Horn
2016 arXiv   pre-print
basis for gradual typing.  ...  This paper presents constructive Galois connections, a variant of Galois connections that is effective both on paper and in proof assistants; is complete with respect to a large subset of classical Galois  ...  Eric also helped with our French translation. We thank the Colony Club in D.C. and the Board & Brew in College Park for providing fruitful environments in which to work.  ... 
arXiv:1511.06965v4 fatcat:tgcjpjba5vcnvey4lmjfj3txri

Formalizing a correctness property of a type-directed partial evaluator

Noriko Hirota, Kenichi Asai
2014 Proceedings of the ACM SIGPLAN 2014 Workshop on Programming Languages meets Program Verification - PLPV '14  
Following the previous approach by Coquand and Ilik, we characterize TDPE as a composition of completeness and soundness theorems of typing rules with respect to the semantics.  ...  This paper presents our experience of formalizing Danvy's typedirected partial evaluator (TDPE) for the call-by-name lambda calculus in the proof assistant Coq.  ...  In fact, the proof term of the soundness theorem is the standard direct-style interpreter: Fixpoint soundness b {A} (t: tm (V b) A) : V b A := match t with | tm_Var _ x => x | tm_Lam _ _ t1 => fun x =>  ... 
doi:10.1145/2541568.2541572 dblp:conf/plpv/HirotaA14 fatcat:xi6hjagdarbutbx64ovivvlpae

Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses [chapter]

Henning Basold, Ekaterina Komendantskaya, Yue Li
2019 Lecture Notes in Computer Science  
with recursion controlled by the later modality; and soundness of both proof systems is proven relative to a novel coalgebraic description of complete Herbrand models.  ...  Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its constructive content is exposed via soundness relative to an intuitionistic first-order logic  ...  This concludes the semantics of types, terms and formulae. We now turn to show that coinductive uniform proofs are sound for this interpretation.  ... 
doi:10.1007/978-3-030-17184-1_28 fatcat:7azord5jkjhlvdxyir54hjsdqq

A short and flexible proof of strong normalization for the calculus of constructions [chapter]

Herman Geuvers
1995 Lecture Notes in Computer Science  
PROOF. Totally similar to the proof of Theorem 3.15. 0 We now come to the interpretation of so called 'large' E-types (Le. where the E-type is actually a ). .15. DEFINITION.  ...  -case QMDpQND p ' With these definitions it is not difficult to verify the Soundness Theorem (3.14) for ee with sum-types. The Strong Normalization follows easily from it.  ... 
doi:10.1007/3-540-60579-7_2 fatcat:v7npnjqinngbhn3zjmo5xhedea

Formal verification of a proof procedure for the description logic ALC

Mohamed Chaabani, Mohamed Mezghiche, Martin Strecker
2013 Electronic Proceedings in Theoretical Computer Science  
In this paper, we present the definition of a proof procedure for the Description Logic ALC, based on a semantic tableau method.  ...  We ensure validity of our prover by proving its soundness, completeness and termination properties using Isabelle proof assistant.  ...  Type definitions are parameterized by the type of role names nr and atomic concepts nc.  ... 
doi:10.4204/eptcs.122.5 fatcat:75xtsyptujfq5jxhiasaho7xfq

Completeness of type assignment in continuous lambda models

Mario Coppo
1984 Theoretical Computer Science  
Moreover, an extension of Curry's system in which type schemes can be assigned to the' fixed point combinator is introduced, together with a notion of type semantics for which it is proved sound and complete  ...  A first result of this paper is a completeness proof with respect to the model P, (as asked by Scott (1976) ).  ...  Definition. (i) Type 3.6. Theorem (Soundness). Bt-+A4 a Bi==,arM. Proof.  ... 
doi:10.1016/0304-3975(84)90005-7 fatcat:zcx5oxkcindd5nr2jmnh7fveja

Self-Formalisation of Higher-Order Logic

Ramana Kumar, Rob Arthan, Magnus O. Myreen, Scott Owens
2016 Journal of automated reasoning  
We present a mechanised semantics for higher-order logic (HOL), and a proof of soundness for the inference system, including the rules for making definitions, implemented by the kernel of the HOL Light  ...  Apart from adding support for definitions and synthesising an implementation, we improve on Harrison's work by making our model of HOL parametric on the universe of sets, and we prove soundness for an  ...  The proof of soundness of type definitions is the longest of the proofs about the rules for extension, taking around 400 lines of proof script compared to around 200 for constant specifications below and  ... 
doi:10.1007/s10817-015-9357-x fatcat:3dcm7pdklzcrhc37yryjzm3f7u

An Intuitionistic Set-theoretical Model of CCω

Masahiro Sato, Jacques Garrigue
2016 Journal of Information Processing  
We prove soundness and show some applications of our model.  ...  It combines a functional view of predicative universes with a collapsed view of the impredicative sort Prop.  ...  Soundness We are now ready to prove the soundness of this type system.  ... 
doi:10.2197/ipsjjip.24.711 fatcat:wvt6ry2fsvcb7igfzycra6p6mq
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