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Decidability of higher-order subtyping with intersection types [chapter]

Adriana B. Compagnoni
1995 Lecture Notes in Computer Science  
The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance 11]. The target calculus, F !  ...  Our main contribution is the proof that subtyping in F ! is decidable. This yields as a corollary the decidability of subtyping in F ! , its intersection free fragment, because the F !  ...  I am also grateful for discussions with Benjamin Pierce, Henk Barendregt, and Ugo de'Liguoro.  ... 
doi:10.1007/bfb0022246 fatcat:73koh4aa7jeodctzkfst4ckwdm

Parametric polymorphism and semantic subtyping

Nils Gesbert, Pierre Genevès, Nabil Layaïda
2011 Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP '11  
We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system.  ...  This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful  ...  We are thankful to Giuseppe Castagna for bringing our attention to the problem of subtyping with arrow types in the polymorphic case.  ... 
doi:10.1145/2034773.2034789 dblp:conf/icfp/GesbertGL11 fatcat:yoc2ewbxyvez7brjci67ppzqgy

Higher-order subtyping and its decidability

Adriana Compagnoni
2004 Information and Computation  
The development culminates with the proof of decidability of typing in F ω ∧ , containing the first proof of decidability of subtyping of a higher-order lambda calculus with subtyping.  ...  We define the typed lambda calculus F ω ∧ (F-omega-meet), a natural generalization of Girard's system F ω (F-omega) with intersection types and bounded polymorphism.  ...  in F ω ∧ is decidable and that type inference in F ω ∧ is decidable. • We present the first proof of decidability of subtyping of a higher-order lambda calculus.  ... 
doi:10.1016/j.ic.2004.01.001 fatcat:gkky6rsrenbtth2hwtvp2n654a

Set-theoretic foundation of parametric polymorphism and subtyping

Giuseppe Castagna, Zhiwu Xu
2011 SIGPLAN notices  
We define and study parametric polymorphism for a type system with recursive, product, union, intersection, negation, and function types.  ...  In particular, we introduce the notion of "convexity" on which our solution is built up and discuss its connections with parametricity as defined by Reynolds to whose study our work sheds new light.  ...  Pietro Abate implemented an early version of our prototype subtype checker. Bow-Yaw Wang drew our attention to the connection with convex theories.  ... 
doi:10.1145/2034574.2034788 fatcat:imjvc4cbfrcttjrrc4dot2tpgm

Set-theoretic foundation of parametric polymorphism and subtyping

Giuseppe Castagna, Zhiwu Xu
2011 Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP '11  
We define and study parametric polymorphism for a type system with recursive, product, union, intersection, negation, and function types.  ...  In particular, we introduce the notion of "convexity" on which our solution is built up and discuss its connections with parametricity as defined by Reynolds to whose study our work sheds new light.  ...  Pietro Abate implemented an early version of our prototype subtype checker. Bow-Yaw Wang drew our attention to the connection with convex theories.  ... 
doi:10.1145/2034773.2034788 dblp:conf/icfp/CastagnaX11 fatcat:r537a3ocjjgedhke63wufk437u

Getting F-bounded polymorphism into shape

Ben Greenman, Fabian Muehlboeck, Ross Tate
2013 Proceedings of the 35th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI '14  
With this Material-Shape Separation, we prove that even naïve type-checking algorithms are sound and complete, some of which address problems that were unsolvable even under the existing proposals for  ...  In particular, we distinguish two new concepts, materials and shapes, and demonstrate through a survey of 13.5 million lines of open-source generic-Java code that these two concepts never actually overlap  ...  We thank Professor Ewan Tempero from the University of Auckland for maintaining the Qualitas Corpus and for providing advice and feedback as we worked with the projects.  ... 
doi:10.1145/2594291.2594308 dblp:conf/pldi/GreenmanMT14 fatcat:obk4jm44enf4ffrlv2f76agfga

Getting F-bounded polymorphism into shape

Ben Greenman, Fabian Muehlboeck, Ross Tate
2014 SIGPLAN notices  
With this Material-Shape Separation, we prove that even naïve type-checking algorithms are sound and complete, some of which address problems that were unsolvable even under the existing proposals for  ...  In particular, we distinguish two new concepts, materials and shapes, and demonstrate through a survey of 13.5 million lines of open-source generic-Java code that these two concepts never actually overlap  ...  We thank Professor Ewan Tempero from the University of Auckland for maintaining the Qualitas Corpus and for providing advice and feedback as we worked with the projects.  ... 
doi:10.1145/2666356.2594308 fatcat:p4ncjvmz6vegxajmmem4nwasjy

Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and β-Rule [chapter]

Steffen van Bakel, Franco Barbanera, Maribel Fernández
2000 Lecture Notes in Computer Science  
We define two type assignment systems for first-order rewriting extended with application, -abstraction, and -reduction (TRS ).  ...  The types used in these systems are a combination of ( -free) intersection and polymorphic types.  ...  The restriction to types of rank 2 of the combined system of polymorphic and intersection types is decidable.  ... 
doi:10.1007/3-540-44557-9_3 fatcat:fweecy2czbbkzgk4b7r4vdpcey

Parametric polymorphism and semantic subtyping

Nils Gesbert, Pierre Genevès, Nabil Layaïda
2011 SIGPLAN notices  
We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system.  ...  This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful  ...  We are thankful to Giuseppe Castagna for bringing our attention to the problem of subtyping with arrow types in the polymorphic case.  ... 
doi:10.1145/2034574.2034789 fatcat:kgn7im7mc5h6bmotvqcxuoxk3y

A Gentle Introduction to Semantic Subtyping [chapter]

Giuseppe Castagna, Alain Frisch
2005 Lecture Notes in Computer Science  
In this work we show step by step how to define a subtyping relation semantically in the presence of functional types and dynamic dispatch on types, without the complexity of denotational models, and how  ...  Subtyping relations are usually defined either syntactically by a formal system or semantically by an interpretation of types into an untyped denotational model.  ...  This article stems out from many interesting discussions we had with other researchers.  ... 
doi:10.1007/11523468_3 fatcat:zlkagtv6pvar7byjkcsrm2pege

A gentle introduction to semantic subtyping

Giuseppe Castagna, Alain Frisch
2005 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '05  
In this work we show step by step how to define a subtyping relation semantically in the presence of functional types and dynamic dispatch on types, without the complexity of denotational models, and how  ...  Subtyping relations are usually defined either syntactically by a formal system or semantically by an interpretation of types into an untyped denotational model.  ...  This article stems out from many interesting discussions we had with other researchers.  ... 
doi:10.1145/1069774.1069793 dblp:conf/ppdp/CastagnaF05 fatcat:oor2c3dddnal3k37id7uicozda

Page 5245 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Sci. 184 (1997), no. 1-2, 247 This is an interesting paper on the analysis of system FY’. This system is an extension of Girard’s higher-order polymorphic /- calculus with subtyping.  ...  includes the intersection of the original one with the relation (subset) that determines the function.  ... 

A tale of intersection types

Viviana Bono, Mariangiola Dezani-Ciancaglini
2020 Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science  
This paper is a light overview of intersection types and some of their applications. CCS Concepts: • Theory of computation → Type theory.  ...  They have been exploited for characterising behaviours of λ-terms and π -calculus processes, building λ-models, verifying properties of higher-order programs, synthesising code, and enriching the expressivity  ...  For this reason, she is very grateful to all authors who contributed to the development and diffusion of intersection types, and she asks for forgiveness to the authors she could not mention here due to  ... 
doi:10.1145/3373718.3394733 dblp:conf/lics/BonoD20 fatcat:wtxau4yu4nbolcm4tpdnuimb6m

Intersections and Unions of Session Types

Coşku Acay, Frank Pfenning
2017 Electronic Proceedings in Theoretical Computer Science  
In this paper, we extend this further by intersection and union types in order to express multiple behavioral properties of processes in a single type.  ...  Prior work has extended the deep, logical connection between the linear sequent calculus and session-typed message-passing concurrent computation with equi-recursive types and a natural notion of subtyping  ...  Contrary to Padovani, Castagna et al. have higher order sessions and give algorithms to decide all semantic relations they describe.  ... 
doi:10.4204/eptcs.242.3 fatcat:ogromml27fecfaesyfjilday6u

Intersection Type Matching with Subtyping [chapter]

Boris Düdder, Moritz Martens, Jakob Rehof
2013 Lecture Notes in Computer Science  
We consider the intersection type matching problem under the standard notion of subtyping for intersection types: Given intersection types τ and σ, where σ is a constant type, does there exist a type substitution  ...  Our algorithm is based on a nondeterministic polynomial time normalization procedure for subtype constraint systems with intersection types.  ...  Our study of intersection type matching with subtyping is motivated from two perspectives.  ... 
doi:10.1007/978-3-642-38946-7_11 fatcat:fhcg33zjujf6bnjv2eez4wyc4m
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