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