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Syntax and Semantics of Dependent Types
 Semantics and Logics of Computation
, 1997
"... ion is written as [x: oe]M instead of x: oe:M and application is written M(N) instead of App [x:oe] (M; N ). 1 Iterated abstractions and applications are written [x 1 : oe 1 ; : : : ; x n : oe n ]M and M(N 1 ; : : : ; N n ), respectively. The lacking type information can be inferred. The universe ..."
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Cited by 40 (4 self)
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ion is written as [x: oe]M instead of x: oe:M and application is written M(N) instead of App [x:oe] (M; N ). 1 Iterated abstractions and applications are written [x 1 : oe 1 ; : : : ; x n : oe n ]M and M(N 1 ; : : : ; N n ), respectively. The lacking type information can be inferred. The universe is written Set instead of U . The Eloperator is omitted. For example the \Pitype is described by the following constant and equality declarations (understood in every valid context): ` \Pi : (oe: Set; : (oe)Set)Set ` App : (oe: Set; : (oe)Set; m: \Pi(oe; ); n: oe) (m) ` : (oe: Set; : (oe)Set; m: (x: oe) (x))\Pi(oe; ) oe: Set; : (oe)Set; m: (x: oe) (x); n: oe ` App(oe; ; (oe; ; m); n) = m(n) Notice, how terms with free variables are represented as framework abstractions (in the type of ) and how substitution is represented as framework application (in the type of App and in the equation). In this way the burden of dealing correctly with variables, substitution, and binding is s...
TypePreserving Compilation of Featherweight Java
, 2001
"... We present an efficient encoding of core Java constructs in a simple, implementable typed intermediate language. The encoding, after type erasure, has the same operational behavior as a standard implementation using vtables and selfapplication for method invocation. Classes inherit superclass metho ..."
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Cited by 34 (8 self)
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We present an efficient encoding of core Java constructs in a simple, implementable typed intermediate language. The encoding, after type erasure, has the same operational behavior as a standard implementation using vtables and selfapplication for method invocation. Classes inherit superclass methods with no overhead. We support mutually recursive classes while preserving separate compilation. Our strategy extends naturally to a significant subset of Java, including interfaces and privacy. The formal translation using Featherweight Java allows comprehensible typepreservation proofs and serves as a starting point for extending the translation to new features.
Short Proofs of Normalization for the simplytyped λcalculus, permutative conversions and Gödel's T
 TO APPEAR: ARCHIVE FOR MATHEMATICAL LOGIC
, 1998
"... Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simplytyped λcalculus and for an extension by sum types with permutative conversions. The analogous treatment of a new sy ..."
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Cited by 15 (1 self)
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Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simplytyped λcalculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by von Plato's generalized elimination rules in natural deduction shows the flexibility of the approach which does not use the strong computability/candidate style a la Tait and Girard. It is also shown that the extension of the system with permutative conversions by rules is still strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of "immediate simplification". By introducing an innitely branching inductive rule the method even extends to Gödel's T.
Weak Normalization for the SimplyTyped LambdaCalculus in Twelf (Extended Abstract)
 In Logical Frameworks and Metalanguages (LFM 04), IJCAR
, 2004
"... Andreas Abel Department of Computer Science, Chalmers University of Technology Rannvagen 6, SWE41296 Goteborg, Sweden Abstract. Weak normalization for the simplytyped calculus is proven in Twelf, an implementation of the Edinburgh Logical Framework. Since due to prooftheoretical restrict ..."
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Cited by 11 (3 self)
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Andreas Abel Department of Computer Science, Chalmers University of Technology Rannvagen 6, SWE41296 Goteborg, Sweden Abstract. Weak normalization for the simplytyped calculus is proven in Twelf, an implementation of the Edinburgh Logical Framework. Since due to prooftheoretical restrictions Twelf Tait's computability method does not seem to be directly usable, a combinatorical proof is adapted and formalized instead.
Regulating data exchange in service oriented applications
 IN FSEN, VOLUME 4767 OF LNCS
, 2007
"... We define a type system for COWS, a formalism for specifying and combining services, while modelling their dynamic behaviour. Our types permit to express policies constraining data exchanges in terms of sets of service partner names attachable to each single datum. Service programmers explicitly wri ..."
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Cited by 9 (7 self)
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We define a type system for COWS, a formalism for specifying and combining services, while modelling their dynamic behaviour. Our types permit to express policies constraining data exchanges in terms of sets of service partner names attachable to each single datum. Service programmers explicitly write only the annotations necessary to specify the wanted policies for communicable data, while a type inference system (statically) derives the minimal additional annotations that ensure consistency of services initial configuration. Then, the language dynamic semantics only performs very simple checks to authorize or block communication. We prove that the type system and the operational semantics are sound. As a consequence, we have the following data protection property: services always comply with the policies regulating the exchange of data among interacting services. We illustrate our approach through a simplified but realistic scenario for a servicebased electronic marketplace.
Fixed points of type constructors and primitive recursion
 Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 2024, 2004, Proceedings, volume 3210 of Lecture Notes in Computer Science
, 2004
"... Our contribution to CSL 04 [AM04] contains a little error, which is easily corrected by 2 elementary editing steps (replacing one character and deleting another). Definition of wellformed contexts (fifth page). Typing contexts should, in contrast to kinding contexts, only contain type variable decla ..."
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Cited by 7 (3 self)
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Our contribution to CSL 04 [AM04] contains a little error, which is easily corrected by 2 elementary editing steps (replacing one character and deleting another). Definition of wellformed contexts (fifth page). Typing contexts should, in contrast to kinding contexts, only contain type variable declarations without variance information. Hence, the second rule is too liberal; we must insist on p = ◦. The corrected set of rules is then: ⋄ cxt ∆ cxt ∆, X ◦κ cxt ∆ cxt ∆ ⊢ A: ∗ ∆, x:A cxt Definition of welltyped terms (immediately following). Since wellformed typing contexts ∆ contain no variance information, hence ◦ ∆ = ∆, we might drop the “◦ ” in the instantiation rule (fifth rule). The new set of rules is consequently, (x:A) ∈ ∆ ∆ cxt ∆ ⊢ x: A ∆, X ◦κ ⊢ t: A ∆ ⊢ t: ∀X κ. A ∆, x:A ⊢ t: B ∆ ⊢ λx.t: A → B ∆ ⊢ t: ∀X κ. A ∆ ⊢ F: κ
Sequent Combinators: A Hilbert System for the Lambda Calculus
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 1999
"... This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert systems, which have led to the more widespread adoption of natural deduction systems in computer science. This suggests that Hilbert systems, with the ..."
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Cited by 5 (4 self)
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This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert systems, which have led to the more widespread adoption of natural deduction systems in computer science. This suggests that Hilbert systems, with their more uniform approach to metavariables and substitution, may be a more suitable framework than lambda calculus for type theories and programming languages.
A Mobility Calculus with Local and Dependent Types
 Processes, Terms and Cycles: Steps on the Road to Infinity, volume 3838 of LNCS
, 2005
"... Abstract. We introduce an ambientbased calculus that combines ambient mobility with process mobility, uses group names to collect ambients with homologous features, and exploits comoves and runtime type checking to implement flexible policies for controlling process activities. Types rely on group ..."
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Cited by 5 (3 self)
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Abstract. We introduce an ambientbased calculus that combines ambient mobility with process mobility, uses group names to collect ambients with homologous features, and exploits comoves and runtime type checking to implement flexible policies for controlling process activities. Types rely on group names and, to support dynamicity, may depend on group variables. Policies can dynamically change also through installation of comoves. The compliance with ambient policies can be checked locally to the ambients and requires no global assumptions. We prove that the type assignment system and the operational semantics of the calculus are ‘sound’, and define a sound and complete type inference algorithm which, when applied to terms whose type decorations only express the desired policies, computes the minimal type annotations required for their execution. As an application of our calculus, we present a couple of examples and linger on the setting up of policies for controlling the activities of the entities involved. 1
Boxed Ambients with Communication Interfaces
 MFCS’04, volume 3153 of LNCS
, 2004
"... We define BACI (Boxed Ambients with Communication Interfaces), an ambient calculus allowing a liberal communication policy. Each ambient carries its local view of the topic of conversation (the type of the information being exchanged) with parents and children that will condition where it is allo ..."
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Cited by 5 (2 self)
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We define BACI (Boxed Ambients with Communication Interfaces), an ambient calculus allowing a liberal communication policy. Each ambient carries its local view of the topic of conversation (the type of the information being exchanged) with parents and children that will condition where it is allowed to stay or migrate to and which ambients may be allowed to enter it. The topic of conversation view of ambients can dynamically change during migration. BACI is flexible enough to allow different topics of conversation between an ambient and different parents, without compromising typesafety: it uses port names for communication and ambient names for mobility. Capabilities and cocapabilities exchange port names and runtime typing information to control mobility. We show the typesoundness of BACI proving that it satisfies the subject reduction property. Moreover we study its behavioural semantics by means of a labelled transition system.
AntiSymmetry of HigherOrder Subtyping
 In Proceedings of the 8th Annual Conference on Computer Science Logic (CSL’99), J. Flum and M. RodríguezArtalejo, Eds. SpringerVerlag LNCS 1683
, 1999
"... . This paper shows that the subtyping relation of a higherorder lambda calculus, F ! , is antisymmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial orderreexive, transitive, and antisymmetric up to equality. While a subtyping relat ..."
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Cited by 4 (1 self)
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. This paper shows that the subtyping relation of a higherorder lambda calculus, F ! , is antisymmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial orderreexive, transitive, and antisymmetric up to equality. While a subtyping relation is reexive and transitive by denition, antisymmetry is a derived property. The result, which may seem obvious to the nonexpert, is technically challenging, and had been an open problem for almost a decade. In this context, typed operational semantics for subtyping oers a powerful new technology to solve the problem: of particular importance is our extended rule for the wellformedness of types with head variables. The paper also gives a presentation of F ! without a relation for equality, apparently the rst such, and shows its equivalence with the traditional presentation. 1 Introduction Objectoriented programming languages such as Smalltalk, C++, Modula 3, and ...