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Syntactic considerations on recursive types
 In Proceedings of the 11th Annual Symposium on Logic in Computer Science
, 1996
"... Abstract We study recursive types from a syntactic perspective. In particular, we compare the formulations of recursive types that are used in programming languages and formal systems. Our main tool is a new syntactic explanation of type expressions as functors. We also introduce a simple logic for ..."
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Cited by 31 (0 self)
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Abstract We study recursive types from a syntactic perspective. In particular, we compare the formulations of recursive types that are used in programming languages and formal systems. Our main tool is a new syntactic explanation of type expressions as functors. We also introduce a simple logic for programs with recursive types in which we carry out our proofs. 1 Introduction Recursive types are common in both programming languages and formal systems. By now, there is a deep and welldeveloped semantic theory of recursive types. The syntactic aspects of recursive types are also well understood in some special cases. In particular, there is an important body of knowledge about covariant recursive types, which include datatypes like natural numbers, lists, and trees. Beyond the covariant case, however, the syntactic understanding of recursive types becomes rather spotty. Consequently, the relations between various alternative formulations of recursive types are generally unclear. Furthermore, the syntactic counterparts to some of the most basic semantic results are unknown.
Generating Type Systems for Process Graphs
, 1999
"... We introduce a hypergraphbased process calculus with a generic type system. That is, a type system checking an invariant property of processes can be generated by instantiating the original type system. We demonstrate the key ideas behind the type system, namely that there exists a hypergraph morph ..."
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Cited by 11 (4 self)
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We introduce a hypergraphbased process calculus with a generic type system. That is, a type system checking an invariant property of processes can be generated by instantiating the original type system. We demonstrate the key ideas behind the type system, namely that there exists a hypergraph morphism from each process graph into its type, and show how it can be used for the analysis of processes. Our examples are input/outputcapabilities, secrecy conditions and avoiding vicious circles occurring in deadlocks. In order to specify the syntax and semantics of the process calculus and the type system, we introduce a method of hypergraph construction using concepts from category theory.
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
Union and intersection types for secure protocol implementations
"... We present a new type system for verifying the security of cryptographic protocol implementations. The type system combines prior work on refinement types, with union, intersection, and polymorphic types, and with the novel ability to reason statically about the disjointness of types. The increased ..."
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Cited by 7 (1 self)
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We present a new type system for verifying the security of cryptographic protocol implementations. The type system combines prior work on refinement types, with union, intersection, and polymorphic types, and with the novel ability to reason statically about the disjointness of types. The increased expressivity enables the analysis of important protocol classes that were previously out of scope for the typebased analyses of protocol implementations. In particular, our types can statically characterize: (i) more usages of asymmetric cryptography, such as signatures of private data and encryptions of authenticated data; (ii) authenticity and integrity properties achieved by showing knowledge of secret data; (iii) applications based on zeroknowledge proofs. The type system comes with a mechanized proof of correctness and an efficient typechecker.
Description and Verification of Mobile Processes with Graph Rewriting Techniques
"... The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congru ..."
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Cited by 5 (4 self)
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The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congruence for relating processes displaying the same behaviour and generic type systems, forming a central part of this work. Based on existing work in graph rewriting...
Weak and Strong Beta Normalisations in Typed λCalculi
 In: Proc. of the 3 rd International Conference on Typed Lambda Calculus and Applications, TLCA'97
, 1997
"... . We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a term into a Iterm, and show that a term is strongly finormalisable if and only if its translation is weakly finormalisable. We t ..."
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Cited by 4 (1 self)
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. We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a term into a Iterm, and show that a term is strongly finormalisable if and only if its translation is weakly finormalisable. We then prove that the translation preserves typability of terms in various typed calculi. This enables us to establish the equivalence between weak and strong finormalisations in these typed calculi. This translation can deal with Curry typing as well as Church typing, strengthening some recent closely related results. This may bring some insights into answering whether weak and strong finormalisations in all pure type systems are equivalent. 1 Introduction In various typed calculi, one of the most interesting and important properties on terms is how they can be fireduced to finormal forms. A term M is said to be weakly finormalisable (WN fi (M )) if it can be fireduced to a fin...
An Algebraic View on Recursive Types
 Applied Categorical Structures
, 1996
"... This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision ..."
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Cited by 1 (0 self)
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This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision
Least and Greatest Fixed Points in Intuitionistic Natural Deduction
, 2002
"... This paper is a comparative study of a number of (intensionalsemantically distinct) least and greatest fixed point operators that naturaldeduction proof systems for intuitionistic logics can be extended with in a prooftheoretically defendable way. Eight pairs of such operators are analysed. The e ..."
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This paper is a comparative study of a number of (intensionalsemantically distinct) least and greatest fixed point operators that naturaldeduction proof systems for intuitionistic logics can be extended with in a prooftheoretically defendable way. Eight pairs of such operators are analysed. The exposition is centered around a cubeshaped classification where each node stands for an axiomatization of one pair of operators as logical constants by intended proof and reduction rules and each arc for a proof and reductionpreserving encoding of one pair in terms of another. The three dimensions of the cube reflect three orthogonal binary options: conventionalstyle vs. Mendlerstyle, basic (``[co]iterative'') vs. enhanced (``primitive[co]recursive''), simple vs. courseofvalue [co]induction. Some of the axiomatizations and encodings are wellknown; others, however, are novel; the classification into a cube is also new. The differences between the least fixed point operators considered are illustrated on the example of the corresponding natural number types.