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Ensuring termination by typability
 In Proceedings of IFIP TCS 2004
, 2004
"... Abstract. A term terminates if all its reduction sequences are of finite length. We show four type systems that ensure termination of welltyped sscalculus processes. The systems are obtained by successive refinements of the types of the simply typed sscalculus. For all (but one of) the type syste ..."
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Abstract. A term terminates if all its reduction sequences are of finite length. We show four type systems that ensure termination of welltyped sscalculus processes. The systems are obtained by successive refinements of the types of the simply typed sscalculus. For all (but one of) the type systems we also present upper bounds to the number of steps welltyped processes take to terminate. The termination proofs use techniques from term rewriting systems. We show the usefulness of the type systems on some nontrivial examples: the encodings of primitive recursive functions, the protocol for encoding separate choice in terms of parallel composition, a symbol table implemented as a dynamic chain of cells. 1 Introduction A term terminates if all its reduction sequences are of finite length. As far as programminglanguages are concerned, termination means that computation in programs will eventually stop. In computer science termination has been extensively investigated in term rewritingsystems [7, 5] and *calculi [9, 4] (where strong normalization is a synonym more commonlyused). Termination has also been discussed in process calculi, notably the
On Type Inference in the Intersection Type Discipline
, 2004
"... We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended # calculus, where one never erases arguments that would be discarded by ordinary #reduction. We show that our notion ..."
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We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended # calculus, where one never erases arguments that would be discarded by ordinary #reduction. We show that our notion of unification allows us to compute a principal typing for any strongly normalizing #expression.
Complexity of strongly normalising λterms via nonidempotent intersection types
"... We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound o ..."
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We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound on the longest βreduction sequence reducing a term to its normal form. We actually present these results in Klop’s extension of λcalculus, where the bound that is read in the typing tree of a term is refined into an exact measure of the longest reduction sequence. This complexity result is, for longest reduction sequences, the counterpart of de Carvalho’s result for linear headreduction sequences.
A Behavioural Model for Klop’s Calculus
 Logic, Model and Computer Science, ENTCS
, 2006
"... Replace this file withprentcsmacro.sty for your meeting, or withentcsmacro.sty for your meeting. Both can be ..."
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Replace this file withprentcsmacro.sty for your meeting, or withentcsmacro.sty for your meeting. Both can be
Normalisation is Insensible to λterm Identity or Difference
"... This paper analyses the computational behaviour of λterm applications. The properties we are interested in are weak normalisation (i.e. there is a terminating reduction) and strong normalisation (i.e. all reductions are terminating). One can prove that the application of a λterm M to a fixed number ..."
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This paper analyses the computational behaviour of λterm applications. The properties we are interested in are weak normalisation (i.e. there is a terminating reduction) and strong normalisation (i.e. all reductions are terminating). One can prove that the application of a λterm M to a fixed number n of copies of the same arbitrary strongly normalising λterm is strongly normalising if and only if the application of M to n different arbitrary strongly normalising λterms is strongly normalising. I.e. one has that M X
Collège doctoral Axiomatisations and Types
, 2005
"... The focus of this thesis are the theoretical foundations for reasoning about algorithms and protocols for modern distributed systems. Two important features of models for these systems are probability and typed mobility: probabilities can be used to quantify unreliable or unpredictable behaviour an ..."
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The focus of this thesis are the theoretical foundations for reasoning about algorithms and protocols for modern distributed systems. Two important features of models for these systems are probability and typed mobility: probabilities can be used to quantify unreliable or unpredictable behaviour and types can be used to guarantee secure behaviour in systems with a mobile structure. In this thesis we develop algebraic and typebased techniques for behavioural reasoning on probabilistic and mobile processes. In the first part of the thesis we study the algebraic theory of a process calculus which combines both nondeterministic and probabilistic behaviour in the style of Segala and Lynch’s probabilistic automata. We consider various strong and weak behavioural equivalences, and we provide complete axiomatisations for finitestate processes, restricted to guarded recursion in the case of the weak equivalences. In the second part of the thesis we investigate the algebraic theory of the πcalculus under the effect of capability types, which are one of the most useful forms of types in mobile process calculi. Capability types allow one to distinguish between the capability to read from a channel, to write
Migration et Mobilite: Semantique et Applications
 Activity Report
, 2003
"... 2003 Activity Report of Project MIMOSA ..."
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"... Abstract A term terminates if all its reduction sequences are of finite length. We show fourtype systems that ensure termination of welltyped sscalculus processes. Thesystems are obtained by successive refinements of the types of the simply typed A term terminates if all its reduction sequences ar ..."
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Abstract A term terminates if all its reduction sequences are of finite length. We show fourtype systems that ensure termination of welltyped sscalculus processes. Thesystems are obtained by successive refinements of the types of the simply typed A term terminates if all its reduction sequences are of finite length. As faras programming languages are concerned, termination means that computation
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"... Abstract A term terminates if all its reduction sequences are of finite length. We show fourtype systems that ensure termination of welltyped sscalculus processes. Thesystems are obtained by successive refinements of the types of the simply typed A term terminates if all its reduction sequences ar ..."
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Abstract A term terminates if all its reduction sequences are of finite length. We show fourtype systems that ensure termination of welltyped sscalculus processes. Thesystems are obtained by successive refinements of the types of the simply typed A term terminates if all its reduction sequences are of finite length. As faras programming languages are concerned, termination means that computation