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Intersection types for explicit substitutions
, 2003
"... We present a new system of intersection types for a compositionfree calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical inte ..."
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Cited by 17 (6 self)
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We present a new system of intersection types for a compositionfree calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.
A typetheoretic foundation of delimited continuations. Higher Order Symbol
 Comput
, 2009
"... Abstract. There is a correspondence between classical logic and programming language calculi with firstclass continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a finegrained analysis of control delimiters a ..."
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Cited by 14 (6 self)
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Abstract. There is a correspondence between classical logic and programming language calculi with firstclass continuations. With the addition of control delimiters, the continuations become composable and the calculi become more expressive. We present a finegrained analysis of control delimiters and formalise that their addition corresponds to the addition of a single dynamicallyscoped variable modelling the special toplevel continuation. From a type perspective, the dynamicallyscoped variable requires effect annotations. In the presence of control, the dynamicallyscoped variable can be interpreted in a purely functional way by applying a storepassing style. At the type level, the effect annotations are mapped within standard classical logic extended with the dual of implication, namely subtraction. A continuationpassingstyle transformation of lambdacalculus with control and subtraction is defined. Combining the translations provides a decomposition of standard CPS transformations for delimited continuations. Incidentally, we also give a direct normalisation proof of the simplytyped lambdacalculus with control and subtraction.
Strong normalisation of Herbelin's explicit substitution calculus with substitution propagation
"... . Herbelin presented (at CSL'94) a simple sequent calculus for minimal implicational logic, extensible to full rstorder intuitionistic logic, with a complete system of cutreduction rules which is both conuent and strongly normalising. Some of the cut rules may be regarded as rules to construct exp ..."
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Cited by 5 (0 self)
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. Herbelin presented (at CSL'94) a simple sequent calculus for minimal implicational logic, extensible to full rstorder intuitionistic logic, with a complete system of cutreduction rules which is both conuent and strongly normalising. Some of the cut rules may be regarded as rules to construct explicit substitutions. He observed that the addition of a cut permutation rule, for propagation of such substitutions, breaks the proof of strong normalisation; the implicit conjecture is that the rule may be added without breaking strong normalisation. We prove this conjecture, thus showing how to model betareduction in his calculus (extended with rules to allow cut permutations). 1 Introduction Herbelin gave in [5] a calculus for minimal implicational logic, using a notation for proof terms that, in contrast to the usual lambdacalculus notation for natural deduction, brings head variables to the surface. It is thus a sequent calculus, with the nice feature that its cutfree terms are in ...