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A Modal Analysis of Staged Computation
 JOURNAL OF THE ACM
, 1996
"... We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of functional languages. Our main technical result is a conservative embedding of Nielson & Nielson's twolevel functional la ..."
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Cited by 213 (23 self)
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We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of functional languages. Our main technical result is a conservative embedding of Nielson & Nielson's twolevel functional language in our language MiniML, which in
Logical Foundations of Eval/Quote Mechanisms, and the Modal Logic S4
 IN PRESS S15708683(05)000431/FLA AID:71 Vol.•••(•••) [DTD5] P.12 (112) JAL:m1a v 1.40 Prn:15/07/2005; 8:08 jal71 by:SL p. 12 12 N. Alechina, D. Shkatov / Journal of Applied Logic
, 1997
"... Starting from the idea that cut elimination is the precise meaning of program execution, we design two languages of constructions for the minimal logic S4, yielding calculi with idealized versions of Lisp's eval and quote. The first, the S4 calculus, is based on Bierman and De Paiva's ..."
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Cited by 5 (0 self)
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Starting from the idea that cut elimination is the precise meaning of program execution, we design two languages of constructions for the minimal logic S4, yielding calculi with idealized versions of Lisp's eval and quote. The first, the S4 calculus, is based on Bierman and De Paiva's proposal, and has all desirable logical properties, except for its nonoperational flavor. The second, the evQcalculus, is more complicated, but has a clear operational meaning: it is a tower of interpreters in the style of Lisp's reflexive tower. Remarkably, this language was developed from purely logical principles, but nonetheless provides some operational insight into eval/quote mechanisms. 1 Introduction Let's consider two dual questions. The first is: is there a proofsasprograms, formulasas types correspondence for the modal logic S4? There is one between minimal and intuitionistic logics and  calculi [How80], and also for classical logic [Gri90] or linear logic [Abr93], so why not S4? A...
A Few Remarks on SKInT
, 1998
"... SKIn and SKInT are two firstorder languages that have been proposed recently by Healfdene Goguen and the author. While SKIn encodes lambdacalculus reduction faithfully, standardizes and is confluent even on open terms, it normalizes only weakly in the simplytyped case. On the other hand, SKInT n ..."
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Cited by 3 (1 self)
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SKIn and SKInT are two firstorder languages that have been proposed recently by Healfdene Goguen and the author. While SKIn encodes lambdacalculus reduction faithfully, standardizes and is confluent even on open terms, it normalizes only weakly in the simplytyped case. On the other hand, SKInT normalizes strongly in the simplytyped case, standardizes and is confluent on open terms, and also encodes lambdacalculus reduction faithfully, although in a less direct way. This report has two goals. First, we show that the natural simple type system for SKInT, seen as a natural deduction system, is not exactly a proof system for intuitionistic logic, but for a very close fragment of the modal logic S4, in which intuitionistic logic is easily coded. This explains why the SKIn and SKInT typing rules are different, and why SKInT encodes lambdacalculus in a less direct way than SKIn. Second, we show that SKInT, like AE and a few other calculi of explicit substitutions, preserves strong nor...
On Computational Interpretations of the Modal Logic S4
"... ap por t de r ech er ch e ..."
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A Proof of Weak Termination of the SimplyTyped λσCalculus
, 1997
"... : We show that reducing any simplytyped oeterm by applying the rules in oe eagerly always terminates, by a translation to the simplytyped calculus, and similarly for oe * terms with oe * eager rewrites. This holds even with term and substitution metavariables. In fact, every reduction termina ..."
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: We show that reducing any simplytyped oeterm by applying the rules in oe eagerly always terminates, by a translation to the simplytyped calculus, and similarly for oe * terms with oe * eager rewrites. This holds even with term and substitution metavariables. In fact, every reduction terminates provided that (fi)redexes are only contracted under socalled safe contexts. The previous results follow because in oe, resp. oe *normal forms, all contexts around terms of sort T are safe. Keywords: oecalculus, explicit substitutions, termination, calculus, simple types (R'esum'e : tsvp) Jean.Goubault@inria.fr Unit'e de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) T'el'ephone : (33 1) 39 63 55 11  T'el'ecopie : (33 1) 39 63 53 Une preuve de terminaison faible du oecalcul simplement typ'e R'esum'e : Nous montrons que r'eduire n'importe quel oeterme simplement typ'e en appliquant toujours les r`egles de oe le plus...
General Terms: Languages,Theory
"... We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λcalculi and functionallanguages. We directly demonstrate the sense in which our λ→2 ecalculus captures staging, and also g ..."
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We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λcalculi and functionallanguages. We directly demonstrate the sense in which our λ→2 ecalculus captures staging, and also give a conservative embedding of Nielson & Nielson’s twolevel functional language in our functional language MiniML2, thus proving that bindingtime correctness is equivalent to modal correctness on this fragment. In addition, MiniML2 can also express immediate evaluation and sharing of code across multiple stages, thus supporting runtime code generation as well as partial evaluation.
F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic—lambda calculus and
"... Abstract. We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed �calculi and functional languages. We directly demonstrate the sense in which our � e 3 �calculus captures stagin ..."
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Abstract. We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed �calculi and functional languages. We directly demonstrate the sense in which our � e 3 �calculus captures staging, and also give a conservative embedding of Nielson and Nielson’s twolevel functional language in our functional language MiniML � , thus proving that bindingtime correctness is equivalent to modal correctness on this fragment. In addition, MiniML � can also express immediate evaluation and sharing of code across multiple stages, thus supporting runtime code generation as well as partial evaluation.
A Model for Knowledge Representation in Distributed Systems
, 2002
"... this article, we present a simplified formalism of distributed systems in order to show some concepts which we think are important in the study of the flow of information between different parts or agents of a system. Then, we use those 1 basic concepts and generalize them to define an algebraic fr ..."
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this article, we present a simplified formalism of distributed systems in order to show some concepts which we think are important in the study of the flow of information between different parts or agents of a system. Then, we use those 1 basic concepts and generalize them to define an algebraic framework for formalizing distributed systems. Finally, we study the logical structure of this framework and show that in this formalism, the distributed systems form a model for the intuitionistic modal logic IS4+KV