Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.

....because of their various applications in computer science. To give the reader a taste for these applications, we list a few. Davies and Pfenning [DP96] use the # modality to give a # calculus for computation in stages. The idea is that a term #t represents a delayed computation. Ghani et al. [GdPR98] investigate refinements of this calculus which are suitable for the design of abstract machines. Similar ideas relating # with staged evaluation and the distinction between run time and compile time semantics have been developed by Moggi et.al. BMTS99] Despeyroux and Pfenning [DPS97] use a box ....

Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.

....direction, we believe that the techniques developed in this paper, are applicable to other calculi. For example, there has recently been an interest in using the modal operator 2 within the context of two level languages. We believe that our work will be of bene t here and our recent paper [10] provides justi cation for this view. Acknowledgements This research was funded by the EPSRC grant GR L28296 under the title The eXplicit Substitution Linear Abstract Machine . ....

N. Ghani, V. de Paiva, and E. Ritter. Explicit substitutions for constructive necessity. In Proc. of ICALP'98, volume 1443 of Lecture Notes in Computer Science, pages 743-754, 1998.

....logic and to appropriate classes of categories are widely known. In this note we pursue an analogous correspondence for a basic intuitionistic (or constructive) modal logic IKwith both necessity (2) and possibility (3) operators. Similar work for intuitionistic S4 (IS4) has appeared in [BdP00, AMPR01, GdPR98]. This is a natural logic to consider, if one is determined to push the frontiers of the CurryHoward Isomorphism, as far as they will go. Modal system K is less symmetric than S4 as far as the modality rules are concerned. Modal S4 has introduction and elimination rules for both necessity and ....

....j ; x: A x: A ; x: Aj x: 2A j N : 2A j a: A M : A j Box M with N for a: 2A j M : 2A ; x: Aj N : B j Unbox M for 2x in N : B where by a: A we mean a 1 : A 1 ; a 2 : A 2 ; a n : A n . 10 Note that, unlike our previous work on dual context S4[GdPR98], here the right hand side of the context does not mean without a box. Actually the left side means with at least one box, possibly more. So there might be boxed formulas on the right hand side of the context. For the reduction rules we consider only rules and commuting conversions. We have one ....

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Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.

....because of their various applications in computer science. To give the reader a taste for these applications, we list a few. Davies and Pfenning [DP96] use the # modality to give a calculus for computation in stages. The idea is that a term #t represents a delayed computation. Ghani et al. [GdPR98] investigate refinements of this calculus which are suitable for the design of abstract machines. Similar ideas relating # with staged evaluation and the distinction between run time and compile time semantics have been developed by Moggi et.al. BMTS99] Despeyroux and Pfenning [DPS97] use a box ....

Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.

....because of their various applications in computer science. To give the reader a taste for these applications, we list a few. Davies and Pfenning [DP96] use the 2 modality to give a calculus for computation in stages. The idea is that a term 2t represents a delayed computation. Ghani et al. [GdPR98] investigate refinements of this calculus which are suitable for the design of abstract machines. Similar ideas relating 2 with staged evaluation and the distinction between run time and compile time semantics have been developed by Moggi et.al. BMTS99] Despeyroux and Pfenning [DPS97] use a box ....

Neil Ghani, Valeria de Paiva, and Eike Ritter. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98, 1998.

....the techniques developed in this paper, are applicable to other calculi. For example, there has recently been an interest in using Linear Explicit Substitutions 27 the modal operator 2 within the context of two level languages. We believe that our work will be of benefit here and our recent paper [10] provides justification for this view. Acknowledgements This research was funded by the EPSRC grant GR L28296 under the title The eXplicit Substitution Linear Abstract Machine . ....

N. Ghani, V. de Paiva, and E. Ritter. Explicit substitutions for constructive necessity. In Proc. of ICALP'98, volume 1443 of Lecture Notes in Computer Science, pages 743--754, 1998.

....2 and 3 modalities. There are several computational interpretations of the constructive modalities 2 and 3. Davies and Pfenning (Davies and Pfenning 1996) use the 2 modality to give a calculus for computation in stages. The idea is that a term 2t represents a delayed computation. Ghani et al.(Ghani et al. 1998) investigate refinements of this calculus which are suitable for the design of abstract machines. Despeyroux and Pfenning (Despeyroux et al. 1997) use a box modality to encode higher order abstract syntax in theoremprovers like Elf and Isabelle. Still another use of the 2 modality, to model the ....

Ghani, Neil, Valeria de Paiva, and Eike Ritter. 1998. Explicit Substitutions for Constructive Necessity. In Proceedings ICALP'98.

....to the process of normalizing natural deduction proofs. There are several computational interpretations of the modalities 2 and 3. Davies and Pfenning [5] use the 2 modality to give a calculus for computation in stages. The idea is that a term 2t represents a delayed computation. Ghani et al.[10] investigate refinements of this calculus which are suitable for the design of abstract machines. Despeyroux and Pfenning [6] use a box modality to encode higher order abstract syntax in theorem provers like Elf and Isabelle. Still another use of the 2 modality, to model the quote mechanism of ....

N. Ghani and V. de Paiva and E. Ritter. Explicit substitutions for constructive necessity. In Proceedings ICALP'98, 1998.

....direction, we believe that the techniques developed in this paper, are applicable to other calculi. For example, there has recently been an interest in using the modal operator 2 within the context of twolevel languages. We believe that our work will be of benefit here and our recent paper [8] provides justification for this view. ....

N. Ghani, V. de Paiva, and E. Ritter. Explicit substitutions for constructive necessity. In Proc. of ICALP'98, volume 1443 of Lecture Notes in Computer Science, pages 743--754, 1998.

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