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Modal Intersection Types, Two-Level Languages, and Staged Synthesis

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Semantics, Logics, and Calculi

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9560))

Abstract

A typed \(\lambda \)-calculus, \(\lambda ^{\cap \Box }\), is introduced, combining intersection types and modal types. We develop the metatheory of \(\lambda ^{\cap \Box }\), with particular emphasis on the theory of subtyping and distributivity of the modal and intersection type operators. We describe how a stratification of \(\lambda ^{\cap \Box }\) leads to a multi-linguistic framework for staged program synthesis, where metaprograms are automatically synthesized which, when executed, generate code in a target language. We survey the basic theory of staged synthesis and illustrate by example how a two-level language theory specialized from \(\lambda ^{\cap \Box }\) can be used to understand the process of staged synthesis.

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Notes

  1. 1.

    The literature on various fragments and interpretations of modal logic is enormous, and we can not attempt here to do any justice to that broader context of related work. For the immediate context of staged computation the reader is referred to [4], and for comparison with other interpretations related to staging we refer to [5].

  2. 2.

    In the following we will sometimes write explicit type annotations in terms in order to indicate particular typings.

  3. 3.

    In some variants of the intersection type theory there is a special type \(\omega \) which we leave out here.

References

  1. Jones, N.D.: Efficient algebraic operations on programs. In: Proceedings of AMAST 1992, Algebraic Methodology and Software Technology, pp. 393–420. Springer (1992)

    Google Scholar 

  2. Nielson, F., Nielson, H.R.: Two-Level Functional Languages. Cambridge University Press, New York (1992)

    Book  MATH  Google Scholar 

  3. Barendregt, H., Coppo, M., Dezani-Ciancaglini, M.: A filter lambda model and the completeness of type assignment. J. Symb. Log. 48(4), 931–940 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Davies, R., Pfenning, F.: A modal analysis of staged computation. J. ACM 48(3), 555–604 (2001)

    Article  MathSciNet  Google Scholar 

  5. Pfenning, F., Davies, R.: A judgmental reconstruction of modal logic. Math. Struct. Comput. Sci. 11(04), 511–540 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Düdder, B., Martens, M., Rehof, J.: Staged composition synthesis. In: Shao, Z. (ed.) ESOP 2014 (ETAPS). LNCS, vol. 8410, pp. 67–86. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Rehof, J., Vardi, M.Y.: Design and synthesis from components. In: Dagstuhl Seminar 14232. Dagstuhl Reports, vol. 7941 (2014). http://dx.doi.org/10.4230/DagRep.4.6.29

  8. Hindley, J.R., Seldin, J.P.: Lambda-Calculus and Combinators, an Introduction. Cambridge University Press, New York (2008)

    Book  MATH  Google Scholar 

  9. Barendregt, H., Dekkers, W., Statman, R.: Lambda Calculus with Types. Perspectives in Logic. Cambridge University Press, New York (2013)

    Book  Google Scholar 

  10. Boolos, G.: The Logic of Provability. Cambridge University Press, New York (1995)

    Google Scholar 

  11. Ghilezan, S.: Strong normalization and typability with intersection types. Notre Dame J. Form. Log. 37(1), 44–52 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rehof, J.: Towards combinatory logic synthesis. In: BEAT 2013, 1st International Workshop on Behavioural Types. ACM (2013)

    Google Scholar 

  13. Düdder, B., Martens, M., Rehof, J., Urzyczyn, P.: Bounded combinatory logic. In: Proceedings of CSL 2012, vol. 16, pp. 243–258. LIPIcs, Schloss Dagstuhl (2012)

    Google Scholar 

  14. Statman, R.: Intuitionistic propositional logic is polynomial-space complete. Theor. Comput. Sci. 9, 67–72 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  15. Bessai, J., Dudenhefner, A., Düdder, B., Martens, M., Rehof, J.: Combinatory logic synthesizer. In: Margaria, T., Steffen, B. (eds.) ISoLA 2014, Part I. LNCS, vol. 8802, pp. 26–40. Springer, Heidelberg (2014)

    Google Scholar 

  16. Düdder, B., Garbe, O., Martens, M., Rehof, J., Urzyczyn, P.: Using inhabitation in bounded combinatory logic with intersection types for GUI synthesis. In: Proceedings of ITRS (2012)

    Google Scholar 

  17. Düdder, B.: Automatic synthesis of component & connector-software architectures with bounded combinatory logic, Ph.D. thesis, Technische Universitt Dortmund, Fakultät fr Informatik, Dortmund (2014)

    Google Scholar 

  18. Düdder, B., Bessai, J., Dudenhefner, A., Chen, T.C., de’Liguoro, U.: Typing classes and mixins with intersection types. In: Proceedings of ITRS 2014, Intersection Types and Related Systems. EPTCS Electronic Proceedings in Theoretical Computer Science, vol. 177, pp. 79–93. Springer (2014)

    Google Scholar 

  19. Bessai, J., Dudenhefner, A., Duedder, B., De’Liguoro, U., Chen, T.C., Rehof, J.: Mixin composition synthesis based on intersection types. In: Proceedings of TLCA 2015, Typed Lambda Calculi and Applications, Warsaw, June 29–July 3 2015. To appear

    Google Scholar 

  20. Düdder, B., Heineman, G.T., Rehof, J.: Towards migrating object-oriented frameworks to enable synthesis of product line members. In: Proceedings of SPLC 2015, 19th International Software Product Line Conference: New Directions in Systems and Software Product Line Engineering. ACM International Conference Proceeding Series (2015)

    Google Scholar 

  21. Haack, C., Howard, B., Stoughton, A., Wells, J.B.: Fully automatic adaptation of software components based on semantic specifications. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 83–98. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  22. Wells, J.B., Yakobowski, B.: Graph-based proof counting and enumeration with applications for program fragment synthesis. In: Etalle, S. (ed.) LOPSTR 2004. LNCS, vol. 3573, pp. 262–277. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Davies, R., Pfenning, F.: Intersection types and computational effects. In: ICFP, pp. 198–208 (2000)

    Google Scholar 

  24. Dezani-Ciancaglini, M., Giannini, P., Della Rocca, S.R.: Intersection, universally quantified, and reference types. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 209–224. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  25. Dezani-Ciangaglini, M., Ronchi Della Rocca, S.: Intersection and Reference Types. Essays dedicated to Henk Barendregt on the occasion of his 60th birthday, pp. 77–86 (2007)

    Google Scholar 

  26. Rehof, J., Urzyczyn, P.: The complexity of inhabitation with explicit intersection. In: Constable, R.L., Silva, A. (eds.) Logic and Program Semantics, Kozen Festschrift. LNCS, vol. 7230, pp. 256–270. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Acknowledgement

The authors should like to thank Dominic Orchard, Jan Bessai, Boris Düdder and Andrej Dudenhefner for very helpful discussions and comments on the paper.

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Authors and Affiliations

  1. DIKU Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Faculty of Computer Science, Technical University of Dortmund, Dortmund, Germany

    Jakob Rehof

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  1. Fritz Henglein
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  2. Jakob Rehof
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Correspondence to Fritz Henglein .

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Editors and Affiliations

  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Christian W. Probst

  2. Imperial College London, London, United Kingdom

    Chris Hankin

  3. Aalborg University, Aalborg, Denmark

    René Rydhof Hansen

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Henglein, F., Rehof, J. (2016). Modal Intersection Types, Two-Level Languages, and Staged Synthesis. In: Probst, C., Hankin, C., Hansen, R. (eds) Semantics, Logics, and Calculi. Lecture Notes in Computer Science(), vol 9560. Springer, Cham. https://doi.org/10.1007/978-3-319-27810-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-27810-0_15

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  • Online ISBN: 978-3-319-27810-0

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