Abstract
The purpose of this article is to illustrate some technical difficulties encountered when trying to extend a logical relation to the Hoare powerdomain. We give a partial solution and some applications. Our vehicle is a simple call-by-value programming language with binary nondeterministic choice. We define both a big-step operational semantics and a denotational semantics using the Hoare powerdomain. Using our logical relation we then show equivalence of the two semantics in the sense of computational adequacy and some type-dependent program equivalences.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S., Jung, A.: Domain theory. Online Lecture Notes, avaliable from CiteSeerX (1994)
Amadio, R.M., Cardelli, L.: Subtyping recursive types, pp. 575–631 (1993)
Benton, N., Hofmann, M., Nigam, V.: Abstract effects and concurrency (under review 2014)
Birkedal, L., Sieczkowski, F., Thamsborg, J.: A concurrent logical relation. In: Cégielski, P., Durand, A. (eds.) CSL. LIPIcs, vol. 16, pp. 107–121. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2012)
Broy, M., Gnatz, R., Wirsing, M.: Semantics of nondeterministic and noncontinuous constructs. In: Gerhart, S.L., et al. (eds.) Program Construction. LNCS, vol. 69, pp. 553–592. Springer, Heidelberg (1979)
Broy, M., Wirsing, M.: On the algebraic specification of nondeterministic programming languages. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 162–179. Springer, Heidelberg (1981)
Katsumata, S.-y.: Relating computational effects by ⊤ ⊤-lifting. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 174–185. Springer, Heidelberg (2011)
Krivine, J.-L.: Classical logic, storage operators and second-order lambda-calculus. Ann. Pure Appl. Logic 68(1), 53–78 (1994)
Plotkin, G.D.: A powerdomain construction. SIAM J. Comput. 5(3), 452–487 (1976)
Plotkin, G.D.: “lcf” considered as a programming language. Theor. Comput. Sci. 5(3), 223–255 (1977)
Sieber, K.: Call-by-value and nondeterminism. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664, pp. 376–390. Springer, Heidelberg (1993)
Smyth, M.B., Plotkin, G.D.: The category-theoretic solution of recursive domain equations. SIAM J. Comput. 11(4), 761–783 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hofmann, M. (2015). Logical Relations and Nondeterminism. In: De Nicola, R., Hennicker, R. (eds) Software, Services, and Systems. Lecture Notes in Computer Science, vol 8950. Springer, Cham. https://doi.org/10.1007/978-3-319-15545-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-15545-6_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15544-9
Online ISBN: 978-3-319-15545-6
eBook Packages: Computer ScienceComputer Science (R0)