By Robert Giegerich, Peter Steffen (auth.), Eerke A. Boiten, Bernhard Möller (eds.)
This ebook constitutes the refereed court cases of the sixth foreign convention on arithmetic of application development, MPC 2002, held in Dagstuhl fortress, Germany, in July 2002.
The eleven revised complete papers provided have been rigorously reviewed and chosen for inclusion within the booklet; additionally offered are one invited paper and the abstracts of 2 invited talks. one of the subject matters lined are programming method, application specification, software transformation, programming paradigms, programming calculi, and programming language semantics.
Read or Download Mathematics of Program Construction: 6th International Conference, MPC 2002 Dagstuhl Castle, Germany, July 8–10, 2002 Proceedings PDF
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Additional info for Mathematics of Program Construction: 6th International Conference, MPC 2002 Dagstuhl Castle, Germany, July 8–10, 2002 Proceedings
The proof of the second equality is completely symmetric. (u . . v) is a straightforward application of the fact that relators distribute through composition and commute with converse. ✷ The pair (g , g ) is a perfect Galois connection between the posets ( B , ) and ( C , ≤ ) if g • g is the identity relation on B . Lemma 10. If the base Galois connections deﬁned in lemma 9 are all perfect then so are the constructed Galois connections. Proof. That the base connections are perfect means that fa • ga = Aa and ha • ka = Ca .
Mn−1 . Suppose that we want to determine whether a product of numbers is divisible by k for some given positive number k . m = m/k where m/k is read as “ m is divisible by k ”. The function dk is the lower adjoint in a Galois connection (dk, kd) between ( Bool , ⇐ ) and ( PosInt , / ) where dk ∈ Bool ← PosInt , kd ∈ PosInt ← Bool and / is the is-divisible-by ordering on positive integers. b . ) The pair algebra corresponding to this Galois connection relates all positive integers to the boolean f alse and the positive integers divisible by k to the boolean true .
S. Rattray, T. Rus, and G. Scollo, editors, Proceedings of the 2nd Conference on Algebraic Methodology and Software Technology, AMAST’91, pages 303–326. Springer-Verlag, Workshops in Computing, 1992. Bru95. Peter J. de Bruin. Inductive Types in Constructive Languages. PhD thesis, Rijksuniversiteit Groningen, 1995. BVW92. C. S. Voermans, and J. van der Woude. A relational theory of datatypes. uk/~rcb/MPC/papers. construction, December 1992. CC77. Patrick Cousot and Radhia Cousot. Abstract interpretation: A unifed lattice model for static analysis of programs by construction or approximation of fixpoints.