Mathematics of Program Construction: 5th International by Mark P. Jones (auth.), Roland Backhouse, José Nuno Oliveira

By Mark P. Jones (auth.), Roland Backhouse, José Nuno Oliveira (eds.)

This quantity comprises the complaints of MPC 2000, the ?fth overseas c- ference on arithmetic of application development. This sequence of meetings goals to advertise the advance of mathematical rules and methods which are demonstrably helpful and usable within the means of developing c- puter courses (whether applied in or software). the point of interest is on recommendations that mix precision with concision, allowing courses to be built by means of formal calculation. inside of this topic, the scope of the sequence is especially varied, together with programming method, application speci?cation and transformation, programming paradigms, programming calculi, and progr- ming language semantics. the standard of the papers submitted to the convention was once mostly very excessive. However,the variety of submissions has lowered in comparison to the pre- ous meetings within the sequence. each one paper used to be refereed by way of a minimum of ?ve and sometimes extra committee contributors. in an effort to continue the excessive criteria of the c- ference the committee took a stringent view on caliber; this has intended that, on occasion, a paper was once rejected even if there has been a foundation for an excellent c- ference or magazine paper however the submitted paper didn't meet the committee’s required criteria. In a couple of circumstances a superb paper was once rejected on account that it didn't ?t in the scope of the conference.

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Additional info for Mathematics of Program Construction: 5th International Conference, MPC 2000, Ponte de Lima, Portugal, July 3-5, 2000 Proceedings

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28 13. Erik Meijer, Maarten Fokkinga, and Ross Paterson. Functional programming with bananas, lenses, envelopes and barbed wire. In John Hughes, editor, Functional Programming Languages and Computer Architecture, pages 124–144. Springer Verlag, June 1991. LNCS 523. 28, 40, 42 14. Atsushi Ohori. A polymorphic record calculus and its compilation. ACM Transactions on Programming Languages and Systems, 17(6):844–895, November 1995. 42 15. Simon Peyton Jones and Erik Meijer. Henk: a typed intermediate language.

In this paper, p, q, and Q range over predicates, with complements p, q, and Q. It is easy to show that the predicates form a Boolean algebra, with + as disjunction, · as conjunction, 0 as false, 1 as true, complementation as negation, and ≤ as implication. , p q = q p) are used silently in proofs, as is the fact x p y = 0 =⇒ x y = x p y Unlike previous axiomatizations of omega-regular languages, the omega algebra axioms support several interesting programming models, where (intuitively) 0 is magic, 1 is skip, + is chaotic nondeterministic choice, · is sequential composition, ≤ is refinement, x∗ is executed by executing x any finite number of times, and xω is executed by executing x an infinite number of times.

We use induction on the derivation of u :: κ. Case u = c: the statement holds trivially since R relates constants. Case u = x : the statement holds since η1 and η2 are related. Case u = t1 t2 : by the induction hypothesis, we have (poly 1 t1 η1 , poly 2 t1 η2 ) ∈ R κ1 → κ2 (t1 θ1 ) . . (t1 θn ) ≡ ∀x1 . . xn ∀v1 v2 (v1 , v2 ) ∈ R κ1 x1 . . xn ⊃ ((poly 1 t1 η1 ) v1 , (poly 2 t1 η2 ) v2 ) ∈ R κ2 ((t1 θ1 ) x1 ) . . ((t1 θn ) xn ) and (poly 1 t2 η1 , poly 2 t2 η2 ) ∈ R κ1 (t2 θ1 ) . . (t2 θn ) , 22 Ralf Hinze which implies (poly 1 t1 t2 η1 , poly 2 t1 t2 η2 ) ∈ R κ2 ((t1 t2 )θ1 ) .

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