Download e-book for kindle: 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.)

ISBN-10: 3540677275

ISBN-13: 9783540677277

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 improvement of mathematical rules and methods which are demonstrably precious and usable within the means of developing c- puter courses (whether applied in or software). the point of interest is on ideas that mix precision with concision, allowing courses to be developed via formal calculation. inside of this subject, the scope of the sequence is particularly different, together with programming technique, 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 regularly 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 through at the least ?ve and infrequently extra committee contributors. for you to preserve the excessive criteria of the c- ference the committee took a stringent view on caliber; this has intended that, often times, a paper was once rejected even supposing there has been a foundation for an outstanding c- ference or magazine paper however the submitted paper didn't meet the committee’s required criteria. In a number of instances an outstanding paper used to be rejected due to the fact 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

Sample text

A:×I :I . i→+I a . Πb: . 22 ”. 3 Type Checking There are numerous properties, such as subject reduction, which are true of Pure Type Systems in general [2]. There are also known type checking algorithms for certain subclasses of PTSs. Although the zip calculus is not a PTS, it is hoped that most results for PTSs will carry over to the “almost PTS” zip calculus. A PTS is functional when the relations A and R are functions (c : s1 ∈ A and c : s2 ∈ A imply s1 = s2 ; (s, t, u1 ) ∈ R and (s, t, u2 ) ∈ R imply u1 = u2 ).

Another example is the derivation of a law, called Abides: case λx. a1,b1 , λy. b2 x Its derivation is case λx. a1,b1 , λy. a2,b2 x = (case λx. a1,b1 , λy. 1 , (case λx. a1,b1 , λy. 2 = (case λx. 1, λy. 1 x) , (case λx. 2, λy. b2 x {× eta } {inst, twice } {× reduce, four times } Here is a generic version of Abides case i λy. j y x = j case i λy. j y x and its derivation is case i λy. j y x {n-tuple eta } = j (case i λy. j = j case i λy. j x = j case i λy. j y {inst } {n-tuple reduce } x which corresponds directly to the non-generic derivation above.

B: . 22 ”. 3 Type Checking There are numerous properties, such as subject reduction, which are true of Pure Type Systems in general [2]. There are also known type checking algorithms for certain subclasses of PTSs. Although the zip calculus is not a PTS, it is hoped that most results for PTSs will carry over to the “almost PTS” zip calculus. A PTS is functional when the relations A and R are functions (c : s1 ∈ A and c : s2 ∈ A imply s1 = s2 ; (s, t, u1 ) ∈ R and (s, t, u2 ) ∈ R imply u1 = u2 ).

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Mathematics of Program Construction: 5th International Conference, MPC 2000, Ponte de Lima, Portugal, July 3-5, 2000 Proceedings by Mark P. Jones (auth.), Roland Backhouse, José Nuno Oliveira (eds.)


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