By Roland Backhouse, Wei Chen, João F. Ferreira (auth.), Claude Bolduc, Jules Desharnais, Béchir Ktari (eds.)

ISBN-10: 3642133207

ISBN-13: 9783642133206

This booklet constitutes the refereed lawsuits of the tenth overseas convention on arithmetic of application development, MPC 2010, held in Québec urban, Canada in June 2010. the nineteen revised complete papers awarded including 1 invited speak and the abstracts of two invited talks have been rigorously reviewed and chosen from 37 submissions. the focal point is on thoughts that mix precision with conciseness, allowing courses to be developed by way of formal calculation. inside this topic, the scope of the sequence is especially diversified, together with programming method, application specification and transformation, application research, programming paradigms, programming calculi, programming language semantics, protection and application logics.

**Read Online or Download Mathematics of Program Construction: 10th International Conference, MPC 2010, Québec City, Canada, June 21-23, 2010. Proceedings PDF**

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**Additional info for Mathematics of Program Construction: 10th International Conference, MPC 2010, Québec City, Canada, June 21-23, 2010. Proceedings**

**Example text**

For imperative programs, speciﬁcations usually consist of preconditions, postconditions and invariants which model the inductive properties implemented in the body of a loop. The correctness of a simple while loop is implied by the following proof obligations: 1. The invariant is established by the initialisation (before the loop starts) 2. Each execution of the loop’s body preserves the invariant, as long as the guard of the loop is true. 3. The invariant establishes the postcondition if the guard of the loop is false.

Our approach extends to heterogeneous relations of type A×B, but this would only overload the presentation. As sets, relations form Boolean algebras and inherit the Boolean operations + of union or join, ∗ of intersection or meet and of complementation; there is an empty relation 0 and a universal relation U = A×A. The relative product x; y of two binary relations x and y is formed by the ordered pairs (a, b) with (a, c) ∈ x and (c, b) ∈ y for some c ∈ A. The converse x∧ of a binary relation x is formed by the ordered pairs (b, a) with (a, b) ∈ x.

It also ignores the operation of converse in y ∧ because y itself does not occur in the code. It therefore uniformly replaces y ∧ by x. Note that this step has little impact on ATP performance. The tool then passes the following postcondition, guard of the loop and invariant to Prover9; it ignores the trivial precondition: guard(x,v,w) <-> -(x;w<=w). post(x,v,w) <-> w=rtc(x);v. inv(x,v,w) <-> v<=w & w<=rtc(x);v. The postcondition says that upon termination the vector w stores all those vertices that are linked by an arrow in the reﬂexive transitive closure of x to a vertex in v.

### Mathematics of Program Construction: 10th International Conference, MPC 2010, Québec City, Canada, June 21-23, 2010. Proceedings by Roland Backhouse, Wei Chen, João F. Ferreira (auth.), Claude Bolduc, Jules Desharnais, Béchir Ktari (eds.)

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