By María Alpuente, Marco Comini, Santiago Escobar, Moreno Falaschi, Salvador Lucas (auth.), Michael Leuschel (eds.)

This ebook constitutes the completely refereed post-proceedings of the twelfth foreign Workshop on common sense dependent software Synthesis and Transformation, LOPSTR 2002, held in Madrid, Spain in September 2002.

The 15 revised complete papers offered including 7 abstracts have been conscientiously chosen in the course of rounds of reviewing and revision from forty submissions. The papers are equipped in topical sections on debugging and kinds, tabling and constraints, summary interpretation, application refinement, verification, partial review, and rewriting and object-oriented development.

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Additional resources for Logic Based Program Synthesis and Transformation: 12th International Workshop, LOPSTR 2002, Madrid, Spain, September 17–20, 2002. Revised Selected Papers

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Gabbay, T. S. ), Handbook of Logic in Computer Science, Oxford University Press, 1992, Ch. 2, pp. 117–309. 3. F. Pfenning, Logical frameworks, in: A. Robinson, A. ), Handbook of Automated Reasoning, Vol. II, Elsevier Science, 2001, Ch. 17, pp. 1063–1147. 4. H. Barendregt, H. Geuvers, Proof-assistants using dependent type systems, in: A. Robinson, A. ), Handbook of Automated Reasoning, Vol. II, Elsevier Science, 2001, Ch. 18, pp. 1149–1238. 5. G. Gentzen, Untersuchungen u ¨ ber das Logische Schliessen, Math.

Three cases are now distinguished: This theorem holds for every system satisfying correctness of contexts, the (var) rule, thinning, and strengthening. A Cut-Free Sequent Calculus for Pure Type Systems 27 1. y = y with y : ∈ ∆. R◦ ∈ Γ, ∆◦ , and since we had ◦ S =β R◦ [t := q ◦ ] and (11), by applying the (κ) rule we get Γ, ∆◦ cf m◦ [x := y q ◦ ] : M ◦ [x := y q ◦ ]. However x = x; then we can apply the substitution lemma of the untyped λ-calculus to get Z ◦ [x := y q ◦ ] ≡ Z[x := y q]◦ , which completes the proof (10).

An ) ∧ ¬(b1 ∨ . . ∨ bm ). – If this test fails then the rule Baselhs ∪ Clhs ⇒ {d} is valid. Since answers only contain primitive constraints and since the set of primitive constraints is closed under negation, then we can perform the satisfiability test by rewriting (a1 ∨. ∨an )∧¬(b1 ∨. ∨bm ) into an equivalent disjunctive normal form, and then use the solver for primitive constraints on each sub-conjunctions. It should be noticed that in cases where the evaluation of one of the two goals does not terminate before the bound of resolution depth is reached then Baselhs ∪ Clhs ⇒ {d} is not considered as valid and the next rule is processed.

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