By Gilles Barthe, Peter Dybjer, Luis Pinto, João Saraiva
This ebook is predicated on fabric provided on the overseas summer time college on utilized Semantics that came about in Caminha, Portugal, in September 2000. We goal to offer a few contemporary advancements in programming language examine, either in semantic thought and in implementation, in a chain of graduate-level lectures. the varsity was once backed through the ESPRIT operating crew 26142 on utilized Semantics(APPSEM),whichoperatedbetweenApril1998andMarch2002.The function of this operating workforce used to be to compile prime reseachers, either in semantic conception and in implementation, with the speci?c objective of enhancing the conversation among theoreticians and practitioners. TheactivitiesofAPPSEMwerestructuredintonineinterdisciplinarythemes: A: Semantics for object-oriented programming B: application structuring C: Integration of practical languages and facts assistants D: Veri?cation tools E: computerized software transformation F: video games, sequentiality, and summary machines G: varieties and kind inference in programming H: Semantics-based optimization I: area concept and genuine quantity computation those issues have been identi?ed as promising for pro?table interplay among semantic thought and perform, and have been selected to give a contribution to the next basic themes: – description of current programming language good points; – layout of recent programming language gains; – implementation and research of programming languages; – transformation and iteration of courses; – veri?cation of courses. The chapters during this quantity supply examples of contemporary advancements protecting a large diversity of subject matters of curiosity to APPSEM.
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Additional info for Applied Semantics: International Summer School, APPSEM 2000 Caminha, Portugal, September 9–15, 2000 Advanced Lectures
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The small type N : ∗ of natural numbers has two constructors 0 : N and s : N → N. Furthermore, the type N comes equipped with a recursor RN that can be used to deﬁne functions and prove properties on natural numbers. The typing rule for RN is Γ a : T (0) Γ a : Πx: N. T (x) → T (s x) Γ Γ n:N RN (n, a, a ) : T (n) and its reduction rules are RN (0, a, a ) → a RN (s n, a, a ) → a n RN (n, a, a ) Observe that the usual rule for recursion can be recovered by setting T to be non-dependent: in this case, we get that RN (n, a, a ) : T provided n : N, a : T and a : N → T → T .
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