By Gilles Barthe, Peter Dybjer, Luis Pinto, João Saraiva
This publication is predicated on fabric provided on the foreign summer time college on utilized Semantics that happened in Caminha, Portugal, in September 2000. We objective to give a few fresh advancements in programming language study, either in semantic concept and in implementation, in a chain of graduate-level lectures. the varsity was once subsidized via the ESPRIT operating crew 26142 on utilized Semantics(APPSEM),whichoperatedbetweenApril1998andMarch2002.The function of this operating team was once to assemble best reseachers, either in semantic conception and in implementation, with the speci?c target of bettering the communique among theoreticians and practitioners. TheactivitiesofAPPSEMwerestructuredintonineinterdisciplinarythemes: A: Semantics for object-oriented programming B: application structuring C: Integration of sensible languages and facts assistants D: Veri?cation tools E: computerized application transformation F: video games, sequentiality, and summary machines G: kinds and kind inference in programming H: Semantics-based optimization I: area concept and genuine quantity computation those topics have been identi?ed as promising for pro?table interplay among semantic concept and perform, and have been selected to give a contribution to the next common subject matters: – description of latest programming language beneficial properties; – layout of latest programming language beneficial properties; – implementation and research of programming languages; – transformation and new release of courses; – veri?cation of courses. The chapters during this quantity provide examples of contemporary advancements overlaying a huge diversity of subject matters of curiosity to APPSEM.
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Extra resources for Applied Semantics: International Summer School, APPSEM 2000 Caminha, Portugal, September 9–15, 2000 Advanced Lectures
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65]. 4 to natural numbers by casting N as a small type and deﬁning N as the smallest set of terms containing neutral terms, 0 and such that, if t N then s t N. Notice that this deﬁnition is inductive. Streams. The small type S : ∗ of streams of booleans has two destructors hd : S → B and tl : S → S. Furthermore, the type S comes equipped with a corecursor RS that can be used to deﬁne constructions on streams. The typing rule for RS is x:X Γ a:X→B Γ a :X→X Γ Γ RS (a, a , x) : S and its reduction rules are hd (RS (x, a, a )) → a x tl (RS (x, a, a )) → RS (a x, a, a ) 24 Gilles Barthe and Thierry Coquand This deﬁnition of streams is closely related to the encoding of abstract datatypes with existential types of J.