Read e-book online Applied Semantics: International Summer School, APPSEM 2000 PDF

Read e-book online Applied Semantics: International Summer School, APPSEM 2000 PDF

By Gilles Barthe, Peter Dybjer, Luis Pinto, João Saraiva

This ebook is predicated on fabric awarded on the overseas summer season college on utilized Semantics that came about in Caminha, Portugal, in September 2000. We goal to offer a few contemporary advancements in programming language learn, either in semantic conception and in implementation, in a chain of graduate-level lectures. the college used to be backed by way of the ESPRIT operating crew 26142 on utilized Semantics(APPSEM),whichoperatedbetweenApril1998andMarch2002.The function of this operating crew was once to compile major reseachers, either in semantic concept and in implementation, with the speci?c target of bettering the communique among theoreticians and practitioners. TheactivitiesofAPPSEMwerestructuredintonineinterdisciplinarythemes: A: Semantics for object-oriented programming B: software structuring C: Integration of useful languages and facts assistants D: Veri?cation equipment E: automated software transformation F: video games, sequentiality, and summary machines G: forms 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 subsequent common issues: – description of current programming language beneficial properties; – layout of recent programming language beneficial properties; – implementation and research of programming languages; – transformation and iteration of courses; – veri?cation of courses. The chapters during this quantity provide examples of contemporary advancements overlaying a vast variety of issues of curiosity to APPSEM.

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Read or Download Applied Semantics: International Summer School, APPSEM 2000 Caminha, Portugal, September 9–15, 2000 Advanced Lectures PDF

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Extra resources for Applied Semantics: International Summer School, APPSEM 2000 Caminha, Portugal, September 9–15, 2000 Advanced Lectures

Sample text

We can reach the same goal (of avoiding any multiplication by 0) using CPS (cf. Remark 3).

Let us write A, B, C, . . terms of type ∗ and K, L, M, . . terms of type ✷. Let Λ be the set of pure (open) λ-terms. The sort ∗ is interpreted by {∅, Λ}, so that [[A]] is ∅ or Λ. x ∈ Λ. L]] to be the set of all functions α such that if t ∈ [[A]] then α(t) ∈ [[L]]x:=t ; – application is defined in the obvious way. B]] are either ∅ or Λ. Now we reason by contradiction to prove that ΓB is not instantiable by closed expressions B, 0, 1, h. If it were, we would have [[B]] = Λ because [[B]] is inhabited.

A → x) → (B → x) → x) λA:∗. (A → ⊥) λA, B : ∗:∧ (A → B) (B → A). λT:∗λx, y:∗. ΠP : T → ∗. (P x) → (P y). Fig. 7. Second-order encoding of logic 6. The Berardi-Paulin embedding. ]. can be used as a foundation for extracting programs from proofs: =x [x]Γ x ∈ V ∪ {∗, ✷} [Πx: A. B]Γ = if Γ A : ∗ and Γ [B]Γ Πx: [A]Γ . [B]Γ,x:A otherwise B:✷ [λx:A. M ]Γ = [M ]Γ,x:A λx:[A]Γ . [M ]Γ if Γ A : ∗ and Γ otherwise [M N ]Γ = [M ]Γ [M ]Γ [N ]Γ if Γ M : A : ✷ and Γ otherwise [ ] = [Γ, x : A] = [Γ ], x : [A]Γ M :B:✷ N :B:∗ Show that if Γ M : A is derivable in λC then [Γ ] [M ]Γ : [A]Γ is derivable in λω.

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