Download Lambda-calculus, types and models by Jean-Louis Krivine, Rene Corvi (translator) PDF

  • admin
  • March 28, 2017
  • Nonfiction 5
  • Comments Off on Download Lambda-calculus, types and models by Jean-Louis Krivine, Rene Corvi (translator) PDF

By Jean-Louis Krivine, Rene Corvi (translator)

Show description

Read or Download Lambda-calculus, types and models PDF

Best nonfiction_5 books

The Autopoiesis of Architecture: A New Framework for Architecture, volume 1

Take a theoretical method of structure with The Autopoiesis of structure, which offers the subject as a self-discipline with its personal certain good judgment. Architecture's notion of itself is addressed in addition to its improvement inside of wider modern society. writer Patrik Schumacher bargains cutting edge therapy that enriches architectural thought with a coordinated arsenal of thoughts facilitating either particular research and insightful comparisons with different domain names, equivalent to paintings, technological know-how and politics.

Feminism, Family, and Identity in Israel: Women's Marital Names

One of many much less mentioned achievements of the women’s stream is the choice to reject the patronymic naming procedure (or the conference of ladies changing their very own kin names through their husbands’ names after they get married). This ebook deals an research of Israeli women’s naming practices whereas tracing vocabularies of nationalism, orientalism and individualism in women’s debts.

Extra info for Lambda-calculus, types and models

Example text

Tn } (this is indeed a saturated subset of Λ). It follows from this definition that x ∈ |B1 , . . , Bn → X|I . Thus : x ∈ | ni=1 Ai ∧ (B1 , . . , Bn → X)|I . Let v ∈ |X|I , with no free variables but x1 , . . , xk . Then v reduces to (x)t1 . . tn by leftmost β-reduction ; we have ti ∈ |Bi |I and therefore, by induction hypothesis, ti ti , where ti is an η-reduced image of ti . Hence v (x)t1 . . tn , which is clearly an η-reduced image of t = (x)t1 . . tn . So we have shown that the interpretation I satisfies all the required properties with respect to the given principal typing of t.

As an immediate consequence, we have : If A is a trivial type, then its value |A|I under any interpretation I is the whole set Λ. 6. Let N0 , N be subsets of Λ, with the following properties : N is saturated, N0 ⊂ N , N0 ⊂ (Λ → N0 ), N ⊃ (N0 → N ). Let I be the interpretation such that |X|I = N for every type variable X. Then |A|I ⊃ N0 for every type A, and |A|I ⊂ N for every non-trivial type A. We first prove, by induction on A, that |A|I ⊃ N0 ; this is obvious whenever A is a type variable, or A = Ω, or A = B ∧ C.

Yl (y)v1 . . vp be another head normal form of t. 24, there exists a term t2 which can be obtained by βreduction from t0 as well as from t1 . Now, in t0 (resp. t1 ) all possible β-reductions have to be made in u1 , . . , un (resp. v1 , . . , vp ). Hence : t2 ≡ λx1 . . λxk (x)u1 . . un ≡ λy1 . . λyl (y)v1 . . vp with ui β ui , vj β vj . This yields the expected result. 3. For every λ-term t, the following conditions are equivalent : i) t is solvable ; ii) t is β-equivalent to a head normal form ; iii) the head reduction of t terminates (with a head normal form).

Download PDF sample

Rated 4.34 of 5 – based on 3 votes