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

By Jean-Louis Krivine, Rene Corvi (translator)

Show description

Read or Download Lambda-calculus, types and models PDF

Best nonfiction_5 books

Speakout Pre Intermediate Workbook with Key and Audio CD Pack

Speakout is a brand new normal English path that is helping grownup newbies achieve self assurance in all ability parts utilizing real fabrics from the BBC. With its wide selection of help fabric, it meets the varied wishes of rookies in various educating occasions and is helping to bridge the distance among the study room and the genuine international.

The First Circle (The Restored Text: The First Uncensored Edition)

The exciting chilly conflict masterwork through the Nobel Prize winner, released in complete for the 1st time Moscow, Christmas Eve, 1949. The Soviet mystery police intercept a choice made to the yankee embassy by way of a Russian diplomat who supplies to carry secrets and techniques in regards to the nascent Soviet Atomic Bomb application. On that very same day, a super mathematician is locked away inside of a Moscow felony that homes the country's brightest minds.

Extra info for Lambda-calculus, types and models

Sample text

Uk is of type X in the context y : U (where U = Ω, Ω, . . , Ω → X). Thus t is of type U1 , . . , Un → X in the context y : U (U1 , . . , Un may be arbitrarily chosen, except when y = xi ; in that case, take Ui = U). D. 22. If x1 : A1 , x2 : A2 , . . , xk : Ak x1 : A1 ∧ A1 , x2 : A2 , . . , xk : Ak t : A. t : A, then : Proof by induction on the number of rules used to obtain : t : A (either rules 1 to 6, page 42 or x1 : A1 , x2 : A2 ,. . , xk : Ak rules 1 to 5, page 51). Consider the last one.

Of terms such that : for every n ≥ 0, tn β0 tn+1 (tn+1 is obtained by reducing a redex in tn ) ; for every n ≥ 0, there exists a p ≥ n such that tp+1 is obtained by reducing the leftmost redex in tp . 12 (Quasi leftmost normalization theorem). Suppose x1 : A1 , . . , xk : Ak DΩ t : A, and Ω does not occur in A,A1 ,. . ,Ak . Then there is no infinite quasi leftmost reduction of t. Chapter 3. Intersection type systems 49 In order to prove it, we again define an adapted pair (N0 , N ) : N is the set of all terms which do not admit an infinite quasi leftmost reduction ; N0 is the set of all terms of the form (x)t1 .

In particular, all variables are in N0 (take n = 0). We have to check conditions (i) and (ii) in the definition of adapted pairs (page 46) : i) N is saturated : clearly, if (u[t/x])t1 . . tn is normalizable by leftmost β-reduction, then so is (λx u)tt1 . . tn . ii) N0 ⊂ N : if t ∈ N0 , say t = (x)t1 . . tn for some variable x and t1 , . . , tn ∈ N , then t1 , . . , tn are all normalizable by leftmost β-reduction, thus t clearly satisfies the same property. The inclusion N0 ⊂ (N → N0 ) is obvious.

Download PDF sample

Rated 4.35 of 5 – based on 17 votes