By Pierre-Louis Curien
This ebook is a revised variation of the monograph which seemed below an identical identify within the sequence study Notes in Theoretical computing device technology, Pit guy, in 1986. as well as a common attempt to enhance typography, English, and presentation, the most novelty of this moment version is the combination of a few new fabric. a part of it truly is mine (mostly together with coauthors). here's short consultant to those additions. i've got augmented the account of specific combinatory common sense with an outline of the confluence houses of rewriting structures of categor ical combinators (Hardin, Yokouchi), and of the newly built cal culi of specific substitutions (Abadi, Cardelli, Curien, Hardin, Levy, and Rios), that are related in spirit to the specific combinatory good judgment, yet are toward the syntax of A-calculus (Section 1.2). The research of the complete abstraction challenge for PCF and extensions of it's been enriched with a brand new complete abstraction outcome: the version of sequential algorithms is totally summary with admire to an extension of PCF with a keep watch over operator (Cartwright, Felleisen, Curien). An order extensional version of error-sensitive sequential algorithms is additionally absolutely summary for a corresponding extension of PCF with a keep an eye on operator and blunders (Sections 2.6 and 4.1). I recommend that sequential algorithms lend themselves to a decomposition of the functionality areas that ends up in types of linear good judgment (Lamarche, Curien), and that connects sequentiality with video games (Joyal, Blass, Abramsky) (Sections 2.1 and 2.6).
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Extra info for Categorical Combinators, Sequential Algorithms, and Functional Programming
As stated, the actions of "freeze" and "unf' are such that arguments are reevaluated each time they are accessed. Mauny has introduced efficient updating instructions to the call-by-name CAM. Only then, the machine can be called lazy, as Mauny has argued [MauTh] (see also [MauSua, Mau]). Lazyness can be considered also for products, or lists. This is particularly attractive for the manipulation of infinite lists, as has been argued by Friedman and Wise [FriWi]. Then both components of a couple, or both the head and the tail of a list should be frozen at compile time, as we did for arguments of functions (see [Mau]).
C = AU. «AV. c)v »u)u =p AU. c). 20. 17 . We prove (2) rule by rule. if,P (x 0 (y oz»~ (ld ox)~ =def Au. P AU. l1 X Au. (AV. (xv ,yv »(zu) =P Au. y(ZV»u) =p,def ( X,,). c = Ax. c ). 1. 17). c has the expected behaviour with respect to the applying and coupling operators. 19. c = AU. c =def,P AU. c U ,u) =PJst,snd AU. c = AU. c)v»u)u =P AU. c = AU. «AV. c)v »u)u =p AU. c). 20. 17 . We prove (2) rule by rule. if,P (x 0 (y oz»~ (ld ox)~ =def Au. P AU. l1 X Au. (AV. (xv ,yv »(zu) =P Au. y(ZV»u) =p,def (
X,,). c = Ax. c ). 1. 17). c has the expected behaviour with respect to the applying and coupling operators. 19. c = AU. c =def,P AU. c U ,u) =PJst,snd AU. c = AU. c)v»u)u =P AU. c = AU. «AV. c)v »u)u =p AU. c). 20. 17 . We prove (2) rule by rule. if,P (x 0 (y oz»~ (ld ox)~ =def Au. P AU. l1 X Au. (AV. (xv ,yv »(zu) =P Au. y(ZV»u) =p,def (