Michel Parigot. On the Representation of Data in Lambda-Calculus. In Proceedings of the 3rd Workshop on Computer Science Logic, Lecture Notes in Computer Science 440, eds. E. Borger, H. Kleine Buning, M. M. Richter, pages 309--321. October 1989. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Inductive Definitions in the System Coq Rules and Properties - Paulin-Mohring (1992) (49 citations) (Correct)
....type and the expected recursive scheme. 14 The case of natural numbers For the natural numbers, it will give us the following representation : nat j X : C : C (X C C) C The recursor is just the identity function. A similar representation was proposed in the framework of AF 2 by M. Parigot [19]. The main drawback of this encoding of natural numbers is that the representation of the nth natural number uses a space proportional to 2 n . This is a problem for practical uses but not for our study of the theoretical properties of the system Coq. The general case. Let I be Ind(X : A)fC 1 j ....
M. Parigot. On the representation of data in lambda-calculus. In CSL'89, volume 440 of LNCS, Kaiserslautern, 1989. Springer-Verlag.
Towards a Practical Programming Language Based on the .. - Lee, Leone.. (1989) (2 citations) (Correct)
....(the problem of filling in omitted type information) is known to be only semi decidable [2, 22] while little is known about the related problem of type inference. Also, there are theoretical results indicating that a functional implementation of datatypes leads to inherent inefficiencies [20, 7]. Thus, a large part of our research is devoted to addressing these problems. In this paper we report on our work in progress, which has thus far resulted in the design and prototype implementation of pure LEAP 1 , a conservative (semantically equivalent) extension of F . Some aspects of LEAP ....
....complication, in that the functions which operate on the representations of inductive types tend to be inherently very inefficient. For example, the succ constructor for natural numbers, if just compiled directly, would count up to a number before adding one to it. Destructors are even worse [7, 20] because in general they need to be implemented using primitive recursion. This makes obtaining the predecessor of a natural number or the tail of a list extremely inefficient. We have developed a general technique for recognizing instances of constructors and some other functions on inductive ....
Michel Parigot. On the representation of data in lambda-calculus. Draft, 1988.
Impredicative Representations of Categorical Datatypes - Altenkirch (1994) (Correct)
....necessary to compute the predecessor of a number, it turns out that the predecessor has a linear complexity. Similar things are true for other algorithms with the notable exception of addition, multiplication and exponentation which have constant complexity. This is discussed by Parigot [Par89], where he shows that there is no one step predecessor for church numbers. He proposes two alternatives, which are not typable in 2nd order calculus 22 . Nax Mendler uses the inefficiency of the predecessor to justify the introduction of general recursion combinators in [Men90] However, I am ....
Michel Parigot. On the representation of data in the lambda-calculus. In E. Borger et al, editor, CSL '89, pages 309 -- 321. LNCS 440, 1989. (extended abstract).
Proof search and induction choices in AF 2 system - Galmiche, Hermann (Correct)
.... But what about construction of proofs and programs and also eOEciency of these programs It appears clearly that there exists a link between the choice of data types denition, and then of induction schema during the proof search, in this logical system and the eOEciency of extracted programs [8]. To get the eOEciency that one might expect some works have introduced new types in AF 2 as inductives types [9] or coinductive types [10] preserving the correctness of the programming method. Another point consists in trying to propose some procedures for inductive proof search that could ....
M. Parigot. On the representation of data in lambda-calculus. In CSL '89, LNCS 440, pages 309321, Kaiserslautern, FRG, October 1989.
A presentation of the Curry-Howard Correspondance. - Berline (1997) (1 citation) (Correct)
....them. The rst point is not a drawback if the logic is powerful enough : then all the functions one will ever wish to compute are indeed representable (Girard [7] 8] cf. 15, p. 161] or [6] and the second limitation, which is even present in the full calculus, can often be locally overcome [25]. The expressive power of a typed calculus is thus limited by its logic, but the positive counterpart is that the computation can be controlled by the logic. This shows up globally : the restricted set of terms may consist only of normalizable terms (that is terms whose computation ends) and ....
M. Parigot, On the representations of data in lambda-calculus, in Proc. CSL'89 (Kaiserlautern), LNCS vol.440, pp.309-321, 1989.
Programming with Inductive and Co-Inductive Types - Greiner (1992) (6 citations) (Correct)
No context found.
Michel Parigot. On the Representation of Data in Lambda-Calculus. In Proceedings of the 3rd Workshop on Computer Science Logic, Lecture Notes in Computer Science 440, eds. E. Borger, H. Kleine Buning, M. M. Richter, pages 309--321. October 1989.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC