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TypeBased Termination of Recursive Definitions
, 2002
"... This article The purpose of this paper is to introduce b, a simply typed calculus that supports typebased recursive definitions. Although heavily inspired from previous work by Giménez (Giménez 1998) and closely related to recent work by Amadio and Coupet (Amadio and CoupetGrimal 1998), the techn ..."
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Cited by 46 (3 self)
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This article The purpose of this paper is to introduce b, a simply typed calculus that supports typebased recursive definitions. Although heavily inspired from previous work by Giménez (Giménez 1998) and closely related to recent work by Amadio and Coupet (Amadio and CoupetGrimal 1998), the technical machinery behind our system puts a slightly different emphasis on the interpretation of types. More precisely, we formalize the notion of typebased termination using a restricted form of type dependency (a.k.a. indexed types), as popularized by (Xi and Pfenning 1998; Xi and Pfenning 1999). This leads to a simple and intuitive system which is robust under several extensions, such as mutually inductive datatypes and mutually recursive function definitions; however, such extensions are not treated in the paper
On Formalised Proofs of Termination of Recursive Functions
 In Proceedings of the Int. Conf. on Principles and Practice of Declarative Programming, volume 1702 of LNCS
, 1999
"... In proof checkers and theorem provers (e.g. Coq [4] and ProPre [13]) recursive de nitions of functions are shown to terminate automatically. ..."
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Cited by 8 (3 self)
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In proof checkers and theorem provers (e.g. Coq [4] and ProPre [13]) recursive de nitions of functions are shown to terminate automatically.
On Automating The Extraction Of Programs From Proofs Using Product Types
, 2002
"... We investigate an automated program synthesis system based on the paradigm of programming by proofs. To automatically extract a term that computes a recursive function given by a set of equations the system must nd a formal proof of the totality of the given function. Because of the particular log ..."
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Cited by 4 (1 self)
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We investigate an automated program synthesis system based on the paradigm of programming by proofs. To automatically extract a term that computes a recursive function given by a set of equations the system must nd a formal proof of the totality of the given function. Because of the particular logical framework, usually such approaches make it dicult to use techniques such as those in rewriting theory. We overcome this diculty for the automated system that we consider by exploiting product types. As a consequence, this would enable the incorporation of termination techniques used in other areas while still extracting programs.
On automating inductive and noninductive termination methods
 In Proceedings of the 5th Asian Computing Science Conference, volume 1742 of LNCS
, 1999
"... Abstract. The Coq and ProPre systems show the automated termination of a recursive function by rst constructing a tree associated with the specication of the function which satises a notion of terminal property and then verifying that this construction process is formally correct. However, those t ..."
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Cited by 4 (2 self)
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Abstract. The Coq and ProPre systems show the automated termination of a recursive function by rst constructing a tree associated with the specication of the function which satises a notion of terminal property and then verifying that this construction process is formally correct. However, those two steps strongly depend on inductive principles and hence Coq and ProPre can only deal with the termination proofs that are inductive. There are however many functions for which the termination proofs are noninductive. In this article, we attempt to extend the class of functions whose proofs can be done automatically a la Coq and ProPre to a larger class including functions whose termination proofs are not inductive. We do this by extending the terminal property notion and replacing the verication step above by one that searches for a decreasing measure which can be used to establish the termination of the function. 1
On Automating the Extraction of Programs from Termination Proofs
"... We investigate an automated program synthesis system that is based on the paradigm of programming by proofs. To automatically extract a #term that computes a recursive function given by a set of equations the system must find a formal proof of the totality of the given function. Because of the p ..."
Abstract
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We investigate an automated program synthesis system that is based on the paradigm of programming by proofs. To automatically extract a #term that computes a recursive function given by a set of equations the system must find a formal proof of the totality of the given function. Because of the particular logical framework, usually such approaches make it di#cult to use termination techniques such as those in rewriting theory. We overcome this di#culty for the automated system that we consider by exploiting product types. As a consequence, this would enable the incorporation of termination techniques used in other areas while still extracting programs.