Results 11  20
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105
From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
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Un Calcul De Constructions Infinies Et Son Application A La Verification De Systemes Communicants
, 1996
"... m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to ..."
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Cited by 21 (0 self)
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m networks and the recent works of Thierry Coquand in type theory have been the most important sources of motivation for the ideas presented here. I wish to specially thank Roberto Amadio, who read the manuscript in a very short delay, providing many helpful comments and remarks. Many thanks also to Luc Boug'e, who accepted to be my oficial supervisor, and to the chair of the jury, Michel Cosnard, who opened to me the doors of the LIP. During these last three years in Lyon I met many wonderful people, who then become wonderful friends. Miguel, Nuria, Veronique, Patricia, Philippe, Pia, Rodrigo, Salvador, Sophie : : : with you I have shared the happiness and sadness of everyday life, those little things which make us to remember someone forever. I also would like to thank the people from "Tango de Soie", for all those funny nights at the Caf'e Moulin Joly. Thanks too to the Uruguayan research community in Computer Science (specially to Cristina Cornes and Alberto Pardo) w
Productivity of Stream Definitions
, 2008
"... We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called ‘productive’ if it can be evaluated continually in such a way that a uniquely determined stream in constructor normal form is obtained as the limit. Whereas prod ..."
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Cited by 20 (4 self)
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We give an algorithm for deciding productivity of a large and natural class of recursive stream definitions. A stream definition is called ‘productive’ if it can be evaluated continually in such a way that a uniquely determined stream in constructor normal form is obtained as the limit. Whereas productivity is undecidable for stream definitions in general, we show that it can be decided for ‘pure’ stream definitions. For every pure stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements, called ‘pebbles’, in a finite ‘pebbleflow net(work)’. And the production of a pebbleflow net associated with a pure stream definition, that is, the amount of pebbles the net is able to produce at its output port, can be calculated by reducing nets to trivial nets.
A certified, corecursive implementation of exact real numbers
 Theoretical Computer Science
, 2006
"... We implement exact real numbers in the logical framework Coq using streams, i.e., infinite sequences, of digits, and characterize constructive real numbers through a minimal axiomatization. We prove that our construction inhabits the axiomatization, working formally with coinductive types and corecu ..."
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Cited by 19 (0 self)
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We implement exact real numbers in the logical framework Coq using streams, i.e., infinite sequences, of digits, and characterize constructive real numbers through a minimal axiomatization. We prove that our construction inhabits the axiomatization, working formally with coinductive types and corecursive proofs. Thus we obtain reliable, corecursive algorithms for computing on real numbers.
A.: Copatterns: Programming infinite structures by observations
, 2013
"... Abel, A., Pientka, B., Thibodeau, D. & Setzer, A. (2013). Copatterns: programming infinite structures by observations. ..."
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Cited by 18 (9 self)
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Abel, A., Pientka, B., Thibodeau, D. & Setzer, A. (2013). Copatterns: programming infinite structures by observations.
A term calculus for (co)recursive definitions on streamlike data structures
 Ann. Pure Appl. Logic
, 2005
"... We consider recursion equations (∗) FX = t(F,X) where X ranges over streams (i.e., elements of S: = N→ N), F is of type stream → stream, and the term t is build up from F, X and previously introduced function symbols. The question is whether such an equation has a (total) solution. It is wellknown a ..."
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We consider recursion equations (∗) FX = t(F,X) where X ranges over streams (i.e., elements of S: = N→ N), F is of type stream → stream, and the term t is build up from F, X and previously introduced function symbols. The question is whether such an equation has a (total) solution. It is wellknown and explicated at many places in the literature (e.g. [2], [4], [6], [7]) that under certain conditions a (unique) solution for (∗)
A Unifying Approach to Recursive and Corecursive Definitions
 IN [5
, 2002
"... In type theory based logical frameworks, recursive and corecursive definitions are subject to syntactic restrictions that ensure their termination and productivity. These restrictions however greately decrease the expressive power of the language. In this work we propose a general approach for s ..."
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Cited by 18 (1 self)
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In type theory based logical frameworks, recursive and corecursive definitions are subject to syntactic restrictions that ensure their termination and productivity. These restrictions however greately decrease the expressive power of the language. In this work we propose a general approach for systematically defining fixed points for a broad class of well given recursive definition. This approach unifies the ones based on wellfounded order to the ones based on complete metrics and contractive functions, thus allowing for mixed recursive/corecursive definitions.
Total Parser Combinators
, 2009
"... A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library’s interface is similar to that of many other parser combinator libraries, with two important differences: one is that the interface clearly specif ..."
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Cited by 16 (4 self)
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A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library’s interface is similar to that of many other parser combinator libraries, with two important differences: one is that the interface clearly specifies which parts of the constructed parsers may be infinite, and which parts have to be finite, using a combination of induction and coinduction; and the other is that the parser type is unusually informative. The library comes with a formal semantics, using which it is proved that the parser combinators are as expressive as possible. The implementation
Some domain theory and denotational semantics in Coq
, 2009
"... Abstract. We present a Coq formalization of constructive ωcpos (extending earlier work by PaulinMohring) up to and including the inverselimit construction of solutions to mixedvariance recursive domain equations, and the existence of invariant relations on those solutions. We then define operatio ..."
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Abstract. We present a Coq formalization of constructive ωcpos (extending earlier work by PaulinMohring) up to and including the inverselimit construction of solutions to mixedvariance recursive domain equations, and the existence of invariant relations on those solutions. We then define operational and denotational semantics for both a simplytyped CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case. 1
Wellfounded Recursion with Copatterns A Unified Approach to Termination and Productivity
, 2013
"... In this paper, we study strong normalization of a core language based on System Fomega which supports programming with finite and infinite structures. Building on our prior work, finite data such as finite lists and trees are defined via constructors and manipulated via pattern matching, while infi ..."
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In this paper, we study strong normalization of a core language based on System Fomega which supports programming with finite and infinite structures. Building on our prior work, finite data such as finite lists and trees are defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. In this work, we take a typebased approach to strong normalization by tracking size information about finite and infinite data in the type. This guarantees compositionality. More importantly, the duality of pattern and copatterns provide a unifying semantic concept which allows us for the first time to elegantly and uniformly support both wellfounded induction and coinduction by mere rewriting. The strong normalization proof is structured around Girard’s reducibility candidates. As such our system allows for nondeterminism and does not rely on coverage. Since System Fomega is general enough that it can be the target of compilation for the Calculus of Constructions, this work is a significant step towards representing observationcentric infinite data in proof assistants such as Coq and Agda.