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From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
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A Complete Characterization of Complete IntersectionType Theories (Extended Abstract)
 ACM TOCL
, 2000
"... M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical ..."
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M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical settheoretical semantics for intersectiontypes: the inference semantics, the simple semantics and the Fsemantics. Keywords Lambda Calculus, Intersection Types, Semantic Completeness, Filter Structures. 1 Introduction Intersectiontypes disciplines originated in [6] to overcome the limitations of Curry 's type assignment system and to provide a characterization of strongly normalizing terms of the lcalculus. But very early on, the issue of completeness became crucial. Intersectiontype theories and filter lmodels have been introduced, in [5], precisely to achieve the completeness for the type assignment system l" BCD W , with respect to Scott's simple semantics. And this result, ...
Perpetuality and Uniform Normalization in Orthogonal Rewrite Systems
 INFORMATION AND COMPUTATION
"... We present two characterizations of perpetual redexes, which are redexes whose contractions retain the possibility of infinite reductions. These characterizations generalize and strengthen existing criteria for the perpetuality of redexes in orthogonal Term Rewriting Systems and the calculus due ..."
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Cited by 7 (2 self)
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We present two characterizations of perpetual redexes, which are redexes whose contractions retain the possibility of infinite reductions. These characterizations generalize and strengthen existing criteria for the perpetuality of redexes in orthogonal Term Rewriting Systems and the calculus due to Bergstra and Klop, and others. To unify our results with those in the literature, we introduce Contextsensitive Conditional Expression Reduction Systems (CCERSs) and prove confluence for orthogonal CCERSs. We then define a perpetual onestep reduction strategy which enables one to construct minimal (w.r.t. Levy's permutation ordering on reductions) infinite reductions in orthogonal CCERSs. We then prove (1) perpetuality (in a specific context) of a redex whose contraction does not erase potentially infinite arguments, which are possibly finite (i.e., strongly normalizable) arguments that may become infinite after a number of outside steps, and (2) perpetuality (in every con...
Labelled Reductions, Runtime Errors, and Operational Subsumption
 of Lecture Notes in Computer Science
, 1997
"... Introduction Consider the "nameswitching" function F def = x:fl 1 = x:l 2 ; l 2 = x:l 1 g in a  calculus with records. Most type systems would reject program (Ffl 1 = 3g):l 2 because the type of F is fl 1 : X; l 2 : Y g ! fl 2 : Y; l 1 : Xg and fl 1 : X; l 2 : Y g cannot be unified ..."
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Cited by 6 (1 self)
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Introduction Consider the "nameswitching" function F def = x:fl 1 = x:l 2 ; l 2 = x:l 1 g in a  calculus with records. Most type systems would reject program (Ffl 1 = 3g):l 2 because the type of F is fl 1 : X; l 2 : Y g ! fl 2 : Y; l 1 : Xg and fl 1 : X; l 2 : Y g cannot be unified with fl 1 : Intg, the type of the record argument. However this program reduces to 3 without error. This shows that the common notion of "erroneous" terms, as implemented in most typed languages, is sometimes
Themes in Final Semantics
 Dipartimento di Informatica, Università di
, 1998
"... C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e ..."
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Cited by 6 (2 self)
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C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: &quot;C'era una volta un re seduto in canap`e
A Uniform Syntactical Method for Proving Coinduction Principles in lambdacalculi
 In: Proc. of TAPSOFT'97
, 1997
"... . Coinductive characterizations of various observational congruences which arise in the semantics of calculus, when terms are evaluated according to various reduction strategies, are discussed. We analyze and extend to nonlazy strategies, both deterministic and nondeterministic, Howe's cong ..."
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Cited by 4 (3 self)
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. Coinductive characterizations of various observational congruences which arise in the semantics of calculus, when terms are evaluated according to various reduction strategies, are discussed. We analyze and extend to nonlazy strategies, both deterministic and nondeterministic, Howe's congruence candidate method for proving the coincidence of the applicative (bisimulation) and the contextual equivalences. This purely syntactical method is based itself on a coinductive argument. Introduction This paper is part of a general project aiming at finding elementary proof principles for reasoning rigorously on infinite computational objects, see [4, 9] for the case of higher order functions, and [8] for the case of higher order processes. In this paper, as in [4, 9], we focus on the behaviour of terms when these are evaluated according to various reduction strategies. We address the problem of showing the coincidence of the applicative (bisimulation) equivalence with the observational ...
Coinductive Characterizations of Applicative Structures
 MATH. STRUCTURES IN COMP. SCI. 9(4):403–435
, 1998
"... We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, ..."
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Cited by 3 (0 self)
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We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss in particular, what we call, the cartesian coinduction principle, which arises when we exploit the elementary observation that functional behaviours can be expressed as cartesian graphs. Using the paradigm of final semantics, the soundness of this principle over an applicative structure can be expressed easily by saying that the applicative structure can be construed as a strongly extensional coalgebra for the functor (P( \Theta )) \Phi (P( \Theta )). In this paper, we present two general methods for showing the soundenss of this principle. The first applies to approximable applicative structures. Many c.p.o. models in...
Operational Subsumption, an Ideal Model of Subtyping
, 1998
"... In a previous paper we have defined a semantic preorder called operational subsumption, which compares terms according to their error generation behaviour. Here we apply this abstract framework to a concrete language, namely the AbadiCardelli object calculus. Unlike most semantic studies of objects ..."
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Cited by 3 (0 self)
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In a previous paper we have defined a semantic preorder called operational subsumption, which compares terms according to their error generation behaviour. Here we apply this abstract framework to a concrete language, namely the AbadiCardelli object calculus. Unlike most semantic studies of objects, which deal with typed equalities and therefore require explicitly typed languages, we start here from a untyped world. Type inference is introduced in a second step, together with an ideal model of types and subtyping. We show how this approach flexibly accommodates for several variants, and finally propose a novel semantic interpretation of structural subtyping as embeddingprojection pairs. 1 Introduction In a previous paper [10] we have defined a semantic preorder called operational subsumption, which compares terms according to their error generation behaviour. Together with the technical device of labeled reductions, used as a syntactic characterization of finite approximations, thi...