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12
Some Results on the Full Abstraction Problem for Restricted Lambda Calculi
 In Proc. of the 18 th International Symposium on Mathematical Foundations of Computer Science, MFCS'93, Springer LNCS
, 1993
"... ion Problem for Restricted Lambda Calculi Furio Honsell and Marina Lenisa Dipartimento di Matematica e Informatica, Universit`a di Udine, via Zanon,6  Italy Email:fhonsell,lenisag@udmi5400.cineca.it dedicated to Corrado Bohm on the occasion of his 70 th birthday Abstract. Issues in the mathemat ..."
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Cited by 14 (1 self)
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ion Problem for Restricted Lambda Calculi Furio Honsell and Marina Lenisa Dipartimento di Matematica e Informatica, Universit`a di Udine, via Zanon,6  Italy Email:fhonsell,lenisag@udmi5400.cineca.it dedicated to Corrado Bohm on the occasion of his 70 th birthday Abstract. Issues in the mathematical semantics of two restrictions of the calculus, i.e. Icalculus and V calculus, are discussed. A fully abstract model for the natural evaluation of the former is defined using complete partial orders and strict Scottcontinuous functions. A correct, albeit nonfully abstract, model for the SECD evaluation of the latter is defined using Girard's coherence spaces and stable functions. These results are used to illustrate the interest of the analysis of the fine structure of mathematical models of programming languages. 1 Introduction D. Scott, in the late sixties, discovered a truly mathematical semantics for  calculus using continuous lattices. His D1 model was the first example of ...
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 5 (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: "C'era una volta un re seduto in canap`e
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...
Semantical Analysis of Perpetual Strategies in λcalculus
, 1998
"... this paper we carry out a semantical investigation of perpetual strategies in ..."
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this paper we carry out a semantical investigation of perpetual strategies in
Callbyvalue Solvability
 Theoretical Informatics and Applications
, 1999
"... The notion of solvability in the callbyvalue calculus is defined and completely characterized, both from an operational and a logical point of view. The operational characterization is given through a reduction machine, performing the classical fireduction, according to an innermost strategy. ..."
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The notion of solvability in the callbyvalue calculus is defined and completely characterized, both from an operational and a logical point of view. The operational characterization is given through a reduction machine, performing the classical fireduction, according to an innermost strategy. In fact, it turns out that the callbyvalue reduction rule is too weak for capturing the solvability property of terms. The logical characterization is given through an intersection type assignment system, assigning types of a given shape to all and only the callbyvalue solvable terms.
Final Semantics for untyped λcalculus
 IN LNCS, VOLUME 902
, 1995
"... Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principl ..."
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Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principles arise naturally as coinduction principles, when the observational equivalences are shown to be induced by the unique mapping into a final Fcoalgebra, for a suitable functor F . This is achieved either by induction on computation steps or exploiting the properties of some, computationally adequate, inverse limit denotational model. The final F coalgebras cannot be given, in general, the structure of a "denotational" λmodel. Nevertheless the "final semantics" can count as compositional in that it induces a congruence. We utilize the intuitive categorical setting of hypersets and functions. The importance of the principles introduced in this paper lies in the fact that they often allow...
Parametric λTheories
, 2007
"... The parametric lambda calculus subsumes different existing λcalculi, in particular the classical λβcalculus and the λβvcalculus of Plotkin. Previously established results on the parametric calculus, such as as confluence and standardization, are primarily syntactical. In this paper our attention ..."
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The parametric lambda calculus subsumes different existing λcalculi, in particular the classical λβcalculus and the λβvcalculus of Plotkin. Previously established results on the parametric calculus, such as as confluence and standardization, are primarily syntactical. In this paper our attention is mainly addressed to semantics, although we start again from a syntactical point of view. We propose an analysis of the notion of contextual preorders of usual operational semantics. Given a contextual preorder, we build parametric complete lattice based on a closure operator. This lattice provides a fully abstract model for the considered preorder, via a completion.
A TypeFree ResourceAware λCalculus
, 1996
"... We introduce and study a functional language λ_R , having two main features. λ_R has the same computational power of the λcalculus. λ_R enjoys the resourceawareness of the typed/typable functional languages which encode the Intuitionistic Linear Logic. ..."
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We introduce and study a functional language λ_R , having two main features. λ_R has the same computational power of the λcalculus. λ_R enjoys the resourceawareness of the typed/typable functional languages which encode the Intuitionistic Linear Logic.
Strong Normalization from an . . .
, 2007
"... A new complete characterization of βstrong normalization is given, both in the classical and in the lazy λcalculus, through the notion of potential valuability inside two suitable parametric calculi. ..."
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A new complete characterization of βstrong normalization is given, both in the classical and in the lazy λcalculus, through the notion of potential valuability inside two suitable parametric calculi.