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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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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 ...