Furio Honsell and Ivan Scagnetto. Mobility types in Coq. Technical report, Dipartimento di Matematica e Informatica, Universita di Udine, Italy, June 2003.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... forcing method; see [Jec77, Section 6] for a brief survey of these matters) Our application of the permutation model of set theory to abstract syntax with variable binding is rather far from this Of course, one can introduce a type of names in a HOAS style signature, as is done for example in [HMS98]; but as the authors of that work say (p. 26) The main drawback of HOAS is the diculty of dealing with metatheoretic issues concerning names. As a consequence, some metatheoretic properties involving substitution and freshness of names. cannot be proved inside the framework and instead ....

.... relevant for the labelled transi tion semantics of process calculi such as the calculus and its relations [MPW92, AbG99, CaG00b] both because complicated forms of binding to do with names and names restriction play a key role there and because analyses based on name abstraction as functions [HMS98, Des00] are not entirely satisfactory. The formalism of permutation actions and nite support has been rediscovered independently by Honda in his work on a general framework for processes [Hon00] It also features in work on nite state transition systems for checking bisimilarity of calculus processes ....

Honsell, F., Miculan, M. and Scagnetto, I.: -Calculus in (co)inductive type theory. Technical report, Dipartimento di Matematica e Informatica, Universita degli Studi di Udine, 1998.

....de ne how fresh names are allocated, but also how unused names are deallocated, so that they can be used again. Besides minimal realizations, a fully satisfactory coalgebraic theory for the calculus would yield the possibility of applying well understood algebraic techniques and proof methods [4 6,17,31]. A coalgebraic semantics for various versions of the calculus has been pro2 posed in [16] but the approach is higher order, and it is not amenable to nite state veri cation. Moreover, the semantics is still parametrized by the set of names of the possible partners, so that an in nite set ....

F. Honsell, M. Miculan, and I. Scagnetto. -calculus in (co)inductive type theory. Technical report, Dipartimento di Matematica e Informatica, Udine, 1998.

....nameless terms [dB72] or categorical combinators [Cur93] these are good for machine implementations, but not, we would argue, for representations intended for machine assisted human reasoning. 2 Of course, one can introduce a type of names in a HOAS style signature, as for example is done in [HMS98]; but as the authors of that work say [p 26] The main drawback of HOAS is the diculty of dealing with metatheoretic issues concerning names. As a consequence, some metatheoretic properties involving substitution and freshness of names. cannot be proved inside the framework and instead ....

.... relevant for the labelled transition semantics of process calculi such as the calculus and its relations [MPW92, AG99, CG00b] both because complicated forms of binding to do with names and names restriction play a key role there and because analyses based on name abstraction as functions [HMS98, Des00] are not entirely satisfactory. The formalism of permutation actions and nite support has been rediscovered independently by Honda in his work on a general framework for processes [Hon00] It also features in work on nite state transition systems for checking bisimilarity of calculus processes ....

F. Honsell, M. Miculan, and I. Scagnetto. -calculus in (co)inductive type theory. Technical report, Dipartimento di Matematica e Informatica, Universita degli Studi di Udine, 1998.

....Indeed, the whole HOAS approach by its very nature disallows a feature that we regard of key practical importance: the ability to manipulate names of bound variables explicitly in computation and proof. Of course, one can introduce a type of names in a HOAS signature, as for example is done in [15]; but as the authors of that work say [p 26] The main drawback of HOAS is the difficulty of dealing with metatheoretic issues concerning names : As a consequence, some metatheoretic properties involving substitution and freshness of names : cannot be proved inside the framework and ....

F. Honsell, M. Miculan, and I. Scagnetto. -calculus in (co)inductive type theory. Technical report, Dipartimento di Matematica e Informatica, Universita degli Studi di Udine, 1998.

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Furio Honsell and Ivan Scagnetto. Mobility types in Coq. Technical report, Dipartimento di Matematica e Informatica, Universita di Udine, Italy, June 2003.

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