R. Amadio and S. Coupet-Grimal. Analysis of a guard condition in type theory. In M. Nivat, editor, Proceedings of FOSSACS'98, volume 1378 of Lecture Notes in Computer Science, pages 48--62. Springer-Verlag, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....sets. In particular, X.#] is the fixpoint of an operator derived from [ #] In previous work [4] we obtained this fixpoint by the theorem of Knaster and Tarski, resp. by accessibility inductive definitions. This time we follow an idea of Mendler [24] reused by Amadio and Coupet Grimal [6]) and reach the fixpoint by transfinite iteration. This technique enables us to give an interpretation to approximation types Y X.#. Let O be some set which we call origin set and # an operator on sets. For an ordinal number # we define the # iterate # by transfinite recursion on # as = ....

....and reducers. We adapted his ideas for the simply typed setting and generalized the type decorations to track more cases of size change. In contrast to Gimenez, our subtyping calculus is restricted to approximation of inductive types, without loss of expressivity. Amadio and Coupet Grimal [6] present a system derived from Gimenez for coinductive types where recursive calls have to be guarded (cf. Coquand [12] They give a proof of strong normalization which follows Mendler, but is restricted to the special case of streams. They sketch the idea of arbitrary approximations i but ....

R. M. Amadio and S. Coupet-Grimal. Analysis of a guard condition in type theory. In M. Nivat, editor, Foundations of Software Science and Computation Structures, First International Conference, FoSSaCS'98, volume 1378 of Lecture Notes in Computer Science. Springer, 1998.

....PVS. We show on examples how it avoids some drawbacks of co induction which needs to consider absent elements in the case of clocked streams. 1 Introduction Co induction has been advocated as providing a good theoretical framework for proving stream programs and several experiments and tools [5, 17, 13, 9, 14, 7, 2] have been recently designed in this setting, mostly based on Coq [6] and PVS [15] Two main proof principles have been used, the Bisimulation Proof Principle originated from Park s work and the In nite Proof Principle due to Coquand. However, when we tried to apply these principles to the ....

R. Amadio and S.Coupet-Grimal. Analysis of a guard condition in type theory. In M.Nivat, editor, Foundations of Software Science and Computation Structures, volume 1378 of Lecture Notes in Computer Science. Springer Verlag, 1998.

....of a corresponding inductive definition branches in two, and the further inductive steps remain asynchronous. In fact, equation (6) may or may not have a unique solution, depending on how we interpret . In logic and process calculus, this issue has mostly been addressed at the level of syntax [2, 7, 13]. The extant characterizations of the guardedness are syntactic conditions that apply to specific languages, and ensure unique fixpoints (e.g. 13, sec. 3.2] We initiated an abstract semantic analysis in [16] but only covered a special class of stream flavored coalgebras. In the meantime, Moss ....

R. Amadio and S. Coupet-Grimal, Analysis of a guard condition in type theory. Rapport 245, Laboratoire d'Informatique Marseille

....strength of recursive definitions. However, oppositely to [14] our calculus may type definitions containing recursive calls which are guarded by more than one constructor (or destructor) and nested recursive definitions. Nested recursive definitions have been also studied by Amadio and Coupet in [1]. Starting from Coquand s notion of guarded definition for simple typed lambda calculus, they provide a semantics based on partial equivalent relations, and use ordinal iteration to interpret recursive types. This semantics lead them to a calculus closed to the one proposed in [11] However, ....

R. Amadio and S. Coupet. Analysis of a guard condition in type theory. Technical Report 3300, INRIA, October 1997. Extended abstract to appear in ETAPS 98 (FoSSaCS).

....of guarded induction. While ordinary induction is usually modelled in terms of the least fixpoints and the initial algebras, guarded induction is based on the unique fixpoints of certain operations, called guarded, on the final coalgebras. So far, such operations were treated syntactically [3,8,9,23]. We analyse them categorically. Guarded induction appears as couched in coinductively constructed domains, but turns out to be reducible to coinduction only in special cases. The applications of the presented analysis span across the gamut of the applications of guarded induction from ....

R.M. Amadio and S. Coupet-Grimal, Analysis of a guard condition in type theory. Rapport 245, Laboratoire d'Informatique Marseille

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R. Amadio and S. Coupet-Grimal. Analysis of a guard condition in type theory. In M. Nivat, editor, Proceedings of FOSSACS'98, volume 1378 of Lecture Notes in Computer Science, pages 48--62. Springer-Verlag, 1998.

No context found.

R. M. Amadio and S. Coupet-Grimal. Analysis of a guard condition in type theory. In M. Nivat, editor, Foundations of Software Science and Computation Structures, First International Conference, FoSSaCS'98, volume 1378 of Lecture Notes in Computer Science. Springer, 1998.

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Roberto M. Amadio and Solange Coupet-Grimal. Analysis of a guard condition in type theory. In FoSSaCS '98, volume 1378 of LNCS. Springer, 1998.

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