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Michael Brandt, Fritz Henglein. Coinductive axiomatization of recursive type equality and subtyping. Fundamenta Informaticae, Invited submission to special issue featuring a selection of contributions to the 3d Int'l Conf. on Typed Lambda Calculi and Applications (TLCA), 1997, 33(4):309-338, 1998.


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We present new sound and complete axiomatizations of type equality and subtype inequality for a first-order type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule, a finitary coinduction principle. The new axiomatizations give rise to a natural operational interpretation of proofs as coercions and to efficient algorithms for constructing explicit coercions efficiently, not only deciding type equality and type containment. More generally, we show how adding the fixpoint rule makes it possible to define inductively a a set coinductively defined as the kernel (greatest fixed point) of an inference system


[ Rectype ] [ Coinduction ] [ Coinduction ]


Michael Brandt
Fritz Henglein

BibTex Reference

   Author = {Brandt, Michael and Henglein, Fritz},
   Title = {Coinductive axiomatization of recursive type equality and subtyping},
   Journal = {Fundamenta Informaticae},
   Volume = {33},
   Number = {4},
   Pages = {309--338},
   Year = {1998}

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