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- W2564982021 abstract "The aim of this short note is two-fold. Our main motivation is to widen the class of maps being definable by Behavioural Differential Equations (BDE) [8]. One way of giving semantics to BDE’s is by using Structural Operational Semantics [7], but this prevents mixing induction and coinduction. Moreover, the ensuing syntactic formats have limited expressiveness, and exclude useful functions from being defined. These issues can be dealt with if we add type systems. The second aim of this note is to advertise an observational approach to infinite structures in Type Theory. For example in Coq, coinductive types are introduced by “constructors, albeit with the power of being infinitely iterated” [3]. There is work on extending type systems with (weakly) final coalgebras (e.g. [6]), but only recently efforts have been made to bring this into theorem provers [2,1]. The use of copatterns in loc. cit. is a way of extending λ-calculus by BDE’s. We want to study which maps one can define in this calculus and under which circumstances it leads to final coalgebras. First of all, we search for the ingredients necessary to obtain final coalgebras. To this end, we organise the types and terms defined in [1] into a category T. Using a fixed set TyVar of type variables, the syntax of our basic types is:" @default.
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- W2564982021 date "2014-01-01" @default.
- W2564982021 modified "2023-09-27" @default.
- W2564982021 title "A note on typed behavioural differential equations" @default.
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