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The purpose of this paper is to study the commutative pseudomeadows, the structure which is defined in the same way as commutative meadows, except that the existence of a multiplicative identity is not required. We extend the characterization of finite commutative meadows, given by I. Bethke, P. Rodenburg, and A. Sevenster in their paper (2015), to the case of commutative pseudomeadows with finitely many idempotents. We also extend the well-known characterization of general commutative meadows as...
This paper presents two extensions of the second order polymorphic
lambda calculus, system F, with monotone (co)inductive types supporting
(co)iteration, primitive (co)recursion and inversion principles as
primitives. One extension is inspired by the usual categorical
approach to programming by means of initial algebras and final
coalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino's
categorical lambda calculus within the framework of parametric
polymorphism....
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