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**1 - 5**of**5**### BOOTSTRAPPING TYPES AND COTYPES IN HASCASL

"... We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions o ..."

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We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type declarations adhering to certain reasonable formats. The latter amounts to modifying known constructions from HOL to avoid unique choice; in categorical terminology, this means that we establish that quasitoposes with an internal natural numbers object support initial algebras and final coalgebras for a range of polynomial functors, thereby partially generalizing corresponding results from topos theory. Moreover, we present similar constructions in categories of internal complete partial orders.

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, 2007

"... Abstract. Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we introduce the categorical notion of a linear actego ..."

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Abstract. Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we introduce the categorical notion of a linear actegory and the related polycategorical notion of a poly-actegory. Not surprisingly the notation used for the term calculus borrows heavily from the (synchronous) π-calculus. The cut elimination procedure for the system provides an operational