This paper introduces an expressive class of indexed quotient-inductive types, called QWI within the framework constructive type theory. They are initial algebras for families equational theories with possibly infinitary operators and equations. We prove that types can be derived from quotient inductive in theory toposes natural number object universes, provided those universes satisfy Weakly I...

We describe the categorical semantics for a simply typed variant and simplified dependently of Cocon , contextual modal type theory where box modality mediates between weak function space that is used to represent higher-order abstract syntax (HOAS) trees strong describes (recursive) computations about them. What makes different from standard theories presence first-class contexts objects are c...

A co-type is a type with instance methods and instance data which enhance the functionality of some other type (its "expanded" type). The instance methods of the co-type correspond approximately to constructors, class methods and binary methods of the expanded type in other class-based OO systems, and the instance data replaces class-based data. This unconventional approach was motivated by the...

CON TENT S Fimbriae and Haemagglutinating Activity in Strains of Protezcs humeri BY W. I. H. SHEDDEN . Aberrant Forms of Mycobacterium phlei Produccd by Streptomycin and thcir Multiplication on Streptomycin-frec Media BY S. E. JUHASZ . . . . . . . . . . Rate of Growth of Bacillus cereus between Divisicns BY J. I?. COLLINS and M. H. RICHMOND. . Chemical Composition and Antigenic Structure of Cel...

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of “type” in programming languages with the concept of the same name in mathematical logic, an identification that is only the result of the convergence of two different paths, which...