A Constructive Approach to Freyd Categories

Closed Freyd- and -categories

We give two classes of sound and complete models for the computational-calculus, or c-calculus. For the rst, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational-calculus. The latter corresponds to an idealisation of stack-based intermediate langu...

Cartesian effect categories are Freyd-categories

Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major consequences when there are side-effects. In this paper Cartesian effect categories are introduced for solving this issue, and they are compared with strong monads,...

Freyd categories are Enriched Lawvere Theories

Lawvere theories provide a categorical formulation of the algebraic theories from universal algebra. Freyd categories are categorical models of first-order effectful programming languages. The notion of sound limit doctrine has been used to classify accessible categories. We provide a definition of Lawvere theory that is enriched in a closed category that is locally presentable with respect to ...

On the Freyd Categories of an Additive Categoryapostolos

A Constructive Approach to “Universals”

But it is beyond the power of human capacity to frame and retain distinct ideas of all the particular things we meet with: every bird and beast men saw; every tree and plant that affected the senses, could not find a place in the most capacious understanding. During the Middle Ages, much of the debate about universals concerned the question whether or not they could be considered to " exist ". ...