Propositions as types

Propositions as Types

Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asser...

Explorer Propositions as Types

Signatures + Propositions Used as Types ?

Languages that distinguish between types and structures use explicit components for the carrier type(s) in structures. Examples are the functional language Standard ML and most algebraic speciication systems. Hence, they have to use general sum types or signatures to give types to structures and to be able to build, for instance, the algebraic hierarchy. Furthermore, in most languages the model...

Linear logic propositions as session types

Throughout the years, several typing disciplines for the π-calculus have been proposed. Arguably, the most widespread of these typing disciplines consists of session types. Session types describe the input/output behavior of processes and traditionally provide strong guarantees about this behavior (i.e., deadlock freedom and fidelity). While these systems exploit a fundamental notion of lineari...

Re e tion and Propositions - as - Types ?