Propositions-as-types and shared state

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...

Re e tion and Propositions - as - Types ?

Speci cation Structures and Propositions - as - Types

Many diierent notions of \property of interest" and methods of verifying such properties arise naturally in programming. A general framework of \Speciication Structures" is presented for combining diierent notions and methods in a coherent fashion. This is then applied to concurrency in the setting of Interaction Categories. As an example, we present a type system for concurrent processes stron...