Propositions as sessions

Sessions as Propositions

Recently, Wadler presented a continuation-passing translation from a session-typed functional language, GV, to a process calculus based on classical linear logic, CP. However, this translation is one-way: CP is more expressive than GV. We propose an extension of GV, called HGV, and give translations showing that it is as expressive as CP. The new translations shed light both on the original tra...

A Semantics for Propositions as Sessions

Session types provide a static guarantee that concurrent programs respect communication protocols. Recently, Caires, Pfenning, and Toninho, and Wadler, have developed a correspondence between propositions of linear logic and session typed π-calculus processes. We relate the cut-elimination semantics of this approach to an operational semantics for session-typed concurrency in a functional langu...

Propositions as Sessions ( DRAFT of 13 March 2012 , revised 16 March 2012 )

Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), by Honda, Kubo, and Vasconcelos (1998), and by Gay and Vasconcelos (2010), among others, this paper presents GV, a line...

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