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...election, replicated input, generation of new channels, and message forwarding. Its logical origin led to straightforward generalizations to support data input and output [19] as well as polymorphism =-=[20, 6]-=-, incorporated as type input and output. This leaves open the question of how to fully and uniformly incorporate the system into a complete functional calculus to support higher-order, message-passing...

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...ification over types, controlled via subtyping. While useful to reason about protocols with message genericity, bounded polymorphism is insufficient to support behavioral genericity. Recently, Wadler =-=[28]-=- proposed a logic-based session type theory which includes the natural typing rules for second-order quantifiers and may support polymorphism of the kind we consider here; however, no analysis of beha...

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...clusively to branch and choice types: each branch is quantified by a type variable with upper and lower bounds; the scope of a variable is a whole branch of communication. In very recent work, Wadler =-=[28]-=- proposes an interpretation of classical linear logic as session types (along the lines of [8]) which includes polymorphism; however, the theory of polymorphic sessions and parametricity is not explor...

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...re sessions are established between more than two peers and messaging is asynchronous. It is not clear whether Kobayashi’s usage types are expressive enough for handling such situations. The works in =-=[2, 26]-=- use linear logic to type processes in the pi-calculus with sessions. While these works guarantee lock-freedom, we conjecture that their techniques can be reused for progress, similarly to what we hav...

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...es and Pfenning [5] have applied Propositions as Types to explain Session Types, a way of describing communication protocols introduced by Honda [25], inspiring a new view of Propositions as Sessions =-=[52]-=-. One key to the correspondence between logic and computation is the study of category theory. Both simply-typed lambda calculus and intuitionistic natural deduction correspond to the notion of a cart...

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...ter resembles a type system based upon logical deduction developed for Scheme (Tobin-Hochstadt and Felleisen, 2010). We expand on the treatment of input and deduction below. Additionally, within type derivations we use abstraction over session types across multiple channels in conjunction with functions over session types. Other research on relating session types and linear type theories (Gay and Vasconcelos, 2010; Caires and Pfenning, 2010) has led to work that incorporates type abstraction as second-order quantification in linear logic, e.g., to establish strong deadlock freedom guarantees (Wadler, 2012), and relational parametricity results (Caires et al., 2013). Dependent session types (Bonelli et al., 2005; Toninho et al., 2011) include abstraction over values. This form of abstraction is supported in our formalization in Coq. (Deniélou and Yoshida, 2011) use polymorphism in connection with session types, but the polymorphism is over roles associated with processes; this kind of role polymorphism is orthogonal to the issues of session polymorphism. Input and Deduction. Existing session type systems only permit an input or label branching process to be typed when the corresponding session t...

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...Caires and Pfenning [3] give a propositions-as-types correspondence between intuitionistic linear logic and session types, interpreting proofs as processes in a restricted pi-calculus, piDILL. Wadler =-=[8]-=- adapts Caires and Pfenning’s work to classical linear logic, interpreting proofs as processes in a restricted pi-calculus, CP. Furthermore, Wadler shows that a core session-typed linear functional la...

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...{y/a} ) a . {li.Pi}i∈I . = a . {i(xi).Pi{xi/a}}i∈I a(X);P . = (νX, x)( a(X, x) | P{x/a} ) It is easy to check that linear redices commute with all other redices, and therefore a “real” 4Several works =-=[17, 5, 20, 2]-=- would not enjoy subject reduction if this example could be transferred: their cut rule requires (νb)(· · · ), which is here missing. These works don’t have “Mix” (here: (CoMix)), which we used in the...

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...ve the comparison with the dualities we studied here and the one of [6] for future work. 13 Two other approaches to defining duality emerged from the connection between session types and propositions =-=[5, 18]-=-. In the intuitionistic setting of Caires and Pfenning [5], duality boils down to the cut-rule, according to which the dual of requiring a behaviour A (on the left of a judgement) is an offer of A (on...