On Polymorphic Sessions and Functions

We study increasingly expressive type systems, from $$F^\mu $$ F μ —an extension of the polymorphic lambda calculus with equirecursive types—to $$F^{\mu ;}_\omega $$ F ω μ ; —the higher-order polymorphic lambda calculus with equirecursive types and context-free session types. Type equivalence is given by a standard bisimulation defined over a novel labelled transition system for types. Our system subsumes the contractive fragment of $$F^\mu _\omega $$ F ω μ as studied in the literature. Decidability results for type equivalence of the various type languages are obtained from the translation of types into objects of an appropriate computational model: finite-state automata, simple grammars and deterministic pushdown automata. We show that type equivalence is decidable for a significant fragment of the type language. We further propose a message-passing, concurrent functional language equipped with the expressive type language and show that it enjoys preservation and absence of runtime errors for typable processes.

Section: Related Workmentioning

confidence: 99%

System $$F^\mu _\omega $$ with Context-free Session Types

Poças

Costa

Mordido

et al. 2023

“…Interestingly, in CLASS such stratification is implicitly guaranteed by the acyclicity inherent to Linear Logic. Linear logical relations were studied in [62,21,72,74]. In this work we recast and extend the technique to Classical Linear Logic, exploring orthogonality [38,8,1], and demonstrate, using a specially devised technique of interference-sensitive reducibility, how logical relations scale to accommodate shared state.…”

Section: Related Workmentioning

confidence: 99%

“…Despite the strength of its type system, CLASS expressiveness and effectiveness substantially overcomes limitations of related works, as we show with compelling program examples that can be algorithmically typed for memory safety, dead-and live-lock freedom with a perhaps surprisingly light type annotation burden. CLASS owes these strong properties to is PaT foundation based on Second-Order Linear Logic, already known to capture the polymorphic session calculus and the linear System F [74], but which we conservatively extend with novel logically motivated constructs for shareable affine state, also based on DiLL co-exponentials [35,67], but to which we give here a different, more general and fundamental interpretation.…”

Section: Introductionmentioning

confidence: 99%

Safe Session-Based Concurrency with Shared Linear State

Rocha

Caires

2023

The Session Abstract Machine

Caires,

Toninho

2024

We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the SAM’s design is its ability to naturally segregate and coordinate sequential with concurrent session behaviours. In particular, implicitly sequential parts of session programs may be efficiently executed by deterministic sequential application of SAM transitions, amenable to compilation, and without concurrent synchronisation mechanisms. We provide an intuitive discussion of the SAM structure and its underlying design, and state and prove its correctness for executing programs in a session calculus corresponding to full classical linear logic $$\textsf{CLL}$$ CLL . We also discuss extensions and applications of the SAM to the execution of linear and session-based programming languages.