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Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience. However, not all effects can be classified as algebraic; some need a more sophisticated handling. In particular, effects that have or create a delimited scope need special care, as their continuation consists of two parts-in and out of the scope-and their modular composition introduces additional complexity. These effects are called scoped and have gained attention by their growing applicability and adoption in popular libraries. While calculi have been designed with algebraic effects & handlers built in to facilitate their use, a calculus that supports scoped effects & handlers in a similar manner does not yet exist. This work fills this gap: we present $\lambda_{\mathit{sc}}$, a calculus with native support for both algebraic and scoped effects & handlers. It addresses the need for polymorphic handlers and explicit clauses for forwarding unknown scoped operations to other handlers. Our calculus is based on Eff, an existing calculus for algebraic effects, extended with Koka-style row polymorphism, and consists of a formal grammar, operational semantics, a (type-safe) type-and-effect system and type inference. We demonstrate $\lambda_{\mathit{sc}}$ on a range of examples.

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The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015) as a formalisation of the core functionality of the query language AQL used in IBM's SystemT) additionally need string-equality selections and it has been shown by Freydenberger and Holldack (ICDT 2016, Theory of Computing Systems 2018) that this leads to high complexity and even undecidability of the typical problems in static analysis and query evaluation. We propose an alternative approach to core spanners: by incorporating the string-equality selections directly into the regular language that represents the underlying regular spanner (instead of treating it as an algebraic operation on the table extracted by the regular spanner), we obtain a fragment of core spanners that, while having slightly weaker expressive power than the full class of core spanners, arguably still covers the intuitive applications of string-equality selections for information extraction and has much better upper complexity bounds of the typical problems in static analysis and query evaluation.

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Can the $\lambda$-calculus be considered a reasonable computational model? Can we use it for measuring the time $\textit{and}$ space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the $\lambda$-calculus, based on a variant over the Krivine abstract machine. For the first time, this cost model is able to accommodate logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value $\lambda$-calculus.

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Recursive types extend the simply-typed lambda calculus (STLC) with the additional expressive power to enable diverging computation and to encode recursive data-types (e.g., lists). Two formulations of recursive types exist: iso-recursive and equi-recursive. The relative advantages of iso- and equi-recursion are well-studied when it comes to their impact on type-inference. However, the relative semantic expressiveness of the two formulations remains unclear so far. This paper studies the semantic expressiveness of STLC with iso- and equi-recursive types, proving that these formulations are equally expressive. In fact, we prove that they are both as expressive as STLC with only term-level recursion. We phrase these equi-expressiveness results in terms of full abstraction of three canonical compilers between these three languages (STLC with iso-, with equi-recursive types and with term-level recursion). Our choice of languages allows us to study expressiveness when interacting over both a simply-typed and a recursively-typed interface. The three proofs all rely on a typed version of a proof technique called approximate backtranslation. Together, our results show that there is no difference in semantic expressiveness between STLCs with iso- and equi-recursive types. In this paper, we focus on a simply-typed setting but we believe our results scale to more powerful type systems like System F.

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We tackle the challenge of ensuring the deadlock-freedom property for message-passing processes that communicate asynchronously in cyclic process networks. Our contributions are twofold. First, we present Asynchronous Priority-based Classical Processes (APCP), a session-typed process framework that supports asynchronous communication, delegation, and recursion in cyclic process networks. Building upon the Curry-Howard correspondences between linear logic and session types, we establish essential meta-theoretical results for APCP, most notably deadlock freedom. Second, we present a new concurrent $\lambda$-calculus with asynchronous session types, dubbed LASTn. We illustrate LASTn by example and establish its meta-theoretical results; in particular, we show how to soundly transfer the deadlock-freedom guarantee from APCP. To this end, we develop a translation of terms in LASTn into processes in APCP that satisfies a strong formulation of operational correspondence.

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