Destructors, responsible for releasing memory and other resources in languages such as C++ and Rust, can lead to stack overflows when releasing a recursive structure that is too deep. In certain cases, it is possible to generate an efficient destructor (non-allocating and tail recursive) using a typed variant of pointer reversal. We extend this technique by making it more modular, in order to handle abstract types, separate compilation, and unboxed types.

We propose a new interface and implementation for managing garbage collector (GC) roots for the OCaml foreign-function interface (FFI), which offers: • better performance than existing root-registration interfaces, • efficient support for multicore OCaml, thanks to a multicore-friendly design, • a reasoning based on resource-management idioms, enabling an easier OCaml FFI in Rust.

This paper reports the good hypothetical performance, in rigorous practical terms, of embedding (borrowing) linearly-allocated values inside garbage-collected values. A companion submission to the ML workshop reports a symmetrical result: how to efficiently embed (own) garbage-collected values inside linearly-allocated values. Taken together, the broader motivation is to show the feasibility of basing linear allocation with re-use (Lafont 1988; Baker 1992) in languages that would still leverage state-of-art garbage collection for non-linear values.

We propose to bring together a dependently-typed theory (ECC) and polarised sequent calculus, by presenting a calculus Ldep suitable as a vehicle for compilation and representation of effectful computations. As a first step in that direction, we show that Ldep advantageously factorize a dependently typed continuation-passing style translation for ECC+call/cc. To avoid the inconsistency of type theory with control operators, we restrict their interaction. Nonetheless, in the pure case, we obtain an unrestricted translation from ECC to itself, thus opening the door to the definition of dependently typed compilation transformations.

The current multicore OCaml implementation bans so-called “naked pointers”, pointers to outside the OCaml heap unless they follow drastic restrictions. A backwards-incompatible change has been proposed to make way for the new multicore GC in OCaml. I argue that out-of-heap pointers are not an anomaly, but are part of a better systems programming future.

The resource-management model of C++ and Rust relies on compiler-generated destructors called predictably and reliably. In current implementations, the generated destructor consumes stack space proportionally to the depth of the structure it destructs. We describe a way to derive destructors for algebraic data types that consume a constant amount of stack and heap. We discuss applicability to C++ and Rust, and also some implication for anyone wishing to extend an ML-style language with first-class resources.

We model exceptions in a linear, effectful setting by relaxing the notion of monadic strength to contexts that are discardable, in the spirit of C++ destructors. This gives rise to a resource modality reminiscent of unique_ptr and move semantics in C++11. We explore consequences in language design for resource management in functional programming languages.

We present a resource-management model for ML-style programming languages, designed to be compatible with the OCaml philosophy and runtime model. This is a proposal to extend the OCaml language with destructors, move semantics, and resource polymorphism, to improve its safety, efficiency, interoperability, and expressiveness. It builds on the ownership-and-borrowing models of systems programming languages (Cyclone, C++11, Rust) and on linear types in functional programming (Linear Lisp, Clean, Alms). It continues a synthesis of resources from systems programming and resources in linear logic initiated by Baker.

It is a combination of many known and some new ideas. On the novel side, it highlights the good mathematical structure of Stroustrup's “Resource acquisition is initialisation” (RAII) idiom for resource management based on destructors, a notion sometimes confused with finalizers, and builds on it a notion of resource polymorphism, inspired by polarisation in proof theory, that mixes C++'s RAII and a tracing garbage collector (GC). In particular, it proposes to identify the types of GCed values with types with trivial destructor: from this definition it deduces a model in which GC is the default allocation mode, and where GCed values can be used without restriction both in owning and borrowing contexts.

The proposal targets a new spot in the design space, with an automatic and predictable resource-management model, at the same time based on lightweight and expressive language abstractions. It is backwards-compatible: current code is expected to run with the same performance, the new abstractions fully combine with the current ones, and it supports a resource-polymorphic extension of libraries. It does so with only a few additions to the runtime, and it integrates with the current GC implementation. It is also compatible with the upcoming multicore extension, and suggests that the Rust model for eliminating data-races applies.

Interesting questions arise for a safe and practical type system, many of which have already been thoroughly investigated in the languages and prototypes Cyclone, Rust, and Alms.

Following renewed interest in duploids arising from the exponential comonad of linear logic (the construction describing polarised intuitionistic translations into linear logic), I summarise here various remarks: • about a decomposition of Girard's “boring” translation as the expression of call-by-value in call-by-name, dual to how thunks are used to express call-by-name in call-by-value • about the coincidence between linear CPS translations and Girard's translations of intuitionistic logic into linear logic, • about a completeness property of historical models of linear logic in the above context • about a rational reconstruction of these translations with the Linear Call-by-Push-Value.

We present Curry-style calculi for intuitionistic (linear) logic with polarised evaluation order and give self-contained proofs of their main properties and of their interpretation into (Linear) Call-by-Push-Value models: subject reduction, confluence, strong normalisation, coherence, soundness, and focusing.

We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as the starting point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context.

Our thesis is that the combination of effects and resources should be considered orthogonally. Model theoretically, this leads to an understanding of our categorical models from two complementary perspectives: (i) as a linearisation of CBPV (Call-by-Push-Value) adjunction models, and (ii) as an extension of linear/non-linear adjunction models with an adjoint resolution of computational effects. When the linear structure is cartesian and the resource structure is trivial we recover Levy's notion of CBPV adjunction model, while when the effect structure is trivial we have Benton's linear/non-linear adjunction models. Further instances of our model theory include the dialogue categories with a resource modality of Melliès and Tabareau, and the [E]EC ([Enriched] Effect Calculus) models of Egger, Møgelberg and Simpson. Our development substantiates the approach by providing a lifting theorem of linear models into cartesian ones.

To each of our categorical models we systematically associate a typed term calculus, each of which corresponds to a variant of the sequent calculi LJ (Intuitionistic Logic) or ILL (Intuitionistic Linear Logic). The adjoint resolution of effects corresponds to polarisation whereby, syntactically, types locally determine a strict or lazy evaluation order and, semantically, the associativity of cuts is relaxed. In particular, our results show that polarisation provides a computational interpretation of CBPV in direct style. Further, we characterise depolarised models: those where the cut is associative, and where the evaluation order is unimportant. We explain possible advantages of this style of calculi for the operational semantics of effects.

The theory of the λ-calculus with extensional sums is more complex than with only pairs and functions. We propose an untyped representation—an intermediate calculus—for the λ-calculus with sums, based on the following principles:  1) Computation is described as the reduction of pairs of an expression and a context; the context must be represented inside-out,  2) Operations are represented abstractly by their transition rule,  3) Positive and negative expressions are respectively eager and lazy; this polarity is an approximation of the type. We offer an introduction from the ground up to our approach, and we review the benefits.

A structure of alternating phases naturally emerges through the study of normal forms, offering a reconstruction of focusing. Considering further purity assumption, we obtain maximal multi-focusing. As an application, we can deduce a syntax-directed algorithm to decide the equivalence of normal forms in the simply-typed λ-calculus with sums, and justify it with our intermediate calculus.

Negation is not involutive in the λC calculus because it does not distinguish captured stacks from continuations. We show that there is a formulae-as-types correspondence between the involutive negation in proof theory, and a notion of high-level access to the stacks studied by Felleisen and Clements.

We introduce polarised, untyped, calculi compatible with extensionality, for both of classical sequent calculus and classical natural deduction, with connectives for an involutive negation. The involution is due to the ℓ delimited control operator that we introduce, which allows us to implement the idea that captured stacks, unlike continuations, can be inspected. Delimiting control also gives a constructive interpretation to falsity. We describe the isomorphism there is between A and ¬¬A, and thus between ¬∀ and ∃¬.

We characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as a reference to Jean-Louis Loday's duplicial algebras. The main result is a reflection Adj→Dupl where Dupl is a category of duploids and duploid functors, and Adj is the category of adjunctions and pseudo maps of adjunctions. The result suggests that the various biases in denotational semantics: indirect, call-by-value, call-by-name... are a way of hiding the fact that composition is not always associative.

We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the duality of computation. We use this kit to provide a term language for a presentation of LK (with conjunction, disjunction, and negation), and to transcribe cut elimination as (non confluent) rewriting. A key slogan here, which may appear here in print for the first time, is that commutative cut elimination rules are explicit substitution propagation rules.

We then describe the focalised proof search discipline (in the classical setting), and narrow down the language and the rewriting rules to a confluent calculus (a variant of the second author's focalising system L). We then define a game of patterns and counterpatterns, leading us to a fully focalised finitary syntax for a synthetic presentation of classical logic, that provides a quotient on (focalised) proofs, abstracting out the order of decomposition of negative connectives.

We develop a polarised variant of Curien and Herbelin's lambda-bar-mu-mu-tilde calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard's classical logic LC or linear logic. This gives a setting in which Krivine's classical realisability extends naturally (in particular to call-by-value), with a presentation in terms of orthogonality. We give examples of applications to the theory of programming languages.

In this version extended with appendices, we in particular give the two-sided formulation of LC with the involutive classical negation. We also show that there is in classical realisability a notion of internal completeness similar to the one of Ludics.

The thesis is a contribution to the understanding of the nature, role, and mechanisms of polarisation in programming languages, proof theory and categorical models. Polarisation corresponds to the idea the associativity of composition of morphisms is an hypothesis that has to be relaxed, and underlies many models of computation.

In our demonstration, we introduce duploids, which model polarisation directly. These compositional structures, which, unlike categories, do not always require composition to be associative, are shown to be in correspondence with certain completed forms of categorical adjunctions (Chapter II). This analysis of polarisation is then extended into a fine-grained decomposition of continuation-passing-style (CPS) transformations, which model and implement higher-order programming languages. As an application we show how polarisation accounts for evaluation order in models of delimited control operators (Chapter III). Finally, we give a formulae-as-types interpretation of an involutive negation, which shows the importance of polarisation for constructiveness in proof theory (Chapter IV).

The cornerstone of our approach is an interactive term-based representation of proofs and programs (L calculi) which exposes the structure of polarities. It is based on the correspondence between abstract machines and sequent calculi, and syntheses various trends: the modelling of control, evaluation order and effects in programming languages, the quest for a relationship between categorical duality and continuations, and the interactive notion of construction in proof theory. We give a gentle introduction to our approach which only assumes elementary knowledge of simply-typed λ calculus and rewriting (Chapter I).