arXiv subjects

Cristina Matache

Publications and source records attributed to Cristina Matache.

7 recordsLinked to original sources

arXiv2026

Finitary Semantics for Full Ground Local State

Full ground local state (FGLS) refers to dynamically allocated mutable state that allows storing ground values and references. It is a key ingredient in many imperative algorithms as it enables (cyclic) data structures. In this work, we treat full ground local state as a computational effect, focusing on one particular denotational model: Kammar et al.'s possible worlds monad on sets indexed over sets of locations. We resolve an outstanding question regarding this FGLS monad: is it finitary? We show that the FGLS monad is not finitary by showing the existence of non-finitary computations in the monad. We then introduce a finitary submonad of Kammar et al.'s monad, give it a concrete description and show that it provides an adequate semantics for FGLS. The submonad we construct paves the way to understanding FGLS in the future via an equational axiomatization suitable for program reasoning.

cs.PL↗

arXiv2026

An Equational Axiomatization of Dynamic Threads via Algebraic Effects: Presheaves on Finite Relations, Labelled Posets, and Parameterized Algebraic Theories

We use the theory of algebraic effects to give a complete equational axiomatization for dynamic threads. Our method is based on parameterized algebraic theories, which give a concrete syntax for strong monads on functor categories, and are a convenient framework for names and binding. Our programs are built from the key primitives `fork' and `wait'. `Fork' creates a child thread and passes its name (thread ID) to the parent thread. `Wait' allows us to wait for given child threads to finish. We provide a parameterized algebraic theory built from fork and wait, together with basic atomic actions and laws such as associativity of `fork'. Our equational axiomatization is complete in two senses. First, for closed expressions, it completely captures equality of labelled posets (pomsets), an established model of concurrency: model complete. Second, any two open expressions are provably equal if they are equal under all closing substitutions: syntactically complete. The benefit of algebraic effects is that the semantic analysis can focus on the algebraic operations of fork and wait. We then extend the analysis to a simple concurrent programming language by giving operational and denotational semantics. The denotational semantics is built using the methods of parameterized algebraic theories and we show that it is sound, adequate, and fully abstract at first order for labelled-poset observations.

cs.PL↗

arXiv2024

Scoped Effects as Parameterized Algebraic Theories

Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the state, and axioms specify observably equivalent expressions. However, many useful programming features depend on additional mechanisms such as delimited scopes or dynamically allocated resources. Such mechanisms can be supported via extensions to algebraic effects including scoped effects and parameterized algebraic theories. We present a fresh perspective on scoped effects by translation into a variation of parameterized algebraic theories. The translation enables a new approach to equational reasoning for scoped effects and gives rise to an alternative characterization of monads in terms of generators and equations involving both scoped and algebraic operations. We demonstrate the power of our fresh perspective by way of equational characterizations of several known models of scoped effects.

cs.PL↗

arXiv2023

Denotational semantics for languages for inference: semirings, monads, and tensors

Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their connections to semirings and tensors. A basic class of examples of algebraic theories comes from considering the theory of modules for a semiring, e.g. the theory of unnormalized distributions, where the semiring is that of the non-negative real numbers. We propose that an interesting perspective is given by studying theories via semirings, and to this end explore several examples of subtheories of module theories, mostly relating to probability. Our main contribution concerns the commutative combination of effects, as studied by Hyland, Plotkin and Power: we observe that while the semiring tensor does not in general determine the tensor of subtheories of module theories, it still does in several fundamental probabilistic examples.

cs.LO↗

arXiv2022

Concrete categories and higher-order recursion (With applications including probability, differentiability, and full abstraction)

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming, and fully abstract logical relations models. We treat recursion in the spirit of synthetic domain theory. We provide a general construction of a lifting monad starting from a class of admissible monomorphisms in the site of the sheaf category. In this way, we obtain a family of models parametrized by a concrete site and a class of monomorphisms, for which we prove a general computational adequacy theorem.

cs.PL↗

arXiv2021

Recursion and Sequentiality in Categories of Sheaves

We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo's, we treat recursion as just one feature in a model built by combining a choice of modular components.

cs.PL↗

arXiv2019

Program Equivalence for Algebraic Effects via Modalities

This dissertation is concerned with the study of program equivalence and algebraic effects as they arise in the theory of programming languages. Algebraic effects represent impure behaviour in a functional programming language, such as input and output, exceptions, nondeterminism etc. all treated in a generic way. Program equivalence aims to identify which programs can be considered equal in some sense. This question has been studied for a long time but has only recently been extended to languages with algebraic effects, which are a newer development. Much work remains to be done in order to understand program equivalence in the presence of algebraic effects. In particular, there is no characterisation of contextual equivalence using a logic. We define a logic whose formulas express properties of higher-order programs with algebraic effects. We then investigate three notions of program equivalence for algebraic effects: logical equivalence induced by the aforementioned logic, applicative bisimilarity and contextual equivalence. For the programming language used in this dissertation, we prove that they all coincide. Therefore, the main novel contribution of the dissertation is defining the first logic for algebraic effects whose induced program equivalence coincides with contextual equivalence.

cs.PL↗