1,229 research outputs found
A foundation for synthesising programming language semantics
Programming or scripting languages used in real-world systems are seldom designed
with a formal semantics in mind from the outset. Therefore, the first step for developing well-founded analysis tools for these systems is to reverse-engineer a formal
semantics. This can take months or years of effort.
Could we automate this process, at least partially? Though desirable, automatically reverse-engineering semantics rules from an implementation is very challenging,
as found by Krishnamurthi, Lerner and Elberty. They propose automatically learning
desugaring translation rules, mapping the language whose semantics we seek to a simplified, core version, whose semantics are much easier to write. The present thesis
contains an analysis of their challenge, as well as the first steps towards a solution.
Scaling methods with the size of the language is very difficult due to state space
explosion, so this thesis proposes an incremental approach to learning the translation
rules. I present a formalisation that both clarifies the informal description of the challenge by Krishnamurthi et al, and re-formulates the problem, shifting the focus to the
conditions for incremental learning. The central definition of the new formalisation is
the desugaring extension problem, i.e. extending a set of established translation rules
by synthesising new ones.
In a synthesis algorithm, the choice of search space is important and non-trivial,
as it needs to strike a good balance between expressiveness and efficiency. The rest
of the thesis focuses on defining search spaces for translation rules via typing rules.
Two prerequisites are required for comparing search spaces. The first is a series of
benchmarks, a set of source and target languages equipped with intended translation
rules between them. The second is an enumerative synthesis algorithm for efficiently
enumerating typed programs. I show how algebraic enumeration techniques can be applied to enumerating well-typed translation rules, and discuss the properties expected
from a type system for ensuring that typed programs be efficiently enumerable.
The thesis presents and empirically evaluates two search spaces. A baseline search
space yields the first practical solution to the challenge. The second search space is
based on a natural heuristic for translation rules, limiting the usage of variables so that
they are used exactly once. I present a linear type system designed to efficiently enumerate translation rules, where this heuristic is enforced. Through informal analysis
and empirical comparison to the baseline, I then show that using linear types can speed
up the synthesis of translation rules by an order of magnitude
Stochastic models of cell population dynamics and tick-borne virus transmission
When modelling cellular population dynamics, many mathematical models consider exponential inter-event times. Despite being the most convenient choice from a mathematical and computational perspective, the exponential distribution overestimates the probability of short division times. In Chapter 3, I consider a multi-stage model of the cell cycle to maintain the advantages of a Markovian model, while improving on exponential times to division. With this structure in place, cell generations are introduced in the model to link theoretical predictions with experimental data. The model with cell generations is parameterised making use of CFSE data and Bayesian methods. Then, in order to study fate correlation of cellular siblings, in Chapter 4, I pro- pose a mathematical model that makes use of the theory of branching processes. Cells are categorised based on their fate, either division or death, which is decided at birth. The applicability of this approach is shown by considering a data set of stimulated B cells produced with time-lapse microscopy.
The last chapter of this thesis aims to shed light on the role of co-feeding and co-transmission in the spread of a vector-borne virus. Thus, a population of ticks interacts with a population of hosts (small or large vertebrates). First, I consider a single infection whose dynamics is modelled through both deterministic and stochastic models. The basic reproduction number is computed by means of the next generation matrix approach. When modelling co-infection with two different viruses (or two strains of the same virus), a deterministic model is proposed to study only co-feeding transmission, accounting also for co-transmission of the virus. A series of stochastic descriptors of interest are computed when considering all the routes of transmission
Modular Analysis of Distributed Hybrid Systems using Post-Regions (Full Version)
We introduce a new approach to analyze distributed hybrid systems by a
generalization of rely-guarantee reasoning. First, we give a system for
deductive verification of class invariants and method contracts in
object-oriented distributed hybrid systems. In a hybrid setting, the object
invariant must not only be the post-condition of a method, but also has to hold
in the post-region of a method. The post-region describes all reachable states
after method termination before another process is guaranteed to run. The
system naturally generalizes rely-guarantee reasoning of discrete
object-oriented languages to hybrid systems and carries over its modularity to
hybrid systems: Only one dL-proof obligation is generated per method. The
post-region can be approximated using lightweight analyses and we give a
general notion of soundness for such analyses. Post-region based verification
is implemented for the Hybrid Active Object language HABS
Categorical structures for deduction
We begin by introducing categorized judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and first-order logic as special kinds of categorized judgemental theories. We believe our analysis sheds light on both the topics, providing a new point of view. In the case of type theory, we provide an abstract definition of type constructor featuring the usual formation, introduction, elimination and computation rules. For first-order logic we offer a deep analysis of structural rules, describing some of their properties, and putting them into context.
We then put one of the main constructions introduced, namely that of categorized judgemental dependent type theories, to the test: we frame it in the general context of categorical models for dependent types, describe a few examples, study its properties, and use it to model subtyping and as a tool to prove intrinsic properties hidden in other models.
Somehow orthogonally, then, we show a different side as to how categories can help the study of deductive systems: we transport a known model from set-based categories to enriched categories, and use the information naturally encoded into it to describe a theory of fuzzy types. We recover structural rules, observe new phenomena, and study different possible enrichments and their interpretation. We open the discussion to include different takes on the topic of definitional equality
To the Last Drop: Affective Economies of Extraction and Sentimentality
The romance of extraction underlies and partly defines Western modernity and our cultural imaginaries. Combining affect studies and environmental humanities, this volume analyzes societies' devotion to extraction and fossil resources. This devotion is shaped by a nostalgic view on settler colonialism as well as by contemporary "affective economies" (Sara Ahmed). The contributors examine the links between forms of extractivism and gendered discourses of sentimentality and the ways in which cultural narratives and practices deploy the sentimental mode (in plots of attachment, sacrifice, and suffering) to promote or challenge extractivism
Rethinking inconsistent mathematics
This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the rolee of logic and ethics in the practice of mathematics
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