5,455 research outputs found
Tracing monadic computations and representing effects
In functional programming, monads are supposed to encapsulate computations,
effectfully producing the final result, but keeping to themselves the means of
acquiring it. For various reasons, we sometimes want to reveal the internals of
a computation. To make that possible, in this paper we introduce monad
transformers that add the ability to automatically accumulate observations
about the course of execution as an effect. We discover that if we treat the
resulting trace as the actual result of the computation, we can find new
functionality in existing monads, notably when working with non-terminating
computations.Comment: In Proceedings MSFP 2012, arXiv:1202.240
Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory
Aim of this paper is to provide preliminary elements for discussion about the
implications of the Hierarchy Theory of Evolution on the design and evolution
of artificial systems and socio-technical organizations. In order to achieve
this goal, a number of analogies are drawn between the System of Leibniz; the
socio-technical architecture known as Fractal Social Organization; resilience
and related disciplines; and Hierarchy Theory. In so doing we hope to provide
elements for reflection and, hopefully, enrich the discussion on the above
topics with considerations pertaining to related fields and disciplines,
including computer science, management science, cybernetics, social systems,
and general systems theory.Comment: To appear in the Proceedings of ANTIFRAGILE'17, 4th International
Workshop on Computational Antifragility and Antifragile Engineerin
Leibnizian Bodies: Phenomena, Aggregates of Monads, or Both?
I propose a straightforward reconciliation of Leibniz’s conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz’s idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. Taking notice of the fact that Leibniz speaks of three respects in which one thing may immediately presuppose others--i.e., with respect to its being, its existence, and its reality--I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in two of these respects. Accordingly, good sense can be made of both the claim that a phenomenon in one monad is an aggregate of other monads (in Leibniz’s technical sense of 'aggregate') and the (equivalent) claim that the latter monads are constituents of the phenomenon (in his technical sense of 'constituent'). So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think
On the 2-categories of weak distributive laws
A weak mixed distributive law (also called weak entwining structure) in a
2-category consists of a monad and a comonad, together with a 2-cell relating
them in a way which generalizes a mixed distributive law due to Beck. We show
that a weak mixed distributive law can be described as a compatible pair of a
monad and a comonad, in 2-categories extending, respectively, the 2-category of
comonads and the 2-category of monads. Based on this observation, we define a
2-category whose 0-cells are weak mixed distributive laws. In a 2-category K
which admits Eilenberg-Moore constructions both for monads and comonads, and in
which idempotent 2-cells split, we construct a fully faithful 2-functor from
this 2-category of weak mixed distributive laws to K^{2 x 2}.Comment: 15 pages LaTeX source, final version to appear in Comm. Algebr
Free Applicative Functors
Applicative functors are a generalisation of monads. Both allow the
expression of effectful computations into an otherwise pure language, like
Haskell. Applicative functors are to be preferred to monads when the structure
of a computation is fixed a priori. That makes it possible to perform certain
kinds of static analysis on applicative values. We define a notion of free
applicative functor, prove that it satisfies the appropriate laws, and that the
construction is left adjoint to a suitable forgetful functor. We show how free
applicative functors can be used to implement embedded DSLs which can be
statically analysed.Comment: In Proceedings MSFP 2014, arXiv:1406.153
Emilie du Chatelet's Metaphysics of Substance
much early modern metaphysics grew with an eye to the new science of its time, but few figures took it as seriously as Emilie du Châtelet. Happily, her oeuvre is now attracting close, renewed attention, and so the time is ripe for looking into her metaphysical foundation for empirical theory. Accordingly, I move here to do just that. I establish two conclusions. First, du Châtelet's basic metaphysics is a robust realism. Idealist strands, while they exist, are confined to non-basic regimes. Second, her substance realism seems internally coherent, so her foundational project appears successful.I have two aims in this paper. Historically, I show that du Châtelet's main source of inspiration was Christian..
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