3,812 research outputs found
What we talk about when we talk about monads
Computer science provides an in-depth understanding of technical aspects of programming concepts, but if we want to understand how programming concepts evolve, how programmers think and talk about them and how they are used in practice, we need to consider a broader perspective that includes historical, philosophical and cognitive aspects. In this paper, we develop such broader understanding of monads, a programming concept that has an infamous formal definition, syntactic support in several programming languages and a reputation for being elegant and powerful, but also intimidating and difficult to grasp.
This paper is not a monad tutorial. It will not tell you what a monad is. Instead, it helps you understand how computer scientists and programmers talk about monads and why they do so. To answer these questions, we review the history of monads in the context of programming and study the development through the perspectives of philosophy of science, philosophy of mathematics and cognitive sciences.
More generally, we present a framework for understanding programming concepts that considers them at three levels: formal, metaphorical and implementation. We base such observations on established results about the scientific method and mathematical entities - cognitive sciences suggest that the metaphors used when thinking about monads are more important than widely accepted, while philosophy of science explains how the research paradigm from which monads originate influences and restricts their use.
Finally, we provide evidence for why a broader philosophical, sociological look at programming concepts should be of interest for programmers. It lets us understand programming concepts better and, fundamentally, choose more appropriate abstractions as illustrated in a number of case studies that conclude the paper
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
The Mathematical Background of Lomonosov's Contribution
This is a short overview of the influence of mathematicians and their ideas
on the creative contribution of Mikhailo Lomonosov on the occasion of the
tercentenary of his birth
Leibniz's Monadology: A New Translation and Guide
A fresh translation and in-depth commentary of Leibniz's seminal text, the Monadology.
Written in 1714, the Monadology is widely considered to be the classic statement of Leibniz's mature philosophy. In the space of 90 numbered paragraphs, totalling little more than 6000 words, Leibniz outlines - and argues for - the core features of his philosophical system. Although rightly regarded as a masterpiece, it is also a very condensed work that generations of students have struggled to understand.
Lloyd Strickland presents a new translation of the Monadology, alongside key parts of the Theodicy, and an in-depth, section-by-section commentary that explains in detail not just what Leibniz is saying in the text but also why he says it. The sharp focus on the various arguments and other justifications Leibniz puts forward makes possible a deeper and more sympathetic understanding of his doctrines
On coalgebras with internal moves
In the first part of the paper we recall the coalgebraic approach to handling
the so-called invisible transitions that appear in different state-based
systems semantics. We claim that these transitions are always part of the unit
of a certain monad. Hence, coalgebras with internal moves are exactly
coalgebras over a monadic type. The rest of the paper is devoted to supporting
our claim by studying two important behavioural equivalences for state-based
systems with internal moves, namely: weak bisimulation and trace semantics.
We continue our research on weak bisimulations for coalgebras over order
enriched monads. The key notions used in this paper and proposed by us in our
previous work are the notions of an order saturation monad and a saturator. A
saturator operator can be intuitively understood as a reflexive, transitive
closure operator. There are two approaches towards defining saturators for
coalgebras with internal moves. Here, we give necessary conditions for them to
yield the same notion of weak bisimulation.
Finally, we propose a definition of trace semantics for coalgebras with
silent moves via a uniform fixed point operator. We compare strong and weak
bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page
Variations on Algebra: monadicity and generalisations of equational theories
Dedicated to Rod Burstal
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