219,072 research outputs found
Patterns for computational effects arising from a monad or a comonad
This paper presents equational-based logics for proving first order
properties of programming languages involving effects. We propose two dual
inference system patterns that can be instanciated with monads or comonads in
order to be used for proving properties of different effects. The first pattern
provides inference rules which can be interpreted in the Kleisli category of a
monad and the coKleisli category of the associated comonad. In a dual way, the
second pattern provides inference rules which can be interpreted in the
coKleisli category of a comonad and the Kleisli category of the associated
monad. The logics combine a 3-tier effect system for terms consisting of pure
terms and two other kinds of effects called 'constructors/observers' and
'modifiers', and a 2-tier system for 'up-to-effects' and 'strong' equations.
Each pattern provides generic rules for dealing with any monad (respectively
comonad), and it can be extended with specific rules for each effect. The paper
presents two use cases: a language with exceptions (using the standard monadic
semantics), and a language with state (using the less standard comonadic
semantics). Finally, we prove that the obtained inference system for states is
Hilbert-Post complete
Breaking a monad-comonad symmetry between computational effects
Computational effects may often be interpreted in the Kleisli category of a
monad or in the coKleisli category of a comonad. The duality between monads and
comonads corresponds, in general, to a symmetry between construction and
observation, for instance between raising an exception and looking up a state.
Thanks to the properties of adjunction one may go one step further: the
coKleisli-on-Kleisli category of a monad provides a kind of observation with
respect to a given construction, while dually the Kleisli-on-coKleisli category
of a comonad provides a kind of construction with respect to a given
observation. In the previous examples this gives rise to catching an exception
and updating a state. However, the interpretation of computational effects is
usually based on a category which is not self-dual, like the category of sets.
This leads to a breaking of the monad-comonad duality. For instance, in a
distributive category the state effect has much better properties than the
exception effect. This remark provides a novel point of view on the usual
mechanism for handling exceptions. The aim of this paper is to build an
equational semantics for handling exceptions based on the coKleisli-on-Kleisli
category of the monad of exceptions. We focus on n-ary functions and
conditionals. We propose a programmer's language for exceptions and we prove
that it has the required behaviour with respect to n-ary functions and
conditionals.Comment: arXiv admin note: substantial text overlap with arXiv:1310.060
Overcoming Psychologism. Twardowski on Actions and Products
This paper is about the topic of psychologism in the work of Kazimierz Twardowski and my aim is to revisit this important issue in light of recent publications from, and on Twardowski’s works. I will first examine the genesis of psychologism in the young Twardowski’s work; secondly, I will examine Twardowski’s picture theory of meaning and Husserl’s criticism in Logical Investigations; the third part is about Twardowski’s recognition and criticism of his psychologism in his lectures on the psychology of thinking; the fourth and fifth parts provide an overview of Twardowski’s paper “Actions and Products” while the sixth part addresses the psychologism issue in the last part of this paper through the delineation of psychology and the humanities. I shall conclude this study with a brief assessment of Twardowski’s solution to psychologism
Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix
We clarify different definitions of the density matrix by proposing the use
of different names, the full density matrix for a single-closed quantum system,
the compressed density matrix for the averaged single molecule state from an
ensemble of molecules, and the reduced density matrix for a part of an
entangled quantum system, respectively. We show that ensembles with the same
compressed density matrix can be physically distinguished by observing
fluctuations of various observables. This is in contrast to a general belief
that ensembles with the same compressed density matrix are identical. Explicit
expression for the fluctuation of an observable in a specified ensemble is
given. We have discussed the nature of nuclear magnetic resonance quantum
computing. We show that the conclusion that there is no quantum entanglement in
the current nuclear magnetic resonance quantum computing experiment is based on
the unjustified belief that ensembles having the same compressed density matrix
are identical physically. Related issues in quantum communication are also
discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200
Several types of types in programming languages
Types are an important part of any modern programming language, but we often
forget that the concept of type we understand nowadays is not the same it was
perceived in the sixties. Moreover, we conflate the concept of "type" in
programming languages with the concept of the same name in mathematical logic,
an identification that is only the result of the convergence of two different
paths, which started apart with different aims. The paper will present several
remarks (some historical, some of more conceptual character) on the subject, as
a basis for a further investigation. The thesis we will argue is that there are
three different characters at play in programming languages, all of them now
called types: the technical concept used in language design to guide
implementation; the general abstraction mechanism used as a modelling tool; the
classifying tool inherited from mathematical logic. We will suggest three
possible dates ad quem for their presence in the programming language
literature, suggesting that the emergence of the concept of type in computer
science is relatively independent from the logical tradition, until the
Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC
Using Ontologies for the Design of Data Warehouses
Obtaining an implementation of a data warehouse is a complex task that forces
designers to acquire wide knowledge of the domain, thus requiring a high level
of expertise and becoming it a prone-to-fail task. Based on our experience, we
have detected a set of situations we have faced up with in real-world projects
in which we believe that the use of ontologies will improve several aspects of
the design of data warehouses. The aim of this article is to describe several
shortcomings of current data warehouse design approaches and discuss the
benefit of using ontologies to overcome them. This work is a starting point for
discussing the convenience of using ontologies in data warehouse design.Comment: 15 pages, 2 figure
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