45,452 research outputs found
Procedural embodiment and magic in linear equations
How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment – perceiving the world, acting on it and reflecting on the effect of the actions – to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not encapsulate algebraic expressions from process to object, they do not solve ‘evaluation equations’ such as by ‘undoing’ the operations on the left, they do not find such equations easier to solve than , and they do not use general principles of ‘do the same thing to both sides.’ Instead they build their own ways of working based on the embodied actions they perform on the symbols, mentally picking them up and moving them around, with the added ‘magic’ of rules such as ‘change sides, change signs.’ We consider the need for a theoretical framework that includes both embodiment and process-object encapsulation of symbolism and the need for communication of theoretical insights to address the practical problems of teachers and students
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using
Krivine's classical realizability---where classical proofs are interpreted as
lambda-terms with the call/cc control operator. We first recall the basic
framework of classical realizability (in classical second-order arithmetic) and
show how to extend it with primitive numerals for faster computations. Then we
show how to perform witness extraction in this framework, by discussing several
techniques depending on the shape of the existential formula. In particular, we
show that in the Sigma01-case, Krivine's witness extraction method reduces to
Friedman's through a well-suited negative translation to intuitionistic
second-order arithmetic. Finally we discuss the advantages of using call/cc
rather than a negative translation, especially from the point of view of an
implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS),
201
The ModelCC Model-Driven Parser Generator
Syntax-directed translation tools require the specification of a language by
means of a formal grammar. This grammar must conform to the specific
requirements of the parser generator to be used. This grammar is then annotated
with semantic actions for the resulting system to perform its desired function.
In this paper, we introduce ModelCC, a model-based parser generator that
decouples language specification from language processing, avoiding some of the
problems caused by grammar-driven parser generators. ModelCC receives a
conceptual model as input, along with constraints that annotate it. It is then
able to create a parser for the desired textual syntax and the generated parser
fully automates the instantiation of the language conceptual model. ModelCC
also includes a reference resolution mechanism so that ModelCC is able to
instantiate abstract syntax graphs, rather than mere abstract syntax trees.Comment: In Proceedings PROLE 2014, arXiv:1501.0169
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