This page shows all publications that appeared in the IASI annual research reports. Authors currently affiliated with the Institute are always listed with the full name.

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Show all publications of the year  ALL, with author Colagrossi A., in the category IASI Research Reports (or show them all):

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IASI Research Report n. 460  (Previous    Next) 


Cioni G., Colagrossi A., Temperini M.

A laboratory for teaching abstract algebra

ABSTRACT

An environment for supporting interactive abstract algebra learning is presented. The environment is based on the definition of an object-oriented programming language integrated with an automated deduction tool. The class construct is enhanced by allowing for defining axioms for the objects in that class. The deduction tool implements a sequent calculus and can perform (besides verification) abduction and generation of properties. To exploit the reasoning capabilities of the programming system we define a set of operators to work over hierarchies of mathematical structures. The object-oriented methodology we follow allows for a clean design of the abstract domains at issue. This combines with the reasoning capabilities and the resulting system comes out to be a laboratory for practising in defining and comparing the structures of abstract algebra. It allows for the definition of hierarchies of mathematical structures, in which an element can be derived by others, sharing and increasing their properties. We present the main features of the environment, and show some significant examples based on work sessions.