Elementary Mathematical Programming.

Elementary Strong Functional Programming

Functional programming is a good idea, but we haven’t got it quite right yet. What we have been doing up to now is weak (or partial) functional programming. What we should be doing is strong (or total) functional programming in which all computations terminate. We propose an elementary discipline of strong functional programming. A key feature of the discipline is that we introduce a type disti...

Persistence of elementary programming skills

An elementary fuzzy programming language

" In this paper, we define a fuzzy imperative programming language (called L), powerful enough to express crisp and fuzzy algorithms. Its small instruction set is designed to enhance readability, and it is proved before that the class of functions that can be programmed in L is equivalent to the class of functions computed by a W-Turing machine and to the W-recursive functions. The language is ...

Mathematical programming based debugging

Verifying that a piece of software has no bugs means proving that it has certain desired properties, such as an array index not taking values outside certain bounds. Abstract interpretation is used in the static analysis of code to establish the inclusion-wise smallest set of values (numerical invariant) that the program variables can attain during program execution. Such sets can be used to de...

Programming as mathematical narrative

This paper describes a narrative-oriented approach to the design and the analysis of a computational system and a set of activities for mathematical learning. Our central contention is that programming can offer a key to resolving the tension between the different representational structures of narrative and mathematical formalism. In the course of describing our approach, we make a distinction...