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Foundations of Constructive Mathematics: Metamathematical Studies
One. Practice and Philosophy of Constructive Mathematics.- I. Examples of Constructive Mathematics.- 1. The Real Numbers.- 2. Constructive Reasoning.- 3. Order in the Reals.- 4. Subfields of R withExpand
Continuity in Intuitionistic Set Theories
Publisher Summary This chapter examines the connections between the two concepts of continuity and constructivity. A connection between constructivity and continuity has long been perceived inExpand
Design principles of Mathpert: software to support education in algebra and calculus
  • M. Beeson
  • Computer Science
  • Computer-Human Interaction in Symbolic…
  • 1998
This paper lists eight design criteria that must be met if we are to provide successful computer support for education in algebra, trigonometry, and calculus. It also describes Mathpert, a piece ofExpand
Recursive models for constructive set theories
  • M. Beeson
  • Mathematics, Computer Science
  • Ann. Math. Log.
  • 1 December 1982
TLDR
It is shown that for implication-free formulae of HAω, satisfaction in the model coincides with mr-HEO realizability, and this model is extended to a recursive model of the constructive set theories of Myhill and Friedman. Expand
Goodman’s theorem and beyond
modified realizability: specific "total realizabilities" in HRO, HEO as X: Kleene's recursive realizability. Clearly "X" is an abstract interpretation of HA in a suitable theory of partialExpand
Logic and Computation in MATHPERT: An Expert System for Learning Mathematics
  • M. Beeson
  • Computer Science
  • Computers and Mathematics
  • 1 May 1989
TLDR
The paper explains how MATHPERT maintains and uses an internal model of its user to produce individually tailored explanations, and how it dynamically generates individualized and helpful error messages by comparing user errors to its own internal solution of the problem. Expand
A constructive version of Tarski's geometry
  • M. Beeson
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 13 July 2014
TLDR
Three constructive versions of Tarski's theory have been modified so that the points they assert to exist are unique and depend continuously on parameters, and it is shown that objects proved to exist can be constructed by ruler and compass. Expand
Mathematical Induction in Otter-Lambda
  • M. Beeson
  • Mathematics, Computer Science
  • Journal of Automated Reasoning
  • 1 April 2006
TLDR
A variety of examples of inductive proofs found by Otter-lambda are presented: some in pure Peano arithmetic, some in Peanos arithmetic with defined predicates, someIn theories combining algebra and the natural numbers, some involving algebraic simplification, and some involving list induction instead of numerical induction. Expand
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