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Learning theoretic aspects of mathematics and logic have been studied by many authors. They study how mathematical and logical objects are algorithmically \learned" (inferred) from nite data. Although they study mathematical objects, the objective of the studies is learning. In this paper, a mathematics of which foundation itself is learning theoretic will(More)
Proof animation is a way of executing proofs to nd errors in the formalization of proofs. It is intended to be \testing in proof engineer-ing". Although the realizability i n terpretation as well as the functional interpretation based on limit-computations were introduced as means for proof animation, they were unrealistic as an architectural basis for(More)