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- Henk Barendregt, Riet Prager, +27 authors Marco Swaen Jan
- 1992

- Susumu Hayashi
- Theor. Comput. Sci.
- 2006

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)

- Yohji Akama, Stefano Berardi, Susumu Hayashi, Ulrich Kohlenbach
- Proceedings of the 19th Annual IEEE Symposium on…
- 2004

The topic of this paper is relative constructivism. We are concerned with classifying nonconstructive principles from the constructive viewpoint. We compare, up to provability in intuitionistic arithmetic, subclassical principles like Markov's principle, (a function-free version of) weak Konig's lemma, Post's theorem, excluded middle for simply existential… (More)

- Susumu Hayashi, Ryosuke Sumitomo, Ken-ichiro Shii
- Theor. Comput. Sci.
- 2002

- Susumu Hayashi
- Inf. Comput.
- 1991

- Susumu Hayashi, Masahiro Nakata
- TYPES
- 2000

The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to 1 0 2-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recur-sive functions, which is… (More)

- Susumu Hayashi
- Theor. Comput. Sci.
- 1985

- Stefano Berardi, Thierry Coquand, Susumu Hayashi
- Ann. Pure Appl. Logic
- 2005

We associate to any game G, in the sense of Set Theory, a variant of it we call bck(G). We show through examples that many relevant non-constructive proofs in Algebra and Combinatorics can be interpreted by recursive winning strategy over some game of the form bck(G). We further support this claim by proving that games of the form bck(G) are a sound and… (More)

- Susumu Hayashi
- Discovery Science
- 2002

- Susumu Hayashi
- TLCA
- 2005

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)