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JUCS
2010
110views more  JUCS 2010»
13 years 4 months ago
On Choice Principles and Fan Theorems
: Veldman proved that the contrapositive of countable binary choice is a theorem of full-fledged intuitionism, to which end he used a principle of continuous choice and the fan the...
Hannes Diener, Peter Schuster
ENTCS
2006
110views more  ENTCS 2006»
13 years 9 months ago
First Steps in Synthetic Computability Theory
Computability theory, which investigates computable functions and computable sets, lies at the foundation of computer science. Its classical presentations usually involve a fair a...
Andrej Bauer
FM
2001
Springer
130views Formal Methods» more  FM 2001»
14 years 2 months ago
Towards a Topos Theoretic Foundation for the Irish School of Constructive Mathematics
The Irish School of Constructive Mathematics (M♣ c ), which extends the VDM, exploits an algebraic notation based upon monoids and their morphisms for the purposes of abstract mo...
Mícheál Mac an Airchinnigh
CIE
2007
Springer
14 years 4 months ago
RZ: A Tool for Bringing Constructive and Computable Mathematics Closer to Programming Practice
Realizability theory is not just a fundamental tool in logic and computability. It also has direct application to the design and implementation of programs, since it can produce co...
Andrej Bauer, Christopher A. Stone