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JUCS
2010
110views more  JUCS 2010»
12 years 11 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 4 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»
13 years 9 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
13 years 10 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