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» Equational properties of iterative monads
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IANDC
2010
107views more  IANDC 2010»
13 years 1 months ago
Equational properties of iterative monads
Iterative monads of Calvin Elgot were introduced to treat the semantics of recursive equations purely algebraically. They are Lawvere theories with the property that all ideal sys...
Jirí Adámek, Stefan Milius, Jiri Vel...
MSCS
2010
103views more  MSCS 2010»
13 years 2 months ago
Iterative reflections of monads
Iterative monads, introduced by Calvin Elgot in the 1970’s, are those ideal monads in which every guarded system of recursive equations has a unique solution. For every ideal mon...
Jirí Adámek, Stefan Milius, Jiri Vel...
LICS
2000
IEEE
13 years 8 months ago
Complete Axioms for Categorical Fixed-Point Operators
We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We p...
Alex K. Simpson, Gordon D. Plotkin
CALCO
2009
Springer
159views Mathematics» more  CALCO 2009»
13 years 11 months ago
Complete Iterativity for Algebras with Effects
Abstract. Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with ...
Stefan Milius, Thorsten Palm, Daniel Schwencke
CALCO
2009
Springer
138views Mathematics» more  CALCO 2009»
13 years 11 months ago
Kleene Monads: Handling Iteration in a Framework of Generic Effects
Abstract. Monads are a well-established tool for modelling various computational effects. They form the semantic basis of Moggi’s computational metalanguage, the metalanguage of ...
Sergey Goncharov, Lutz Schröder, Till Mossako...