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Value Recursion in Monadic Computations
 OGI School of Science and Engineering, OHSU
, 2002
"... viii 1 ..."
Free Iterative Theories
 A Coalgebraic View, Math. Structures Comput. Sci
"... Summary. We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣtree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points ..."
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Summary. We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣtree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Rat is the monad of free rational theories and every free rational theory has a continuous completion. Key words: Iteration theory, rational theory, monad, EilenbergMoore algebra. 1
Kleene Algebra with Products and Iteration Theories
"... We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism. ..."
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We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism.