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Convexity, duality, and effects
 IFIP Theoretical Computer Science 2010, number 82(1) in IFIP Adv. in Inf. and Comm. Techn
, 2010
"... This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call ‘convex functors’; they include what are usually called probability distribution functors. T ..."
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Cited by 3 (2 self)
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This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call ‘convex functors’; they include what are usually called probability distribution functors. These relationships take the form of three adjunctions. Two of these three are ‘dual ’ adjunctions for convex sets, one time with the Boolean truth values {0, 1} as dualising object, and one time with the probablity values [0, 1]. The third adjunction is between effect algebras and convex functors. 1
Coalgebraic Walks, in Quantum and Turing Computation
, 2010
"... Abstract. The paper investigates nondeterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Nondeterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras ..."
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Cited by 1 (1 self)
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Abstract. The paper investigates nondeterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Nondeterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad is also used to describe Turing machines coalgebraically, namely as controlled ‘walks ’ on a tape. 1
A proof order for decreasing diagrams  Interpreting conversions in involutive monoids
, 2012
"... We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids. ..."
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We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids.
Decreasing proof orders  Interpreting conversions in involutive monoids
, 2012
"... We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids. ..."
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We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids.