Structural congruence for bialgebraic semantics

Rot, Jurriaan; Bonsangue, Marcello M.

doi:10.1016/j.jlamp.2016.08.001

Cited by 3 publications

(2 citation statements)

References 36 publications

(76 reference statements)

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“…The functor , for the complete monoid (Example 2.3), is ordered as a complete lattice [25], so also -ordered. Similar to the above, the functor is -ordered when restricted to countable sets, i.e., satisfies the above assumption.…”

Section: Liftings For Countably Accessible Functorsmentioning

confidence: 99%

Distributive laws for monotone specifications

Rot

2019

Acta Informatica

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Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical generalisation of the classical GSOS rule format, as well as its categorical dual, coGSOS. Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence. Unfortunately, the combination of the two formats does not feature these desirable properties. We show that monotone specifications—that disallow negative premises—do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.

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Section: Liftings For Countably Accessible Functorsmentioning

confidence: 99%

Distributive laws for monotone specifications

Rot

2019

Acta Informatica

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“…The functor (P f −) A does not satisfy the above assumption. The functor (M −) A , for the complete monoid R + ∪ {∞} (Example 4), is ordered as a complete lattice [19], so also DCPO ⊥ -ordered. Similar to the above, the functor (M c −) A is DCPO ⊥ -ordered when restricted to countable sets, i.e., satisfies the above assumption.…”

Section: Liftings For Countably Accessible Functorsmentioning

confidence: 99%

Distributive Laws for Monotone Specifications

Rot¹

2017

Electron. Proc. Theor. Comput. Sci.

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Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical generalisation of the classical GSOS rule format, as well as its categorical dual, coGSOS. Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence. Unfortunately, the combination of the two formats does not feature these desirable properties. We show that monotone specifications-that disallow negative premises-do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.

show abstract