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------------------------------------------------------------------------ -- Code related to the paper "Up-to Techniques using Sized Types" -- -- Nils Anders Danielsson ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} module README where ------------------------------------------------------------------------ -- Pointers to results from the paper -- In order to more easily find code corresponding to results from the -- paper, see the following module. Note that some of the code -- referenced below is not discussed at all in the paper. import README.Pointers-to-results-from-the-paper ------------------------------------------------------------------------ -- Some preliminaries -- Overloaded "equational" reasoning combinators. import Equational-reasoning -- Unary and binary relations. import Relation ------------------------------------------------------------------------ -- Containers -- Indexed containers. import Indexed-container -- Container combinators. import Indexed-container.Combinators -- The delay monad defined as the greatest fixpoint of an indexed -- container. import Indexed-container.Delay-monad ------------------------------------------------------------------------ -- Up-to techniques -- Up-to techniques, compatibility, size-preserving functions, and the -- companion. import Up-to -- Closure properties for Compatible and Size-preserving. -- -- (Some negative results in this module depend on code presented -- further down.) import Up-to.Closure -- Up-to techniques via. import Up-to.Via ------------------------------------------------------------------------ -- Labelled transition systems -- Labelled transition systems (LTSs). import Labelled-transition-system import Labelled-transition-system.Equational-reasoning-instances -- CCS. import Labelled-transition-system.CCS -- A labelled transition system for the delay monad. import Labelled-transition-system.Delay-monad -- An LTS from Section 6.2.5 of "Enhancements of the bisimulation -- proof method" by Pous and Sangiorgi. import Labelled-transition-system.6-2-5 ------------------------------------------------------------------------ -- Similarity -- The one-sided Step function, used to define similarity and the -- two-sided Step function. import Similarity.Step -- A parametrised coinductive definition that can be used to define -- various forms of similarity. import Similarity.General -- For more information about similarity, see "Similarity, continued" -- below. ------------------------------------------------------------------------ -- Strong bisimilarity -- The Step function, used to define strong and weak bisimilarity as -- well as expansion. import Bisimilarity.Step -- A parametrised coinductive definition that can be used to define -- strong and weak bisimilarity as well as expansion. import Bisimilarity.General -- A coinductive definition of (strong) bisimilarity. import Bisimilarity import Bisimilarity.Equational-reasoning-instances -- The classical definition of (strong) bisimilarity. import Bisimilarity.Classical import Bisimilarity.Classical.Equational-reasoning-instances -- A comparison of the two definitions of bisimilarity. import Bisimilarity.Comparison -- Some results related to strong bisimilarity for the delay monad. import Bisimilarity.Delay-monad -- Some results related to CCS, implemented without using a fixed form -- of bisimilarity. import Bisimilarity.CCS.General -- Various results or examples related to CCS, implemented using the -- coinductive definition of bisimilarity. import Bisimilarity.CCS import Bisimilarity.CCS.Examples import Bisimilarity.CCS.Examples.Natural-numbers -- Some of the results/examples above have also been implemented using -- the classical definition of bisimilarity. import Bisimilarity.CCS.Classical import Bisimilarity.CCS.Examples.Classical -- Up-to techniques for strong bisimilarity. import Bisimilarity.Up-to import Bisimilarity.Up-to.CCS import Bisimilarity.Up-to.Counterexamples -- Some results related to an LTS from Section 6.2.5 of "Enhancements -- of the bisimulation proof method" by Pous and Sangiorgi, -- implemented using the coinductive definition of bisimilarity. import Bisimilarity.6-2-5 ------------------------------------------------------------------------ -- Expansion -- A coinductive definition of the expansion ordering. import Expansion import Expansion.Equational-reasoning-instances -- Lemmas related to expansion and CCS. import Expansion.CCS -- Some results related to expansion for the delay monad. import Expansion.Delay-monad ------------------------------------------------------------------------ -- Weak bisimilarity -- A coinductive definition of weak bisimilarity. import Bisimilarity.Weak import Bisimilarity.Weak.Equational-reasoning-instances -- An alternative (non-standard) coinductive definition of weak -- bisimilarity. import Bisimilarity.Weak.Alternative import Bisimilarity.Weak.Alternative.Equational-reasoning-instances -- An alternative (non-standard) classical definition of weak -- bisimilarity. import Bisimilarity.Weak.Alternative.Classical -- A comparison of the two alternative definitions of weak -- bisimilarity. import Bisimilarity.Weak.Alternative.Comparison -- The two coinductive definitions of weak bisimilarity are pointwise -- logically equivalent. import Bisimilarity.Weak.Equivalent -- Lemmas related to weak bisimilarity and CCS. import Bisimilarity.Weak.CCS -- Examples/exercises related to CCS from "Enhancements of the -- bisimulation proof method" by Pous and Sangiorgi. import Bisimilarity.Weak.CCS.Examples -- Some results about various forms of coinductively defined weak -- bisimilarity for the delay monad. import Bisimilarity.Weak.Delay-monad -- Up-to techniques for the standard coinductive definition of weak -- bisimilarity. import Bisimilarity.Weak.Up-to import Bisimilarity.Weak.Up-to.CCS -- Up-to techniques for the delay monad and the alternative -- coinductive definition of weak bisimilarity. import Bisimilarity.Weak.Alternative.Up-to.Delay-monad ------------------------------------------------------------------------ -- Similarity, continued -- A coinductive definition of (strong) similarity. import Similarity import Similarity.Equational-reasoning-instances -- Lemmas related to strong similarity for CCS. import Similarity.CCS -- A coinductive definition of weak similarity. import Similarity.Weak import Similarity.Weak.Equational-reasoning-instances -- An up-to technique for weak similarity. import Similarity.Weak.Up-to
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