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------------------------------------------------------------------------ -- Code related to the delay monad -- -- Nils Anders Danielsson ------------------------------------------------------------------------ {-# OPTIONS --cubical --sized-types #-} module README where -- The concept referred to as the delay monad here is the monad -- presented by Capretta in "General Recursion via Coinductive Types". ------------------------------------------------------------------------ -- The delay monad -- The delay monad, defined coinductively. import Delay-monad -- A type used to index a combined definition of strong and weak -- bisimilarity and expansion. import Delay-monad.Bisimilarity.Kind -- A combined definition of strong and weak bisimilarity and -- expansion, along with various properties. import Delay-monad.Bisimilarity -- Strong bisimilarity for partially defined values, along with a -- proof showing that this relation is pointwise isomorphic to path -- equality. import Delay-monad.Bisimilarity.For-all-sizes -- A variant of weak bisimilarity that can be used to relate the -- number of steps in two computations. import Delay-monad.Quantitative-weak-bisimilarity -- Termination. import Delay-monad.Termination -- Alternative definitions of weak bisimilarity. import Delay-monad.Bisimilarity.Alternative -- An observation about weak bisimilarity. import Delay-monad.Bisimilarity.Observation -- Some negative results related to weak bisimilarity and expansion. import Delay-monad.Bisimilarity.Negative -- An example showing that transitivity-like proofs that are not -- size-preserving can sometimes be used in a compositional way. import Delay-monad.Bisimilarity.Transitivity-constructor -- A partial order. import Delay-monad.Partial-order -- Least upper bounds. import Delay-monad.Least-upper-bound -- The delay monad is a monad up to strong bisimilarity. import Delay-monad.Monad -- The "always true" predicate, □. import Delay-monad.Always -- A combinator for running two (independent) computations in -- sequence. import Delay-monad.Sequential -- A combinator for running two computations in parallel. import Delay-monad.Parallel ------------------------------------------------------------------------ -- A variant of the delay monad with a sized type parameter -- The delay monad, defined coinductively, with a sized type -- parameter. import Delay-monad.Sized -- A combined definition of strong and weak bisimilarity and -- expansion, along with various properties. import Delay-monad.Sized.Bisimilarity -- Strong bisimilarity for partially defined values, along with a -- proof showing that this relation is pointwise isomorphic to path -- equality. import Delay-monad.Sized.Bisimilarity.For-all-sizes -- Termination. import Delay-monad.Sized.Termination -- Alternative definitions of weak bisimilarity. import Delay-monad.Sized.Bisimilarity.Alternative -- Some negative results related to weak bisimilarity and expansion. import Delay-monad.Sized.Bisimilarity.Negative -- A partial order. import Delay-monad.Sized.Partial-order -- Least upper bounds. import Delay-monad.Sized.Least-upper-bound -- A monad-like structure. import Delay-monad.Sized.Monad -- The "always true" predicate, □. import Delay-monad.Sized.Always
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