a6cd7156a1
Free monads are useful for many tree-like structures and domain specific languages. If f is a Functor then the free Monad on f is the type of trees whose nodes are labeled with the constructors of f. The word "free" is used in the sense of "unrestricted" rather than "zero-cost": Free f makes no constraining assumptions beyond those given by f and the definition of Monad. As used here it is a standard term from the mathematical theory of adjoint functors. Cofree comonads are dual to free monads. They provide convenient ways to talk about branching streams and rose-trees, and can be used to annotate syntax trees. The cofree comonad can be seen as a stream parameterized by a Functor that controls its branching factor.
14 lines
727 B
Text
14 lines
727 B
Text
Free monads are useful for many tree-like structures and domain specific
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languages.
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If f is a Functor then the free Monad on f is the type of trees whose nodes
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are labeled with the constructors of f. The word "free" is used in the
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sense of "unrestricted" rather than "zero-cost": Free f makes no
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constraining assumptions beyond those given by f and the definition of
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Monad. As used here it is a standard term from the mathematical theory of
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adjoint functors.
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Cofree comonads are dual to free monads. They provide convenient ways to
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talk about branching streams and rose-trees, and can be used to annotate
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syntax trees. The cofree comonad can be seen as a stream parameterized by a
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Functor that controls its branching factor.
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