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This is even true for plain Haskell functions (pattern matching handles the “parsing” step, rendering is either done by the identity (in the trivial case) or “show”). However, we can use an algebraic/category theoretic concept (“the monad”) to encapsulate the folding and unfolding of a data structure into another.

The monad defines a “bind” operator >>=, which takes a monad element and a function on the monad element’s underlying type back to the monad. The monad element is unfolded (as defined by >>=), and f is applied to refold it, perhaps in terms of a different kind of data structure.

Of course, a parser is automatically a state machine and lots of other “equivalent” things, and so by changing the emphasis of interpretation, one can construct them all using the same simple Haskell notation.

From a different point of view, a programming language’s “object system” is a specific monad operating on a tree of object-oriented classes to seek methods. “Generalized object systems” can be built, and the monads are them.

]]>This is even true for plain Haskell functions (pattern matching handles the “parsing” step, rendering is either done by the identity (in the trivial case) or “show”). However, we can use an algebraic/category theoretic concept (“the monad”) to encapsulate the folding and unfolding of a data structure into another.

The monad defines a “bind” operator >>=, which takes a monad element and a function on the monad element’s underlying type back to the monad. The monad element is unfolded (as defined by >>=), and f is applied to refold it, perhaps in terms of a different kind of data structure.

Of course, a parser is automatically a state machine and lots of other “equivalent” things, and so by changing the emphasis of interpretation, one can construct them all using the same simple Haskell notation.

From a different point of view, a programming language’s “object system” is a specific monad operating on a tree of object-oriented classes to seek methods. “Generalized object systems” can be built, and the monads are them.

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