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Content Tagged with Haskell + mathematics

"A comonad is a special way at looking at a data structure that allows one to work with the individual members of that data structure in the context of the entire data structure." Comonads are the dual structure to monads.

Haskell is based on the lambda calculus. "Since every expression is a unary function, and every argument and result are functions too, lambda calculus is quite interesting and unique within both computation and mathematics." . Building on earlier work by Kleene and constructing a Gödel numbering for lambda expressions, he constructs a lambda expression e which closely follows the proof of Gödel's first incompleteness theorem. If e is applied to its own Gödel number, a contradiction results.

~"given the non-recursive left-fold we can: instantiate it into the ordinary left fold, or instantiate in into a stream." Also there is some deep mystery linking fixed points, folds, and call/cc.

"An alternative title for this post is, what is the type of differentiation? Hint: it's not quite (R→R)→(R→R), because how would you make sure the input function is differentiable?)"

remarkably clear explanation of the fixed-point combinator in haskell

"Vectors are represented by lists with type-encoded lengths. The constructor is :., which acts like a cons both at the value and type levels, with () taking the place of nil. So x:.y:.z:.() is a 3d vector."

"Broadly, defunctionalization is transforming a program to eliminate higher-order functions."