an optimization technique used primarily to speed up computer programs by having function calls avoid repeating the calculation of results for previously-processed inputs.
http://en.wikipedia.org/wiki/Associative_array
Map
http://en.wikipedia.org/wiki/Red-black_tree
= Self-balancing Binary Search Tree
http://www.haskell.org/haskellwiki/Smart_constructors
http://www.haskell.org/haskellwiki/Type_arithmetic
Type arithmetic (or type-level computation) are calculations on the type-level, often implemented in Haskell using functional dependencies to represent functions.
data Zero data Succ a class Add a b ab | a b -> ab, a ab -> b instance Add Zero b b instance (Add a b ab) => Add (Succ a) b (Succ ab)
http://www.haskell.org/haskellwiki/Fundeps
Functional dependencies are used to constrain the parameters of type classes
http://www.haskell.org/haskellwiki/Peano_numbers
Peano numbers are a simple way of representing the natural numbers using only a zero value and a successor function.
http://en.wikipedia.org/wiki/Curry-Howard
The Curry–Howard correspondence is the direct relationship between computer programs and proofs in programming language theory and proof theory. Also known as Curry–Howard isomorphism, proofs-as-programs correspondence and formulae-as-types correspondence, it is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard.
