Dependently typed Haskell heaps
This is my first attempt to do "real" dependently typed programming in Haskell: An implementation of leftists heaps (following [Chris Okasaki's "Purely Functional Data Structures"] (http://www.cambridge.org/gb/academic/subjects/computer-science/programming-languages-and-applied-logic/purely-functional-data-structures)) where both the heap invariant and the leftist property are statically ensured by the type system.
To encode those invariants, I abstract the concept of type-level natural number into a type class, of which I provide two implementations:
- simple, unary "Peano" numbers, which are of course highly inefficient, but easier to understand and
- binary numbers, which are more efficient, but also more complicated.
Using the binary encoding of type-level natural numbers, I can quickly sort a list of 50000 elements.