Interpreting types as abstract values [The Abstract of the lecture notes] We expound a view of type checking as evaluation with `abstract values'. Whereas dynamic semantics, evaluation, deals with (dynamic) values like 0, 1, etc., static semantics, type checking, deals with approximations like int. A type system is sound if it correctly approximates the dynamic behavior and predicts its outcome: if the static semantics predicts that a term has the type int, the dynamic evaluation of the term, if it terminates, will yield an integer. As object language, we use simply-typed and let-polymorphic lambda calculi with integers and integer operations as constants. We use Haskell as a metalanguage in which to write evaluators, type checkers, type reconstructors and inferencers for the object language.
"Generalized Algebraic Data Structures" have become a a hot new topic. They have recently been added to the GHC compiler. They support the construction, maintenance, and propagation of semantic properties of programs using powerful old ideas about types (the Curry-Howard Isomorphism) in surprisingly easy to understand new ways. The language Omega was designed and implemented to demonstrate their utility. Here a a few talks I gave that explains how they work. Also class lectures
Purely functional arrays are notoriously difficult to implement and use efficiently due to the absence of destructive updates and the resultant frequent copying. Deforestation frameworks such as stream fusion achieve signficant improvements here but fail for a number of important operations which can nevertheless benefit from elimination of temporaries. To mitigate this problem, we extend stream fusion with support for in-place execution of array operations. This optimisation, which we call recycling, is easy to implement and can significantly reduce array allocation and copying in purely functional array algorithms.