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.
demonstrates that sprintf and sscanf can indeed use exactly the same formatting specification, which is a first-class value. We demonstrate typed sprintf and typed sscanf sharing the same formatting specification. Our solution is surprisingly trivial: it defines a simple embedded domain-specific language of formatting patterns. The functions sprintf and sscanf are two interpreters of the language, to build or parse a string according to the given pattern. Our solution relies only on GADTs. We demonstrate that lambda-abstractions at the type level are expressible already in the Hindley-Milner type system; GADT with the included polymorphic recursion help us use the abstractions.