<theory>function application (A B) is only synctactically valid if A has type s --> t, where the type of B is s (or an instance or s in a polymorphic language) and t is any type. If the types allowed for terms are restricted, e.g. to Hindley-Milner types then no term may be applied to itself, thus avoiding one kind of non-terminating evaluation. Most functional programming languages, e.g. Haskell, ML, are closely based on variants of the typed lambda-calculus.
Last updated: 1995-03-25