General Observations
Given the standard semantics, the simply typed lambda calculus is strongly normalizing: that is, well-typed terms always reduce to a value, i.e., a abstraction. This is because recursion is not allowed by the typing rules: it is impossible to find types for fixed-point combinators and the looping term . Recursion can be added to the language by either having a special operator of type or adding general recursive types, though both eliminate strong normalization.
Since it is strongly normalizing, it is decidable whether or not a simply typed lambda calculus program halts: it does! We can therefore conclude that the language is not Turing complete.
Read more about this topic: Simply Typed Lambda Calculus
Famous quotes containing the words general and/or observations:
“We do not need to minimize the poverty of the ghetto or the suffering inflicted by whites on blacks in order to see that the increasingly dangerous and unpredictable conditions of middle- class life have given rise to similar strategies for survival. Indeed the attraction of black culture for disaffected whites suggests that black culture now speaks to a general condition.”
—Christopher Lasch (b. 1932)
“All observations point to the fact that the intellectual woman is masculinized; in her, warm, intuitive knowledge has yielded to cold unproductive thinking.”
—Helene Deutsch (1884–1982)