> "types are syntax, not semantics". That's a bad paraphrase of the original: > One main theme of this work is the importance of notations in mathematics and

> "types are syntax, not semantics". That's a bad paraphrase of the original: > One main theme of this work is the importance of notations in mathematics and computer science: new questions were asked and solved only because of the use of AUTOMATH notation, itself a variation of λ-notation introduced by A. Church for representing functions. The notation is syntax, but types are the semantics (specifically, denotational semantics) that the notation is used for. In particular, the notation is a syntax that can be mechanically maniplated, so that computers can make semantic computations. en.wikipedia.org/wiki//Type_theory > . Any static program analysis, such as the type checking algorithms in the semantic analysis phase of compiler, has a connection to type theory. en.wikipedia.org/wiki/Denotational_semantics