15-816 Linear Logic
Lecture 19: Linear Type Theory

From a judgmental point of view, the principal judgments of logic are A is a proposition and A is true. Understanding proofs is critical, but the proofs themselves are not part of the judgments. In contrast, the main judgments of a type theory are A is a type and M is an object of type A. Alternatively we can all these A is a proposition and M is a proof for A. In other words, the main distinction between logic and type theory is the internal notion of proof that is present in type theory.

The linear lambda-calculus introduced earlier is a propositional linear type theory. In this lecture we present a first-order linear type theory including universal and existential quantification. We then show how to exploit the additional expressive power through a major example, namely the formalization of the operational semantics for our linear functional language. We can give successively more accurate specification, from simply call-by-name to lazy evaluation.

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Frank Pfenning