15816 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 lambdacalculus introduced earlier is a propositional
linear type theory. In this lecture we present a firstorder 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 callbyname to lazy evaluation.
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Frank Pfenning
