Computation & Deduction
Spring 1997
Frank Pfenning

Lecture 3: Type Preservation

We complete the presentation of Mini-ML and prove some properties of the language. Specifically, we prove value soundness, which states that the result of evaluation is indeed a value, and type preservation, which states that the value of an expression of type t will also have type t. These theorems introduce the fundamental techniques and notions that will accompany us throughout the course. In particular, we will see proofs by induction on the structure of derivations and applications of inversion principles. We will also encounter the fundamental properties of parametric and hypothetical judgments, which are usually expressed as substitution lemmas.
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