To solve the problem raised in the last episode, I propose schematic affine recursion. We saw that affine lambda calculus (where lambda-bound variables are used at most once) plus structural recursion does not enforce termination, even if you restrict the recursor so that the function to be iterated is closed when you reduce ("closed at reduction"). You have to restrict it so that recursion terms are disallowed entirely unless the function to be iterated is closed ("closed at cons...
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To solve the problem raised in the last episode, I propose schematic affine recursion. We saw that affine lambda calculus (where lambda-bound variables are used at most once) plus structural recursion does not enforce termination, even if you restrict the recursor so that the function to be iterated is closed when you reduce ("closed at reduction"). You have to restrict it so that recursion terms are disallowed entirely unless the function to be iterated is closed ("closed at cons...
Introduction to Formalizing Programming Languages Theory
Iowa Type Theory Commute
12 minutes
11 months ago
Introduction to Formalizing Programming Languages Theory
In this episode, I begin discussing the question and history of formalizing results in Programming Languages Theory using interactive theorem provers like Rocq (formerly Coq) and Agda.
Iowa Type Theory Commute
To solve the problem raised in the last episode, I propose schematic affine recursion. We saw that affine lambda calculus (where lambda-bound variables are used at most once) plus structural recursion does not enforce termination, even if you restrict the recursor so that the function to be iterated is closed when you reduce ("closed at reduction"). You have to restrict it so that recursion terms are disallowed entirely unless the function to be iterated is closed ("closed at cons...
