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...
In this episode, I describe the first proof of normalization for STLC, written by Alan Turing in the 1940s. See this short note for Turing's original proof and some historical comments.
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...
