Substitution Without Copy and Paste
By: Thorsten Altenkirch, Nathaniel Burke, Philip Wadler
Potential Business Impact:
Makes computer code easier to write and check.
Defining substitution for a language with binders like the simply typed $\lambda$-calculus requires repetition, defining substitution and renaming separately. To verify the categorical properties of this calculus, we must repeat the same argument many times. We present a lightweight method that avoids repetition and that gives rise to a simply typed category with families (CwF) isomorphic to the initial simply typed CwF. Our paper is a literate Agda script.
Similar Papers
Type Theory with Single Substitutions
Logic in Computer Science
Simplifies how computers understand math rules.
On the Formal Metatheory of the Pure Type Systems using One-sorted Variable Names and Multiple Substitutions
Logic in Computer Science
Makes computer math rules work better.
The Groupoid-syntax of Type Theory is a Set
Logic in Computer Science
Makes math rules work with more kinds of math.