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De Bruijn notation, and why it's useful
2025-05-26 At least a familiarity with the lambda calculus, including how it is evaluated. Some base knowledge of programming languages is also assumed.
We can perform what's called "beta reduction" on this term — essentially, function application, applying f to the lambda. Generally to avoid this, we need to rename everything in our "substituted" term to names that are free (do not occur) in the "subsitutee" so nothing is accidentally captured. This post is not intended to explain them, but I will list several here so that the curious reader may read further (tip: when searching, append "lambda calculus" to find the right results quicker):
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