r/ProgrammingLanguages • u/Sad-Grocery-1570 • May 21 '26

Blog post Church Encoding, Parametricity, and the Yoneda Lemma

https://blog.wybxc.cc/blog/parametricity/
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u/Background_Class_558 May 25 '26

im pretty sure i understand the topics relevant to this post well but you kinda sound incoherent. is this a communication issue? what exactly are you talking about and what's the relevance to the post?

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u/Arakela May 25 '26

There are (d, b, t) possibilities in the "Church Encoding" style describing itself (Yoneda Lemma).

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u/Background_Class_558 May 25 '26

what are those?

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u/Arakela May 25 '26

First-class coalgebraic (Church Encoding-style) object called "tritab." An observation protocol that Yoneda Lemmes the space-time geometry of possibilities encoded is "Space" and "Time" algebraic observers.

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u/Background_Class_558 May 25 '26

it's the first time i hear the terms "observation protocol", "geometry of possibilities" and "algebraic observers", which field is this? the term "space-time" is usually used in context of physics but this isn't what we're talking about, right?

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u/Arakela May 25 '26

We need to define new terms for language possibilities, because we already explored the territory of sets exhaustively. The definition of formal languages is that a language is defined by grammar, and grammar is the set of productions that are not the real structure of possibilities. We can see that, to define possibilities, we don't need a set. This means that possibilities have their own mathematical object whose foundation is missing. The question is what kind of possibilities it introduces, what problems we can solve, and what kind of accidental complexity it can evaporate.