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Treat partiality and construct Kleene's first algebra #7

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rahulc29 opened this issue Jan 23, 2024 · 1 comment

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rahulc29 commented Jan 23, 2024

An outline :

Define the lifting monad $\mathcal{L}$
Define the syntax primitive recursive functions
Define $\mu$
Interpret the syntax of partial recursive functions using the $\mathcal{L}$
Use the syntax of partial recursive functions to create a (partial) combinatory algbera. No need for Godel codes.
This should be equivalent to Kleene's first algebra.

rahulc29 mentioned this issue

Construct the effective topos #8

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rahulc29 commented Jan 30, 2024

I'm not sure it would be possible to create a PCA using just the syntax. Godel codes are likely necessary.

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