Clean up APIs for terminal and initial objects#647
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Our previous definition was directly in terms of contractibility, which led to some gnarly goals.
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| Extensional-Initial | ||
| : ∀ {ℓr} | ||
| → ⦃ sa : Extensional Ob ℓr ⦄ | ||
| → Extensional (Initial C) ℓr |
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We use it to prove ⊥-is-prop later down in this file.
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Description
Previously, we defined initial and terminal objects directly via contractibility. This led to some really baroque goals, as things like
term.!unfolded toterm _ . centre. This PR definesis-initialandis-terminalrecords, and ports over all code to use the new records. I've also take the opportunity to sprinkle around someINLINEpragrams on helper functions that create initial/terminal objects.On a whole, the code looks a lot clearer, though there are some places where things get a bit uglier.