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Upper natural numbers #602

Merged
merged 68 commits into from
Jun 8, 2022
Merged

Upper natural numbers #602

merged 68 commits into from
Jun 8, 2022

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felixwellen
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This PR constructs the upper natural numbers. They complete the naturals in some sense. For example, every collection of upper naturals constructively has a minimal element. The goal of this PR is to construct arithmetic operations on the upper natural numbers

felixwellen and others added 30 commits September 15, 2021 14:51
…ded elements are preserved by the arithmetic operations
Also promote the rendered version in README w/ some adjectives stolen from the stdlib
# Conflicts:
#	Cubical/Algebra/CommMonoid/Base.agda
#	Cubical/Data/Nat/Order.agda
@felixwellen felixwellen marked this pull request as ready for review June 1, 2022 12:47
@felixwellen felixwellen changed the title WIP: Upper natural numbers Upper natural numbers Jun 1, 2022
@mortberg mortberg self-requested a review June 1, 2022 14:26
@felixwellen
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Ohno. That wasn't obsolete... I guess I should wake up first.

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Just in case there are any doubts: This PR still wants to be reviewed by @mortberg

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Lots of minor comments. Sorry for forgetting to finish the review :-)

Cubical/Algebra/CommMonoid/Base.agda Outdated Show resolved Hide resolved
Cubical/Algebra/CommSemiring/Base.agda Outdated Show resolved Hide resolved
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Cubical/Algebra/CommSemiring/Instances/UpperNat.agda Outdated Show resolved Hide resolved
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Cubical/Algebra/OrderedCommMonoid/Instances.agda Outdated Show resolved Hide resolved
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@@ -425,3 +425,17 @@ module EmbeddingIdentityPrinciple {B : Type ℓ} {ℓ₁} (f g : Embedding B ℓ
f ≡ g
open EmbeddingIdentityPrinciple renaming (f≃g to _≃Emb_) using (EmbeddingIP) public
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Why open public?

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As far as I know, this is not code I wrote. Good question though.

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There is another instance of this in the file. Should I just change both?

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@mortberg mortberg Jun 7, 2022

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Yes, I guess that would be good

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@felixwellen felixwellen requested a review from mortberg June 3, 2022 15:11
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Apart from the thing about the public imports I think this is ready to be merged! So please just fix that and check if the CI is still happy, then let's merge!

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Should be good to merge now! (travelling...)

@mortberg mortberg merged commit 0728ea8 into agda:master Jun 8, 2022
@felixwellen felixwellen deleted the upper-nat branch June 13, 2022 16:32
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4 participants