Add boolean builtins in Nat
#1262
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| infixl 0 _UsingEq | ||
| infixl 0 _i0:>_UsingEqP | ||
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| _UsingEq : (a : A) → singl a |
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Add a comment showing how this can be used
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Is the comment I just added enough?
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It looke like this has exactly the same use case as inspect. Is this not redundant?
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Thank you, I completely missed it. Do you know exactly how should I use it?
Right now I'm trying to case-split on inspect (_≡ᵇ n) m in the proof of discreteness of ℕ, but this doesn't seem to work, since it only gives me the path, but not each boolean case.
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Nevermind, I got it.
Is this what you meant?
discreteℕ : Discrete ℕ
discreteℕ zero zero = yes refl
discreteℕ zero (suc n) = no znots
discreteℕ (suc m) zero = no snotz
discreteℕ (suc m) (suc n) with m ≡ᵇ n | inspect (m ≡ᵇ_) n
... | false | [ p ]ᵢ = no (subst Bool→Type p ∘ ≡→≡ᵇ)
... | true | [ p ]ᵢ = yes (≡ᵇ→≡ (subst Bool→Type (sym p) tt))
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@LorenzoMolena since thowse will be heavily used and critical for performance of various definition, to be safe, I would double check performance benchmark for every variant when you are making changes. |
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@felixwellen I just tried the approach suggested by @anshwad10, i.e. using However, I find whilst the corrent definition on the PR is a bit more concise. I’d prefer to keep |
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You can keep |
This PR refactors the definitions of
min,max,discreteℕ,<-split, and_≟_to use boolean builtins, improving the performance of their computation.
For
minandmax, this improvement applies unconditionally, while for the otherfunctions it depends on whether proof terms are ignored
(e.g., when defining functions by cases via
_≟_).The main changes are:
Nat.Base: imports the previously missing boolean builtins.Nat.PropertiesandNat.Order: update the implementations of the functions listed above.Prelude: adds aliases forisContrSingl ... .fstandisContrSinglP ... .fstto support with-abstraction without losing information about the orginal terms
(a workaround for the "with-abstraction equality" available in standard Agda but missing in Cubical).
DirectSum.Equiv-DSHIT-DSFun,Instances.NatMax, andTruncation.Properties:adjusted for compatibility with the updated definitions.
Some notes:
_≟_remains in the file under the name_≟'_.Please let me know if this structure and approach are appropriate.