Add foldrImplGoLemma to Data.Vect (#2835)

Co-authored-by: CodingCellist <teh6@st-andrews.ac.uk>
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Andor Penzes 2023-11-30 10:07:41 +00:00 committed by GitHub
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3 changed files with 17 additions and 1 deletions

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@ -154,6 +154,7 @@
assumption in `setByte` that the value is between 0 and 255. assumption in `setByte` that the value is between 0 and 255.
* Adds RefC support for 16- and 32-bit access in `Data.Buffer`. * Adds RefC support for 16- and 32-bit access in `Data.Buffer`.
* Add `Show` instance to `Data.Vect.Quantifiers.All` and add a few helpers for listy * Add `Show` instance to `Data.Vect.Quantifiers.All` and add a few helpers for listy
computations on the `All` type. computations on the `All` type.
* Add an alias for `HVect` to `All id` in `Data.Vect.Quantifiers.All`. This is the * Add an alias for `HVect` to `All id` in `Data.Vect.Quantifiers.All`. This is the
@ -248,6 +249,8 @@
* A more generalised way of applicative mapping of `TTImp` expression was added, * A more generalised way of applicative mapping of `TTImp` expression was added,
called `mapATTImp`; the original `mapMTTimp` was implemented through the new one. called `mapATTImp`; the original `mapMTTimp` was implemented through the new one.
* Adds `Data.Vect.foldrImplGoLemma`.
#### System #### System
* Changes `getNProcessors` to return the number of online processors rather than * Changes `getNProcessors` to return the number of online processors rather than

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@ -7,6 +7,7 @@ Aleksei Volkov
Alex Gryzlov Alex Gryzlov
Alex Silva Alex Silva
Alissa Tung Alissa Tung
Andor Penzes
Andre Kuhlenschmidt Andre Kuhlenschmidt
André Videla André Videla
Andy Lok Andy Lok

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@ -6,8 +6,9 @@ import Data.Nat
import public Data.Fin import public Data.Fin
import public Data.Zippable import public Data.Zippable
import Decidable.Equality
import Control.Function import Control.Function
import Decidable.Equality
import Syntax.PreorderReasoning
%default total %default total
@ -413,6 +414,17 @@ foldrImpl : (t -> acc -> acc) -> acc -> (acc -> acc) -> Vect n t -> acc
foldrImpl f e go [] = go e foldrImpl f e go [] = go e
foldrImpl f e go (x::xs) = foldrImpl f e (go . (f x)) xs foldrImpl f e go (x::xs) = foldrImpl f e (go . (f x)) xs
export
foldrImplGoLemma
: (x : a) -> (xs : Vect n a) -> (f : a -> b -> b) -> (e : b) -> (go : b -> b)
-> go (foldrImpl f e (f x) xs) === foldrImpl f e (go . (f x)) xs
foldrImplGoLemma z [] f e go = Refl
foldrImplGoLemma z (y :: ys) f e go = Calc $
|~ go (foldrImpl f e ((f z) . (f y)) ys)
~~ go ((f z) (foldrImpl f e (f y) ys)) ... (cong go (sym (foldrImplGoLemma y ys f e (f z))))
~~ (go . (f z)) (foldrImpl f e (f y) ys) ... (cong go Refl)
~~ foldrImpl f e (go . (f z) . (f y)) ys ... (foldrImplGoLemma y ys f e (go . (f z)))
public export public export
implementation Foldable (Vect n) where implementation Foldable (Vect n) where
foldr f e xs = foldrImpl f e id xs foldr f e xs = foldrImpl f e id xs