[Agda] Re: with + continuation
Peter Divianszky
divipp at gmail.com
Sat Nov 17 13:07:09 CET 2012
On 17/11/2012 12:57, Peter Divianszky wrote:
> Hi,
>
> It would be nice if one could write the following in Agda:
>
> ---------------------
> module _ (f : (A → B) → C) (g : A → B) where
>
> c : C
> c withcont f
> ... | a = g a
> ---------------------
>
> Given 'f : (A → B) → C', 'withcont f' would give a value of 'A' and it
> would replace the goal 'C' with 'B'.
>
> This could be useful in the following situation:
>
> ---------------------
> open import Data.List using (List; []; _∷_)
> open import Data.Empty using (⊥)
> open import Relation.Nullary using (Dec; yes; no)
> open import Relation.Binary using (Decidable)
> open import Relation.Binary.PropositionalEquality using (_≡_; refl)
>
> module Try {A : Set} {{eq : Decidable {A = A} _≡_}} where
>
> infix 2 _∈_ _∈?_
>
> data _∈_ (x : A) : List A → Set where
> here : ∀ {xs} → x ∈ x ∷ xs
> there : ∀ {y ys} → x ∈ ys → x ∈ y ∷ ys
>
> _∈?_ : ∀ (x : A) ys → Dec (x ∈ ys)
> x ∈? [] = no λ ()
> x ∈? y ∷ ys with eq x y
> .y ∈? y ∷ ys | yes refl = yes here
> x ∈? y ∷ ys | no ¬p with x ∈? ys
> x ∈? y ∷ ys | no ¬p | yes q = yes (there q)
> x ∈? y ∷ ys | no ¬p | no ¬q = no (f x refl) where
> f : ∀ a → x ≡ a → (a ∈ y ∷ ys) → ⊥
> f .y e here = ¬p e
> f a e (there r) with a | e
> f a e (there r) | .x | refl = ¬q r
> ---------------------
>
> This works but I find the following definition of _∈?_ easier to read:
>
> ---------------------
> _∈?_ : ∀ (x : A) ys → Dec (x ∈ ys)
> x ∈? [] = no λ ()
> x ∈? y ∷ ys with eq x y
> .y ∈? y ∷ ys | yes refl = yes here
> x ∈? y ∷ ys | no ¬p with x ∈? ys
> x ∈? y ∷ ys | no ¬p | yes q = yes (there q)
> x ∈? y ∷ ys | no ¬p | no ¬q withcont no
> .y ∈? y ∷ ys | no ¬p | no ¬q | here = ¬p e
> x ∈? y ∷ ys | no ¬p | no ¬q | there r = ¬q r
> ---------------------
>
> What do you think, is there any chance for 'withcont'?
>
> Cheers,
> Peter
>
I made a typo, 'e' should be 'refl':
---------------------
_∈?_ : ∀ (x : A) ys → Dec (x ∈ ys)
x ∈? [] = no λ ()
x ∈? y ∷ ys with eq x y
.y ∈? y ∷ ys | yes refl = yes here
x ∈? y ∷ ys | no ¬p with x ∈? ys
x ∈? y ∷ ys | no ¬p | yes q = yes (there q)
x ∈? y ∷ ys | no ¬p | no ¬q withcont no
.y ∈? y ∷ ys | no ¬p | no ¬q | here = ¬p refl
x ∈? y ∷ ys | no ¬p | no ¬q | there r = ¬q r
---------------------
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