[Agda] Agda Questions.

[Andreas Abel]

Sounds like you want us to solve your homework. ;) --Andreas

On 20.09.2015 23:36, Ismail Alyassiri wrote:
>> {--
>>    Hello guys, I am trying to gather many proofs using Agda now that I
>> am studying it on own.
>> Bellow, I have a few problems I would love your help of solving. Thank
>> you in advances guys.
>>
>>
>>
>>
>> --}
>> module list-todo where
>>
>> open import lib
>>
>> {- define this function so that it removes the last element from a list.
>>    If the list is empty, you can just return the empty list. -}
>> removelast : ∀{ℓ}{A : Set ℓ} → 𝕃 A → 𝕃 A
>> removelast = {!!}
>>
>> {- once you have a correct definition of removelast, the yellow
>> highlighting
>>    for the following two tests will disappear. -}
>> test1-removelast : removelast (1 :: 2 :: 3 :: 4 :: []) ≡ 1 :: 2 :: 3 :: []
>> test1-removelast = refl
>>
>> test2-removelast : removelast ('a' :: 'b' :: 'z' :: 'y' :: 'z' :: [])
>> ≡ 'a' :: 'b' :: 'z' :: 'y' :: []
>> test2-removelast = refl
>>
>> concat[] : ∀ {ℓ}{A : Set ℓ}(n : ℕ) → concat{A = A} (repeat n []) ≡ []
>> concat[] = {!!}
>>
>> -- you have to implement removelast above in order to do this problem
>> removelast++ : ∀{ℓ}{A : Set ℓ}(l1 l2 : 𝕃 A) → is-empty l2 ≡ ff →
>> removelast (l1 ++ l2) ≡ l1 ++ removelast l2
>> removelast++ = {!!}
>>
>> shorter-trans : ∀{ℓ}{A : Set ℓ}(l1 l2 l3 : 𝕃 A) →
>>                  l1 shorter l2 ≡ tt →
>>                  l2 shorter l3 ≡ tt →
>>                  l1 shorter l3 ≡ tt
>> shorter-trans = {!!}
>>
>> list-all-any : ∀{ℓ}{A : Set ℓ}(pred : A → 𝔹)(l : 𝕃 A) →
>>                 list-all pred l ≡ ~ (list-any (λ a → ~ (pred a)) l)
>> list-all-any = {!!}
>>
>> filter-list-all : ∀{ℓ}{A : Set ℓ}(pred : A → 𝔹)(l : 𝕃 A) →
>>                    list-all pred l ≡ tt →
>>                    filter pred l ≡ l
>> filter-list-all = {!!}
>>
>> filter-member : ∀{ℓ}{A : Set ℓ}(eq : A → A → 𝔹)(a : A)(pred : A →
>> 𝔹)(l : 𝕃 A) →
>>                 list-member eq a (filter pred l) ≡ tt →
>>                 list-member eq a l ≡ tt ∧ pred a ≡ tt
>> filter-member = {!!}
>>
>>
>> zip-unzip : ∀{ℓ₁ ℓ₂}{A : Set ℓ₁}{B : Set ℓ₂}(x : 𝕃 A)(y : 𝕃 B) →
>>             length x ≡ length y → unzip (zip x y) ≡ x , y
>> zip-unzip = {!!}
>
>
>
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-- 
Andreas Abel  <><      Du bist der geliebte Mensch.

Department of Computer Science and Engineering
Chalmers and Gothenburg University, Sweden

andreas.abel at gu.se
http://www2.tcs.ifi.lmu.de/~abel/