Questions tagged [plfa]
9 questions
3
votes
1 answer
Termination checking failed to prove ∃-even′ : ∀ {n : ℕ} → ∃[ m ] ( 2 * m ≡ n) → even n
The PLFA exercise: what if we write the arithmetic more "naturally" in Quantifiers chapter (https://plfa.github.io/Quantifiers/) ?
∃-even′ : ∀ {n : ℕ} → ∃[ m ] ( 2 * m ≡ n) → even n
∃-odd′ : ∀ {n : ℕ} → ∃[ m ] (2 * m + 1 ≡ n) → odd n
I have…
jiamo
- 1,406
- 1
- 17
- 29
3
votes
3 answers
How to prove ¬ 2 < 1 in agda?
I think I must missing something to prove ¬ 2 < 1.
I have
¬1<0 : ¬ (1 < 0)
¬1<0 = λ()
¬0<0 : ¬ (0 < 0)
¬0<0 = λ()
¬2<0 : ¬ (2 < 0)
¬2<0 = λ()
contraposition : ∀ {A B : Set}
→ (A → B)
-----------
→ (¬ B → ¬ A)
contraposition f ¬y x = ¬y (f x)…
jiamo
- 1,406
- 1
- 17
- 29
3
votes
2 answers
How to get around the implicit vs explicit function type error?
This is from the last chapter of PLFA book.
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym; trans; cong)
open import Data.Product using (_×_; ∃; ∃-syntax; Σ; Σ-syntax) renaming (_,_ to ⟨_,_⟩)
infix 0 _≃_
record _≃_…
Marko Grdinić
- 3,798
- 3
- 18
- 21
3
votes
1 answer
Is functional extensionality with dependent functions consistent?
postulate
extensionality : ∀ {A B : Set} {f g : A → B}
→ (∀ (x : A) → f x ≡ g x)
-----------------------
→ f ≡ g
I know that the above definition is consistent, but what if a little twist on it is made?
postulate
extensionality' :…
Marko Grdinić
- 3,798
- 3
- 18
- 21
2
votes
1 answer
Agda: Function for Propositional Equality
I have been working my way through Programming Language Foundations in Agda, and currently I'm up to "Decidable: Booleans and decision procedures". It seems that, at least for the example given in detail, a function for deciding if something is true…
Sam_W
- 47
- 4
2
votes
0 answers
How do multiple rewrites expand into with?
I am a beginner in PLFA, when I read the Induction section, I accidentally wrote a +-swap proof that I can't understand:
+-suc': ∀ (m n: ℕ) → m + suc n ≡ suc (m + n)
+-suc' zero n = refl
+-suc' (suc m) n rewrite +-suc' m n = refl
+-swap: ∀ (m n p:…
Noah Ma
- 21
- 3
2
votes
1 answer
What is a valid type signature for the `Any-∃` exercise?
#### Exercise `Any-∃`
Show that `Any P xs` is isomorphic to `∃[ x ∈ xs ] P x`.
Leaving aside the fact that ∃[ x ∈ xs ] P x is not even valid syntax - only Σ[ x ∈ xs ] P x could be valid, none of the type signatures I've tried typecheck for that…
Marko Grdinić
- 3,798
- 3
- 18
- 21
2
votes
1 answer
Agda on windows: `→ ` not in scope
I'm trying to run chapter 1 of Programming Language Foundations in Agda on a Windows machine.
This is a fresh install of Agda 2.5.2 and Emacs 25.1.1 from the MSI and untouched Agda code from the textbook.
I'm getting this error:
Not in scope:
ΓåÆ…
Max Heiber
- 14,346
- 12
- 59
- 97
1
vote
1 answer
Agda error when checking the inferred type
I'm trying to show that the sum of two odd numbers is even.
What is wrong with the last line?
data odd : ℕ → Set …
Max Heiber
- 14,346
- 12
- 59
- 97