agda

In AgdaIntro, the view section explains : ..that with doesn’t remember the connection between the with-term and the patterns. That means when you defines data False : Set where record True : Set where isTrue : Bool -> Set isTrue true = True isTrue false = False infixr 30 _:all:_ data All {A : Set}(P : A -> Set) : List A -> Set where all[] : All P [] _:all:_ : forall {x xs} -> P x -> All P xs -> All P (x :: xs) satisfies : {A : Set} -> (A -> Bool) -> A -> Set satisfies p x = isTrue (p x) data Find {A : Set}(p : A -> Bool) : List A -> Set where found : (xs : List A)(y : A) -> satisfies p y ->

I can't figure out why my path induction isn't type checking correctly. It says "C x should be a function type, but it isn't" when referring to C (refl x). Perhaps my definition of refl is wrong or is there something wrong with my {}'s and ()'s? data _≡_ {A : Set}(a : A) : A → Set where refl : a ≡ a infix 4 _≡_ pathInd : ∀ {u} → {A : Set} → (C : {x y : A} → x ≡ y → Set u) → (c : (x : A) → C (refl x)) → ({x y : A} (p : x ≡ y) → C p) pathInd C c (refl x) = c x refl is not a function. Here is the definition you need: pathInd : ∀ {u} → {A : Set} → (C : {x y : A} → x ≡ y → Set u) → (c : (x : A) → C

For example, Agda allows me to write this: open import Data.Vec open import Data.Nat myVec : Vec ℕ _ myVec = 0 ∷ 1 ∷ 2 ∷ 3 ∷ [] and myVec will have type Vec ℕ 4 as expected. But if I try the same in Idris: import Data.Vect myVec : Vect _ Nat myVec = [0, 1, 2, 3] I get an error message from the typechecker: When checking right hand side of myVec with expected type Vect len Nat Type mismatch between Vect 4 Nat (Type of [0, 1, 2, 3]) and Vect len Nat (Expected type) Specifically: Type mismatch between 4 and len Is there a way to define myVec in Idris without manually specifying the index of the

Agda is a nice programming language to explore dependent types and play around with intuitionistic type theory and to experiment with the implementation of these things. But are there already examples for “real” programs written in Agda? Maybe even examples that show off its features (similar to how xmonad is often mentioned as an example of a “real” Haskell program)? 来源： https://stackoverflow.com/questions/10931316/are-there-examples-agda-code-running-in-production

I want to create a helper function, that will take a term from a an indexed or parametrized type and return that type parameter. showLen : {len : ℕ} {A : Set} -> Vec A len -> ℕ showLen ? = len showType : {len : ℕ} {A : Set} -> Vec A len -> Set showType ? = A Is this possible? (I can see how showType [] might have issues, but what about when the Type is indexed?) If you get rid of the implicit arguments, you can implement this quite easily: showLen : (len : ℕ) (A : Set) → Vec A len → ℕ showLen len _ _ = len In fact, we can do both at once: open import Data.Product showBoth : (len : ℕ) (A : Set)

With the following definition of equality, we have refl as constructor data _≡_ {a} {A : Set a} (x : A) : A → Set a where refl : x ≡ x and we can prove that function are congruent on equality cong : ∀ { a b} { A : Set a } { B : Set b } (f : A → B ) {m n} → m ≡ n → f m ≡ f n cong f refl = refl I am not sure I can parse what is going on exactly here. I think we are pattern matching refl on hidden parameters : if we replace the first occurence by refl by another identifier, we get a type error. after pattern matching, I imagine that m and n are the same by the definition of refl. then magic