idris

What I have so far is: module Foo postulate P : 'P postulate NP : 'NP complexityProof : P = NP complexityProof = ?complexityProof_rhs But on trying to load the file, I just get: When elaborating type of Foo.complexityProof: When elaborating argument y to type constructor =: Can't unify 'NP with 'P Specifically: Can't unify "NP" with "P" A little suprised at the error, as I thought Idris, having heterogeneous "John Major" equality, was fine with differing types on the left and right-hand side of =. There's a different symbol for that, now? From the documentation: Note : Idris's equality type is

Implementing vector addition in some of the dependently typed languages (such as Idris) is fairly straightforward. As per the example on Wikipedia : import Data.Vect %default total pairAdd : Num a => Vect n a -> Vect n a -> Vect n a pairAdd Nil Nil = Nil pairAdd (x :: xs) (y :: ys) = x + y :: pairAdd xs ys (Note how Idris' totality checker automatically infers that addition of Nil and non- Nil vectors is a logical impossibility.) I am trying to implement the equivalent functionality in Coq, using a custom vector implementation, albeit very similar to the one provided in the official Coq

The natToFin function from the standard library has the following signature: natToFin : Nat -> (n : Nat) -> Maybe (Fin n) natToFin 4 5 returns Just (FS (FS (FS (FS FZ)))) : Maybe (Fin 5) , while natToFin 5 5 returns Nothing . I would like a function with the following signature: myNatToFin : (m : Nat) -> (n : Nat) -> { auto p : n `GT` m } -> Fin n It behaves the same as the standard lib function but doesn't need to return a Maybe because it is always possible to generate a Fin n from m given that n is greater than m . How do I implement myNatToFin ? You can do it directly by recursing on m , n

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

In Haskell , I might implement if like this: if' True x y = x if' False x y = y spin 0 = () spin n = spin (n - 1) This behaves how I expect : haskell> if' True (spin 1000000) () -- takes a moment haskell> if' False (spin 1000000) () -- immediate In Racket , I could implement a flawed if like this: (define (if2 cond x y) (if cond x y)) (define (spin n) (if (= n 0) (void) (spin (- n 1)))) This behaves how I expect : racket> (if2 #t (spin 100000000) (void)) -- takes a moment racket> (if2 #f (spin 100000000) (void)) -- takes a moment In Idris , I might implement if like this: if' : Bool -> a -> a

What is the syntax to constrain a function argument in an interface which takes a function? I tried: interface Num a => Color (f : a -> Type) where defs... But it says the Name a is not bound in interface... Cactus Your interface actually has two parameters: a and f . But f should be enough to pick an implementation : interface Num a => Color (a : Type) (f : a -> Type) | f where f here is called a determining parameter . Here's a nonsensical full example: import Data.Fin interface Num a => Color (a : Type) (f : a -> Type) | f where foo : (x : a) -> f (1 + x) Color Nat Fin where foo _ = FZ x :