agda

Instead of using Agda on a filesystem (with EMACS, terminal, etc.), is it possible to use it directly from Haskell, as a library? For example: -- UsingAgda.hs import Agda -- Prints the type of a term on some Agda code main :: IO () main = typeOf "true" agdaCode where agdaCode :: String agdaCode = unlines ["module Hello where " ," " ,"data Bool : Set where" ," true : Bool " ," false : Bool "] The code above would output Bool , because true : Bool on that Agda code. Yes, it is possible. Agda was designed as a Haskell library plus a main module. You can see a couple of small examples here . As a

I'm interested in dependently typed languages. Finite numbers seem very usable to me. For example, to safely index fixed-size arrays. But the definition is not clear for me. The data type for finite numbers in Idris can be the following: (And probably similar in Agda) data FiniteNum : Natural -> Type where FZero : FiniteNum (Succ k) FSucc : FiniteNum k -> FiniteNum (Succ k) And it seems to work: exampleFN : FiniteNum (Succ (Succ Zero)) exampleFN = FSucc FZero -- typechecks -- exampleFN = FSucc (FSucc FZero) -- won't typecheck But how does this work? What does k mean? And how come that the type

I am trying to parse a string with natural numbers in Agda. e.g., the result of stringListToℕ "1,2,3" should be Just (1 ∷ 2 ∷ 3 ∷ []) My current code is not quite right or by any means nice, but it works. However it returns the type: Maybe (List (Maybe ℕ)) The Question is: How to implement the function stringListToℕ in a nice way (compared to my code); it should have the type Maybe (List ℕ) (optional, not important) How can I convert the type Maybe (List (Maybe ℕ)) to Maybe (List ℕ) ? My Code: charToℕ : Char → Maybe ℕ charToℕ '0' = just 0 charToℕ '1' = just 1 charToℕ '2' = just 2 charToℕ '3' =

This is a follow-up question to Getting path induction to work in Agda I wonder when that construct may be more expressive. It seems to me we can always express the same like so: f : forall {A} -> {x y : A} -> x == y -> "some type" f refl = instance of "some type" for p == refl Here Agda will do path induction given the example which is the same as c : (x : A) -> C refl from that question: pathInd : forall {A} -> (C : {x y : A} -> x == y -> Set) -> (c : (x : A) -> C refl) -> {x y : A} -> (p : x == y) -> C p It seems this function is isomorphic to: f' : forall {A} -> {x y : A} -> x == y ->

It has been stated a few places that all agda programs terminate. However I can construct a function like this: stall : ∀ n → ℕ stall 0 = 0 stall x = stall x The syntax highlighter doesn't seem to like it, but there are no compilation errors. Computing the normal form of stall 0 results in 0 . Computing the result of stall 1 causes Emacs to hang in what looks a lot like a non-terminating loop. Is this a bug? Or can Agda sometimes run forever? Or is something more subtle going on? In fact, there are compilation errors. The agda executable finds an error and passes that information to agda-mode

Since the _+_ -Operation for Nat is usually defined recursively in the first argument, its obviously non-trivial for the type-checker to know that i + 0 == i . However, I frequently run into this issue when I write functions on fixed-size Vectors. One example: How can I define an Agda-function swap : {A : Set}{m n : Nat} -> Vec A (n + m) -> Vec A (m + n) which puts the first n values at the end of the vector? Since a simple solution in Haskell would be swap 0 xs = xs swap n (x:xs) = swap (n-1) (xs ++ [x]) I tried it analogously in Agda like this: swap : {A : Set}{m n : Nat} -> Vec A (n + m) ->