[Agda] list member error
Serge D. Mechveliani
mechvel at botik.ru
Fri Dec 28 19:47:03 CET 2012
Please, what is wrong in the below program?
(Agda-2.3.2, MAlonzo, lib-0.6, Debian Linux,
in the below source I replace \sqcup --> max, \:: --> ::, \~~ --> ~~
)
---------------------------------------------------------------------
module Main where
open import Foreign.Haskell
open import IO.Primitive
open import Data.String as String using (toCostring)
open import Level using (Level; suc; max)
open import Relation.Binary using (Setoid; module Setoid)
open import Data.List using (List; []; _::_)
data Elem {c l : Level} {A : Setoid c l} :
Setoid.Carrier A -> List (Setoid.Carrier A) -> Set (suc (max c l))
-- "x is in the list xs by _~~_"
where
inHead : let open Setoid {{...}} in
(x y : Carrier) -> x ~~ y -> (xs : List Carrier) ->
Elem x (y :: xs)
inTail : let C = Setoid.Carrier A
in (x y : C) -> (xs : List C) -> Elem x xs -> Elem x (y :: xs)
main : IO Unit
main = putStrLn (toCostring "done")
---------------------------------------------------------------------
For example, I intend the following proof for Elem 1 [3, 1] :
let p : Elem 1 [1]
p = inHead 1 1 1~~1 []
in
inTail 1 3 [1] p
(is the above definition all right?)
The report concerns the two lines for inTail :
------------------------------------------------------------------------
Finished Main.
Unsolved metas at the following locations:
/home/mechvel/doconA/0.01/reports/2/Main.agda:17,12-18,74
/home/mechvel/doconA/0.01/reports/2/Main.agda:18,46-50
------------------------------------------------------------------------
Does "Finished Main" mean that the error occurs after the type checking?
The precise code is attached here as Main.agda.zip.
Thanks,
------
Sergei
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