Hmmmm…
OK,
Any idea of a timescale
Maybe I jump ship to agda temporarily.
From: Richard Eisenberg [mailto:eir@cis.upenn.edu]
Sent: 18 May 2015 2:05 PM
To: Nicholls, Mark
Cc: haskell-cafe@haskell.org
Subject: Re: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
On May 18, 2015, at 5:02 AM, "Nicholls, Mark"
{-# LANGUAGE DataKinds #-} {-# LANGUAGE ExplicitForAll #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE StandaloneDeriving #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE ScopedTypeVariables #-}
import Prelude hiding (head, tail, (++), (+), replicate) import qualified Prelude as P
naturals
data Nat where Z :: Nat S :: Nat -> Nat
I can now define + and * and prove things about them…1 * x == x etc….nice..but lets put that on one side. Borrow bits and bobs from singletons
data family Sing (a :: k)
Borrow bits and bobs from singletons..i.e. the isomorphic values…my proofs in nat now map to SNat…double nice.
type SNat = (Sing :: Nat -> *)
Create the integers by following my nose……(the integers are the equivalence class of pairs of naturals….) i.e. we have “positive” or “negative” or “zero”…
data Ints (a :: Nat) (b :: Nat) where Minus :: SNat a -> Ints 'Z a Zero :: Ints 'Z 'Z Plus :: SNat a -> Ints a 'Z
Ok….this works as a set of values….but…. I can’t prove anything about these because the data constructors for my integers aren’t “promotable”…..so I cant do the same trick I did with Nat. “:k Zero” ….. Data constructor ‘Zero’ comes from an un-promotable type ‘Ints’ In a type in a GHCi command: Zero I’ve tried rejigging this in various futile and ignorant manners….but the bottom line is its…”un-promotable”…..look at the docs, and it says something vague about GADT’s…but that isnt the problem directly. Is there a nifty way around this log jam? (I can start proving things about ‘(Nat,Nat)….but this will soon become a bit clumsy….) Or do I just stop here and wrestle with getting agda installed and lose another few months in the agda-café (which appears to be a very nice place somewhere in finland….hmmmm…I think that’s something different). (I’ve already allegedly descended into cabal hell following my nose with an agda install… setup.exe: The program cpphs version >=1.18.6 && <1.19 is required but the version found at C:\Users\nichom\AppData\Roaming\cabal\bin\cpphs.exe is version 1.19). computer science would be good, if it wasn’t for the computers. CONFIDENTIALITY NOTICE This e-mail (and any attached files) is confidential and protected by copyright (and other intellectual property rights). If you are not the intended recipient please e-mail the sender and then delete the email and any attached files immediately. Any further use or dissemination is prohibited. While MTV Networks Europe has taken steps to ensure that this email and any attachments are virus free, it is your responsibility to ensure that this message and any attachments are virus free and do not affect your systems / data. 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