[Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
Nicholls, Mark
nicholls.mark at vimn.com
Mon May 18 13:36:48 UTC 2015
Ok…so that gives me…..10 months to get my head around agda…before converting my knowledge back….ideally I want this to work in Haskell.
Thanks.
From: Richard Eisenberg [mailto:eir at cis.upenn.edu]
Sent: 18 May 2015 2:24 PM
To: Nicholls, Mark
Cc: haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
On May 18, 2015, at 9:06 AM, "Nicholls, Mark" <nicholls.mark at vimn.com<mailto:nicholls.mark at vimn.com>> wrote:
Hmmmm…
OK,
Any idea of a timescale
In ways that would be hard to predict, promoting all types is a fairly massive change to GHC. If I merge in August, I'll be quite pleased. But it really should be there by 7.12, which should occur by Feb/Mar '16.
Richard
Maybe I jump ship to agda temporarily.
From: Richard Eisenberg [mailto:eir at cis.upenn.edu<http://cis.upenn.edu>]
Sent: 18 May 2015 2:05 PM
To: Nicholls, Mark
Cc: haskell-cafe at haskell.org<mailto:haskell-cafe at 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" <nicholls.mark at vimn.com<mailto:nicholls.mark at vimn.com>> wrote:
The problem being the any definition containing promoted types, cannot be promoted.
Is that a fair summary?
Yes. Only "simple" types can be promoted.
But this will all change in 7.12, where just about anything will promote. For now, you may want to switch to Agda, but come back in a year's time. :)
Richard
From: Haskell-Cafe [mailto:haskell-cafe-bounces at haskell.org<mailto:cafe-bounces at haskell.org>] On Behalf Of Nicholls, Mark
Sent: 15 May 2015 1:35 PM
To: Andras Slemmer
Cc: haskell-cafe at haskell.org<mailto:haskell-cafe at haskell.org>
Subject: Re: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
Its inhabited, and I can potentials readon about positive and negative and zero…because these are mapped to type constructors….but they are not isomorphic to the integers…they are just 3 sub classes of the class of integers…
That aint much good.
I assume its because the even the type of my data constructor Zero is…
Ints 'Z 'Z
If I wanted an isomorphic type constructor…it would need to be?
'Ints ''Z ''Z
(I know haskell doesn’t promote the type Ints to a kind ‘Ints, it irritatingly promotes it to Ints….)
‘’Z doesn’t exist…?
hmmm
From: Nicholls, Mark
Sent: 15 May 2015 1:03 PM
To: 'Andras Slemmer'
Cc: 'haskell-cafe at haskell.org<mailto:haskell-cafe at haskell.org>'
Subject: RE: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
Ignore me…of course it’s inhabited…..
From: Nicholls, Mark
Sent: 15 May 2015 12:58 PM
To: 'Andras Slemmer'
Cc: haskell-cafe at haskell.org<mailto:haskell-cafe at haskell.org>
Subject: RE: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
Ah, ok that’s a vote for agda.
Your ints definition isn’t directly inhabited…..but maybe that doesn’t matter….thanks I’ll struggle on a bit.
(yes my definition is mildly problematic mathematically, I have 3 (coincident) zeros).
From: Andras Slemmer [mailto:0slemi0 at gmail.com]
Sent: 15 May 2015 10:50 AM
To: Nicholls, Mark
Cc: haskell-cafe at haskell.org<mailto:haskell-cafe at haskell.org>
Subject: Re: [Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’
If you want to stick to your Ints datastructure then you need a stronger dependent type theory that allows you to reason about "double-promoted" types.
However in this case you don't really need that complexity:
data Ints
= Zero
| Minus Nat
| Plus Nat
is sufficient enough. Although this definition is probably not the one you want to use... take a look athttp://www.cse.chalmers.se/~nad/repos/lib/src/Data/Integer.agda for hints
On 14 May 2015 at 18:36, Nicholls, Mark <nicholls.mark at vimn.com<mailto:nicholls.mark at vimn.com>> wrote:
Hello,
I clearly don’t really know what I’m doing…but at least I know it….
Here we defined the Naturals…and then attempt to construct the Integers….
> {-# 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.
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