[Haskell-cafe] Data constructor ‘Minus’ comes from an un-promotable type ‘Ints’

Fri May 15 12:35:30 UTC 2015

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'
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 at http://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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