Ignore me…of course it’s inhabited….. From: Nicholls, Mark Sent: 15 May 2015 12:58 PM To: 'Andras Slemmer' Cc: haskell-cafe@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@gmail.com] Sent: 15 May 2015 10:50 AM To: Nicholls, Mark Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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 mailto:nicholls.mark@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. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT.

So…just to wrap this one up…. We can define the naturals in the canonical way using DataKind etc….and create singleton instances… But…. There is no way to define the Integers FROM this definition and create singleton Integer instances. The problem being the any definition containing promoted types, cannot be promoted. Is that a fair summary? From: Haskell-Cafe [mailto:haskell-cafe-bounces@haskell.org] On Behalf Of Nicholls, Mark Sent: 15 May 2015 1:35 PM To: Andras Slemmer Cc: haskell-cafe@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@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@haskell.orgmailto:haskell-cafe@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@gmail.com] Sent: 15 May 2015 10:50 AM To: Nicholls, Mark Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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 mailto:nicholls.mark@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. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT.

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" mailto:nicholls.mark@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@haskell.orgmailto:cafe-bounces@haskell.org] On Behalf Of Nicholls, Mark Sent: 15 May 2015 1:35 PM To: Andras Slemmer Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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@haskell.orgmailto:haskell-cafe@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@haskell.orgmailto:haskell-cafe@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@gmail.com] Sent: 15 May 2015 10:50 AM To: Nicholls, Mark Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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 mailto:nicholls.mark@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. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT.

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@cis.upenn.edu] Sent: 18 May 2015 2:24 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 9:06 AM, "Nicholls, Mark" mailto:nicholls.mark@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@cis.upenn.eduhttp://cis.upenn.edu] Sent: 18 May 2015 2:05 PM To: Nicholls, Mark Cc: haskell-cafe@haskell.orgmailto: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" mailto:nicholls.mark@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@haskell.orgmailto:cafe-bounces@haskell.org] On Behalf Of Nicholls, Mark Sent: 15 May 2015 1:35 PM To: Andras Slemmer Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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@haskell.orgmailto:haskell-cafe@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@haskell.orgmailto:haskell-cafe@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@gmail.com] Sent: 15 May 2015 10:50 AM To: Nicholls, Mark Cc: haskell-cafe@haskell.orgmailto:haskell-cafe@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 mailto:nicholls.mark@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. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. If you communicate with us by e-mail, you acknowledge and assume these risks, and you agree to take appropriate measures to minimise these risks when e-mailing us. MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.orgmailto:Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe 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. Communicating by email is not 100% secure and carries risks such as delay, data corruption, non-delivery, wrongful interception and unauthorised amendment. 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Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT.

Wow, that's exciting news! 18 трав. 2015 16:05 "Richard Eisenberg" пише:

On May 18, 2015, at 5:02 AM, "Nicholls, Mark" 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@haskell.org] *On Behalf Of *Nicholls, Mark *Sent:* 15 May 2015 1:35 PM *To:* Andras Slemmer *Cc:* haskell-cafe@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@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@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@gmail.com <0slemi0@gmail.com>] *Sent:* 15 May 2015 10:50 AM *To:* Nicholls, Mark *Cc:* haskell-cafe@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 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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MTV Networks International, MTV Networks UK & Ireland, Greenhouse, Nickelodeon Viacom Consumer Products, VBSi, Viacom Brand Solutions International, Be Viacom, Viacom International Media Networks and VIMN and Comedy Central are all trading names of MTV Networks Europe. MTV Networks Europe is a partnership between MTV Networks Europe Inc. and Viacom Networks Europe Inc. Address for service in Great Britain is 17-29 Hawley Crescent, London, NW1 8TT.

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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.

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