indexed writer monad

Nicholls, Mark

25 Mar 2015 25 Mar '15

2:32 p.m.

Anyone? I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support). So I thought I'd do some research in Haskell. I know little or nothing about indexed monad (though I have built the indexed state monad in C#). So I would assume there would be an indexed monoid (that looks at bit like a tuple?)... e.g. (a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e) ? There seems to be some stuff about "update monads", but it doesn't really look like a writer. I could do with playing around with an indexed writer, in order to get my head around what I'm doing....then try and capture what I'm doing...then try (and fail) to port it back. 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.

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Roman Cheplyaka

25 Mar 25 Mar

2:45 p.m.

An indexed monoid is just a Category. On 25/03/15 16:32, Nicholls, Mark wrote:

...

Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn’t support).

So I thought I’d do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?)…

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about “update monads”, but it doesn’t really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I’m doing….then try and capture what I’m doing…then try (and fail) to port it back.

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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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Nicholls, Mark

3:22 p.m.

Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet. Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good". Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café). -----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad An indexed monoid is just a Category. On 25/03/15 16:32, Nicholls, Mark wrote:

...

Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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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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.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe

Roman Cheplyaka

4:03 p.m.

Sorry, I didn't mean to scare you off. By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other. But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else. On 25/03/15 17:22, Nicholls, Mark wrote:

...

Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

On 25/03/15 16:32, Nicholls, Mark wrote:

...
Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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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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.

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.

Nicholls, Mark

4:27 p.m.

Ok... Well lets just take the indexed writer So....for a writer we're going... e.g. (a,[c]) -> (a -> (b,[c])) -> (b,[c]) If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ? (I've never actually used one!) But what if I want to "log" different types... I want to "log" a string, then an integer bla bla... So I won't get the monoid [String] I should get something like a nest 2 tuple. do log 1 log "a" log 3 log "sdds" return 23 I could get a (Integer,(String,(Integer,(String,END)))) and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list. Maybe my use of "indexed" isn't correct. So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically (these are types) (a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e) Which are encoded as nested 2 tuples (with an End marker) (a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ? That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled). Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world). -----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad Sorry, I didn't mean to scare you off. By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other. But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else. On 25/03/15 17:22, Nicholls, Mark wrote:

...

Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

On 25/03/15 16:32, Nicholls, Mark wrote:

...
Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

CONFIDENTIALITY NOTICE

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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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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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Roman Cheplyaka

9:30 p.m.

Alright, this does look like an indexed writer monad. Here's the indexed writer monad definition: newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) } Here c is a Category, ie. an indexed Monoid. Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works. In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid. The indexed 'tell' will be tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ()) And to run an indexed monad, you apply that i->j function to your end marker. Does this help? On 25/03/15 18:27, Nicholls, Mark wrote:

...

Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

On 25/03/15 17:22, Nicholls, Mark wrote:

...
Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

On 25/03/15 16:32, Nicholls, Mark wrote:

...
Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

CONFIDENTIALITY NOTICE

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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.

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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.

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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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.

Nicholls, Mark

26 Mar 26 Mar

8:26 a.m.

It does So im not barking up the wrong tree? Let me have a go, understand though that haskell comes about 5th in my list of languages by proffieciency, turning type cartwheels in fbound oo types is how my brain is wired, not seemingly trivial handstands in haskell It may take me several days (this is not part of my day job)!

...

On 25 Mar 2015, at 21:31, Roman Cheplyaka wrote:

Alright, this does look like an indexed writer monad.

Here's the indexed writer monad definition:

newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) }

Here c is a Category, ie. an indexed Monoid.

Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works.

In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid.

The indexed 'tell' will be

tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ())

And to run an indexed monad, you apply that i->j function to your end marker.

Does this help?

...
On 25/03/15 18:27, Nicholls, Mark wrote: Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

...
On 25/03/15 17:22, Nicholls, Mark wrote: Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

...
On 25/03/15 16:32, Nicholls, Mark wrote: Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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Nicholls, Mark

8 Apr 8 Apr

12:33 p.m.

Hmmm...remember me. I have returned to this....after some time. My Haskell is embryonic. Control.Category seems to be available without installing any magic (maybe I've installed that magic before).

...

import Control.Category

Success... An IxMonad seems a harder feat. Installing packages and using them a leap into the unknown for me...I can drive a car, but assembling one is harder. I install the indexed package by using cabal? Cabal install indexed? https://hackage.haskell.org/package/indexed Seemed to do something. Then I want to use that package... So I want to import it.. It all seems to live in a module called Control.Monad.Indexed So...

...

import Control.Monad.Indexed

Would have been my guess Boom...unknown... That’s before I jump through the IxFunctor,IxPointed,IxApplicative,IxMonad hoops.

...

On 25 Mar 2015, at 21:31, Roman Cheplyaka wrote:

Alright, this does look like an indexed writer monad.

Here's the indexed writer monad definition:

newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) }

Here c is a Category, ie. an indexed Monoid.

Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works.

In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid.

The indexed 'tell' will be

tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ())

And to run an indexed monad, you apply that i->j function to your end marker.

Does this help?

...
On 25/03/15 18:27, Nicholls, Mark wrote: Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

...
On 25/03/15 17:22, Nicholls, Mark wrote: Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

...
On 25/03/15 16:32, Nicholls, Mark wrote: Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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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.

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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.

Magnus Therning

12:36 p.m.

On 8 April 2015 at 14:33, Nicholls, Mark wrote:

...

Hmmm...remember me.

I have returned to this....after some time.

My Haskell is embryonic.

Control.Category seems to be available without installing any magic (maybe I've installed that magic before).

...
import Control.Category

Success...

An IxMonad seems a harder feat.

Installing packages and using them a leap into the unknown for me...I can drive a car, but assembling one is harder.

I install the indexed package by using cabal?

Cabal install indexed?

https://hackage.haskell.org/package/indexed

Seemed to do something.

Then I want to use that package...

So I want to import it.. It all seems to live in a module called Control.Monad.Indexed

So...

...
import Control.Monad.Indexed

Would have been my guess

Boom...unknown...

Nicholls, Mark

1:21 p.m.

Genius Maybe this Haskell lark isnt as hard as I thought.... Now for the ix hoops. On 8 April 2015 at 14:33, Nicholls, Mark wrote:

...

Hmmm...remember me.

I have returned to this....after some time.

My Haskell is embryonic.

Control.Category seems to be available without installing any magic (maybe I've installed that magic before).

...
import Control.Category

Success...

An IxMonad seems a harder feat.

Installing packages and using them a leap into the unknown for me...I can drive a car, but assembling one is harder.

I install the indexed package by using cabal?

Cabal install indexed?

https://hackage.haskell.org/package/indexed

Seemed to do something.

Then I want to use that package...

So I want to import it.. It all seems to live in a module called Control.Monad.Indexed

So...

...
import Control.Monad.Indexed

Would have been my guess

Boom...unknown...

Possibly silly question but... did you restart `ghci` after installing indexed? /M -- Magnus Therning OpenPGP: 0xAB4DFBA4 email: magnus@therning.org jabber: magnus@therning.org twitter: magthe http://therning.org/magnus 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.

Nicholls, Mark

9 Apr 9 Apr

3:31 p.m.

Brilliant...that was actually easier than imagined, I followed the types and it all dropped out the bottom, the hardest thing was constructing a meaningful expression without do notation...but now I've got the do notation working as well. I need to play with this...and then workout...how to apply this new knowledge to my writer like thing. Thanks again.

...

On 25 Mar 2015, at 21:31, Roman Cheplyaka wrote:

Alright, this does look like an indexed writer monad.

Here's the indexed writer monad definition:

newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) }

Here c is a Category, ie. an indexed Monoid.

Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works.

In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid.

The indexed 'tell' will be

tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ())

And to run an indexed monad, you apply that i->j function to your end marker.

Does this help?

...
On 25/03/15 18:27, Nicholls, Mark wrote: Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

...
On 25/03/15 17:22, Nicholls, Mark wrote: Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

...
On 25/03/15 16:32, Nicholls, Mark wrote: Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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.

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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.

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Nicholls, Mark

10 Apr 10 Apr

1:32 p.m.

Looking at this again.... I've done that, but noted that my "monoid" was constructed backwards... e.g.

...

myWriter2@(IxWriter (logs,a2)) = do x <- (ireturn 3) tell x y <- (ireturn 5) tell y tell (show y) return (x + y)

Gives logs :: j -> (((j, Integer), Integer), String) if I wanted to access the head (i.e. the 1 inner inner inner Integer), I have to evaluate the whole expression (pretty much). This made me try to work out how to build the monoid the other way around.... i.e. logs :: j -> (Integer,(Integer,(String,j))) but that doesn’t seem to be consistent with the signature of ibind (or at least not in my head). Don't I want a Control.Effect instead? Then I think I can construct the correct signature in the type family Plus? I'll have a go, but it would be nice to know I'm not disappearing into a dead end.

...

On 25 Mar 2015, at 21:31, Roman Cheplyaka wrote:

Alright, this does look like an indexed writer monad.

Here's the indexed writer monad definition:

newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) }

Here c is a Category, ie. an indexed Monoid.

Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works.

In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid.

The indexed 'tell' will be

tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ())

And to run an indexed monad, you apply that i->j function to your end marker.

Does this help?

...
On 25/03/15 18:27, Nicholls, Mark wrote: Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

...
On 25/03/15 17:22, Nicholls, Mark wrote: Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

...
On 25/03/15 16:32, Nicholls, Mark wrote: Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

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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.

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.

Nicholls, Mark

3:12 p.m.

And Control.Effect.WriteOnceWriter Is what I'm after I think. -----Original Message----- From: Nicholls, Mark Sent: 10 April 2015 2:33 PM To: 'Roman Cheplyaka' Cc: 'haskell-cafe@haskell.org' Subject: RE: [Haskell-cafe] indexed writer monad Looking at this again.... I've done that, but noted that my "monoid" was constructed backwards... e.g.

...

myWriter2@(IxWriter (logs,a2)) = do x <- (ireturn 3) tell x y <- (ireturn 5) tell y tell (show y) return (x + y)

...

On 25 Mar 2015, at 21:31, Roman Cheplyaka wrote:

Alright, this does look like an indexed writer monad.

Here's the indexed writer monad definition:

newtype IxWriter c i j a = IxWriter { runIxWriter :: (c i j, a) }

Here c is a Category, ie. an indexed Monoid.

Under that constraint, you can make this an indexed monad (from the 'indexed' package). That should be a good exercise that'll help you to understand how this all works.

In practice, you'll probably only need c = (->), so your writer becomes isomorphic to (i -> j, a). This is similar to the ordinary writer monad that uses difference lists as its monoid.

The indexed 'tell' will be

tell :: a -> IxWriter (->) z (z, a) () tell a = IxWriter (\z -> (z,a), ())

And to run an indexed monad, you apply that i->j function to your end marker.

Does this help?

...
On 25/03/15 18:27, Nicholls, Mark wrote: Ok...

Well lets just take the indexed writer

So....for a writer we're going...

e.g.

(a,[c]) -> (a -> (b,[c])) -> (b,[c])

If I use the logging use case metaphor... So I "log" a few Strings (probably)....and out pops a (t,[String]) ?

(I've never actually used one!)

But what if I want to "log" different types...

I want to "log" a string, then an integer bla bla...

So I won't get the monoid [String]

I should get something like a nest 2 tuple.

do log 1 log "a" log 3 log "sdds" return 23

I could get a (Integer,(String,(Integer,(String,END))))

and then I could dereference this indexed monoid(?)...by splitting it into a head of a specific type and a tail...like a list.

Maybe my use of "indexed" isn't correct.

So it seems to me, that writer monad is dependent on the monoid append (of lists usually?)....and my "special" monad would be dependent on a "special" monoid append of basically

(these are types)

(a,b) ++ (c,d) = (a,b,c,d) (a,b,c,d) ++ (e) = (a,b,c,d,e)

Which are encoded as nested 2 tuples (with an End marker)

(a,(b,End) ++ (c,(d,End)) = (a,(b, (c,(d,End))) ?

That sort of implies some sort of type family trickery...which isnt toooo bad (I've dabbled).

Looks like an ixmonad to me....In my pigoeon Haskell I could probably wrestle with some code for a few days....but does such a thing already exist?...I don't want to reinvent the wheel, just mess about with it, and turn it into a cog (and then fail to map it back to my OO world).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 4:03 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

Sorry, I didn't mean to scare you off.

By Category, I didn't mean the math concept; I meant simply the class from the Control.Category module. You don't need to learn any category theory to understand it. Since you seem to know already what Monoid is, try to compare those two classes, notice the similarities and see how (and why) one could be called an indexed version of the other.

But if you don't know what "indexed" means, how do you know you need it? Perhaps you could describe your problem, and we could tell you what abstraction would fit that use case, be it indexed monad or something else.

...
On 25/03/15 17:22, Nicholls, Mark wrote: Ah that assumes I know what a category is! (I did find some code that claimed the same thing)....maths doesn't scare me (much), and I suspect its nothing complicated (sounds like a category is a tuple then! Probably not), but I don't want to read a book on category theory to write a bit of code...yet.

Ideally there would be a chapter in something like "learn you an indexed Haskell for the great good".

Then I could take the code, use it...mess about with it...break it...put it back together in a slightly different shape and....bingo...it either works...or I find theres a good reason why it doesn't....(or I post a message to the café).

-----Original Message----- From: Roman Cheplyaka [mailto:roma@ro-che.info] Sent: 25 March 2015 2:46 PM To: Nicholls, Mark; haskell-cafe@haskell.org Subject: Re: [Haskell-cafe] indexed writer monad

An indexed monoid is just a Category.

...
On 25/03/15 16:32, Nicholls, Mark wrote: Anyone?

I can handle monads, but I have something (actually in F#) that feels like it should be something like a indexed writer monad (which F# probably wouldn't support).

So I thought I'd do some research in Haskell.

I know little or nothing about indexed monad (though I have built the indexed state monad in C#).

So I would assume there would be an indexed monoid (that looks at bit like a tuple?).

e.g.

(a,b) ++ (c,d) = (a,b,c,d)

(a,b,c,d) ++ (e) = (a,b,c,d,e)

?

There seems to be some stuff about "update monads", but it doesn't really look like a writer.

I could do with playing around with an indexed writer, in order to get my head around what I'm doing..then try and capture what I'm doing.then try (and fail) to port it back.

CONFIDENTIALITY NOTICE

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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.

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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.

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.

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Magnus Therning
Nicholls, Mark
Roman Cheplyaka