Discrepency in monoids constraint on Semigroups, Monoids and Groups tutorial

[N-J-Martin]

I have been updating the Semigroups, Monoids and Groups google notebook tutorial, here, to use the latest conjure version (Version 9) as described by Issue #597 . However I noticed that when describing monoids, it says there has to be some element of the semigroup, e, that acts as an identity such that for all integers i and a function R,
R(i,e) = R(e,i) = e.

However what the example code shows is:
R((e,i)) = i /\ R((i,e)) = i.

Here, the e in the described constraint is replaced by i in the constraint actually used. They seem to be saying two different things. This discrepancy is also present in the original tutorial here.

As you wrote the original tutorial @ChrisJefferson (I can't seem to tag Alice Lynch) I was wondering if you could confirm the intention here?

Thank you!

[ChrisJefferson]

Hi, the code is correct (I believe, on phone so I am assuming we are quantifying over i). An example of a monoid is integers (except zero) under multiplication, where 1 is the identity. Another common example is string concatenation, where the identity is empty string (just to hopefully give some understanding!) Get Outlook for iOS<https://aka.ms/o0ukef>

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________________________________ From: N-J-Martin ***@***.***> Sent: Friday, November 10, 2023 1:18:49 AM To: conjure-cp/conjure ***@***.***> Cc: Christopher Jefferson ***@***.***>; Mention ***@***.***> Subject: {Disarmed} [conjure-cp/conjure] Discrepency in monoids constraint on Semigroups, Monoids and Groups tutorial (Issue #607) I have been updating the Semigroups, Monoids and Groups google notebook tutorial, here<https://github.com/conjure-cp/conjure/blob/main/docs/tutorials/notebooks/Semigroups%2C_Monoids_and_Groups.ipynb>, to use the latest conjure version (Version 9) as described by Issue #597<#597> . However I noticed that when describing monoids, it says there has to be some element of the semigroup, e, that acts as an identity such that for all integers i and a function R, R(i,e) = R(e,i) = e. However what the example code shows is: R((e,i)) = i /\ R((i,e)) = i. Here, the e in the described constraint is replaced by i in the constraint actually used. They seem to be saying two different things. This discrepancy is also present in the original tutorial here<https://conjure.readthedocs.io/en/latest/tutorials/Groups.html>. As you wrote the original tutorial @ChrisJefferson<https://github.com/ChrisJefferson> (I can't seem to tag Alice Lynch) I was wondering if you could confirm the intention here? Thank you! — Reply to this email directly, view it on GitHub<#607>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AAGGEB6DQWSLR7LUHYIMIJDYDUF7TAVCNFSM6AAAAAA7E5KEJGVHI2DSMVQWIX3LMV43ASLTON2WKOZRHE4DMMBXHA3TGOI>. You are receiving this because you were mentioned.Message ID: ***@***.***> [ { ***@***.***": "http://schema.org", ***@***.***": "EmailMessage", "potentialAction": { ***@***.***": "ViewAction", "target": "#607", "url": "#607", "name": "View Issue" }, "description": "View this Issue on GitHub", "publisher": { ***@***.***": "Organization", "name": "GitHub", "url": "https://github.com" } } ]

[N-J-Martin]

Thank you! That make a lot more sense now and helps a lot!