Talk:Combinatory categorial grammar

Target Audience?
Is it possible to obtain an explanation of this concept that relies on "conventional" background and not one that includes several thick books...perhaps an explanation like one would give to a younger brother or sister, not ones professor.

Accuracy question
I haven't seen CCG before today, but from reading this it seems as though the type raising: $$\dfrac{\alpha : X}{\alpha : T/(X\backslash T)}T_>$$ should in fact be: $$\dfrac{\alpha : X}{\alpha : T/(T\backslash X)}T_>$$ as is used in the example below? To verify, follow $$\alpha$$ with $$\beta : T\backslash X$$ —Preceding unsigned comment added by 74.125.56.17 (talk) 03:56, 24 September 2010 (UTC)

Yes, I did my doctoral thesis on CCG and can confirm that T/(X\T) is definitely in error. —Preceding unsigned comment added by 110.174.4.24 (talk) 13:46, 9 November 2010 (UTC)

I stumbled over the same issue when reading the article. It seems that the notation is slightly messed up, but also in the linked paper [| Lexicalization and Generative Power in CCG]. The natural notation would be to read X/Y as right division of X by Y (which is actually the case), and Y\X as left division of X by Y (which is not the case in this article). Then, the raising rules could be checked by division, and would also make sense in type theory where we have the isomorphism between X and (forall T. (X -> T) -> T) by parametricity. Writing the latter as either T <- (X -> T) or (T <- X) -> T would then give the raising laws, if interpreting T <- X as T/X (corresponding to the rule for forward application) and X -> T as X\T (for backward application). The raising laws would turn X into either T/(X\T) or (T/X)\T. 129.16.23.112 (talk) 15:28, 6 November 2017 (UTC)