Re: Notions of Type
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 18 Aug 2006 14:14:24 GMT
Message-ID: <4XjFg.51105$pu3.597633_at_ursa-nb00s0.nbnet.nb.ca>
>
> I'm not exactly sure what that would mean.
>
> In fact, I lack a pithy definition of algebra. (And worse, there are
> many senses of the word.) But one thing is common, and that
> is a datatype and binary operators that are closed over that
> datatype. Sometimes associativity of those operators is
> considered a requirement, but it seems a distant second
> to closure.
Date: Fri, 18 Aug 2006 14:14:24 GMT
Message-ID: <4XjFg.51105$pu3.597633_at_ursa-nb00s0.nbnet.nb.ca>
Marshall wrote:
> erk wrote:
>
>>Marshall wrote: >> >>>erk wrote: >>> >>>>Sorry if this is obvious to everyone else, but does an algebra include >>>>only operations defined on values of the type in question? >>> >>>Yes. >> >>I read elsewhere (and I'm not saying it's right) that an algebra could >>be defined as a closure over a set of types. Is that untrue?
>
> I'm not exactly sure what that would mean.
>
> In fact, I lack a pithy definition of algebra. (And worse, there are
> many senses of the word.) But one thing is common, and that
> is a datatype and binary operators that are closed over that
> datatype. Sometimes associativity of those operators is
> considered a requirement, but it seems a distant second
> to closure.
Why binary? I sincerely doubt that requirement. Received on Fri Aug 18 2006 - 16:14:24 CEST