[Haskell-cafe] why the name lambda calculus?
Jack Henahan
jhenahan at uvm.edu
Wed Aug 24 18:12:34 CEST 2011
It's always been my understanding that calculi were systems that defined particular symbols and the legal methods of their manipulation in the context of a particular calculus. The point, generally (har har), seems to be abstraction. The lambda calculus describes computation without actually implementing it, the predicate/propositional calculi describe logic without necessarily containing any explicit logical statements.
Algebras, on the other hand, are structures whose properties are defined by a (usually) small number of properties and axioms. A Boolean algebra is a 6-tuple (A, ∧, ∨, ¬, ⊥, ⊤) such that for all a, b, c in A, associativity, commutativity, absorption, distributivity, and complement axioms all hold. An algebra over a field describes a vector space with a bilinear vector product. The other axioms that must hold depend on the particular vector space, though.
Jack Henahan
jhenahan at uvm.edu
==
Computer science is no more about computers than astronomy is about telescopes.
-- Edsger Dijkstra
==
-------------- next part --------------
A non-text attachment was scrubbed...
Name: 398E692F.gpg
Type: application/x-apple-msg-attachment
Size: 17822 bytes
Desc: not available
URL: <http://www.haskell.org/pipermail/haskell-cafe/attachments/20110824/4961d212/attachment-0001.bin>
-------------- next part --------------
On Aug 24, 2011, at 9:20 AM, Dominic Mulligan wrote:
> On Wed, 2011-08-24 at 14:01 +0100, Tony Finch wrote:
>> Ezra Cooper <ezra at ezrakilty.net> wrote:
>>>
>>> I believe this to be a general trait of things described as
>>> "calculi"--that they have some form of name-binders, but I have never
>>> seen that observation written down.
>>
>> Combinator calculi are a counter-example.
>
> As is the propositional calculus. I seem to remember Joe Wells once
> asking Wilfrid Hodges what he thought the definition of a calculus was.
> He didn't provide a convincing definition.
>
>
>
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
More information about the Haskell-Cafe
mailing list