[Haskell-cafe] why the name lambda calculus?

[Jack Henahan]

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
==
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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.
> 
> 
> 
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