[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
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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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