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 jhena...@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 <e...@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@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe
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