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"Algebra" and "calculus" are often used for historical reasons rather than technical ones. But as it were, LC cannot be expressed as a universal algebra. Not q
by tel 10y ago
"Algebra" and "calculus" are often used for historical reasons rather than technical ones.
But as it were, LC cannot be expressed as a universal algebra. Not quite. The lambda terms introduce local binding which throws off an algebraic representation. The best you can do is have a (sorted) representation which includes free variables and then have a quotient of that algebra be LC. Even that doesn't quite work, though, since `x` is not a valid LC term.
- 0xdeadbeefbabe 10y ago> The lambda terms introduce local binding which throws off an algebraic representation. Doesn't rho for renaming in relational algebra also have local binding? It's good to know the reasons are historical though.
- tel 10y agoCould be that the relational algebra isn't so much an algebra either. Also could be that the renaming isn't really part of the "core" algebra. I'm not in particular familiar with the relational algebra, though.