Content deleted Content added
Line 371:
:::: * A value in mathematics is a canonical form
:::: Or any other reference that gives a coherent picture of this. I dont think you can say that LC is just it's own theory and has no relationship to mathematics. That doesn't seem useful to me. Better to explain the relationship, it least for the readers benefit. Regards [[User:Thepigdog|Thepigdog]] ([[User talk:Thepigdog|talk]]) 00:15, 15 January 2014 (UTC)
::::: "Mathematics" is the thing which is not a theory. ZFC set theory is a (mathematical) theory. Euclidean geometry is a (mathematical) theory. First order arithmetic is a (mathematical) theory. Lambda calculus is a (mathematical) theory. I'm not sure of the best way to interpret "value" in the context of this discussion, but "equals" is easy; it's whatever the axioms of the theory say, and the axioms of lambda calculus say it's convertibility (see Barendregt for example; I don't have my copy handy just at the moment). With regard to a fixed point combinator in "mathematics", i.e. the (informal) meta-theoretic question, I'm less sure what to say. The meta-theoretic concept of a fixed point is reasonably clear, because the meta-theoretic concept of a (first order) function is reasonably clear, but I don't think a combinator is, because higher-order functions aren't (at least to me). [[User:Haklo|Haklo]] ([[User talk:Haklo|talk]]) 00:50, 15 January 2014 (UTC)
==Its not magic==
| |||