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If you're confused by a mathematical or technical text, it can help to simply accept that, and read on for a bit (I've heard from professional mathematicians th

If you're confused by a mathematical or technical text, it can help to simply accept that, and read on for a bit (I've heard from professional mathematicians that this is commonplace in their readings) In this case, we find after the abstract and the contents list that the idea is that a function is a general expression like x^2+1, with a variable x. Applying this function to an argument, e.g. 2, results in the value 5. Edit: So that should make sense of the idea of a function, on one hand, and the application of the function, on the other. The idea behind lambda calculus was to come up with a certain primitive set of operations that were precise enough that they could be defined mechanistically (and this was before the days when computers existed that could carry these out mechanistically), but also were rich enough that they could be used in combination to compute any function hitherto devised

billforsternz 1y ago
Thanks, so application comes down to plugging in values, I got as far as "plugging in values" in the subject document (except that I didn't realise that's what application meant). Then I kind of recoiled from reforming, say f(x) = x^2 + 1 so f(1) = 1^2 + 1 = 2 into something seemingly more complicated for reasons that are difficult to discern for me as a reader and no doubt difficult to describe as an expert writer. I have the same difficulty with your last paragraph.
- griffzhowl 1y ago
  The idea is that it's a set of basic rules that can be used to model any computation (lambda calculus is Turing-complete). So think of it as a programming language with a very minimal set of primitive/builtin operations, which is really what it is. The reason things can seem more complicated than they need to be is that this set of primitive operations is so minimal; and the reason it's so minimal is that Alonzo Church came up with it in the 1930s when they were trying to get to the very bare bones of the concept of computation. Lambda calculus is the grandfather of all functional programming languages. Lisp was a more or less direct implementation of it

billforsternz 1y ago

Thanks, so application comes down to plugging in values, I got as far as "plugging in values" in the subject document (except that I didn't realise that's what application meant). Then I kind of recoiled from reforming, say f(x) = x^2 + 1 so f(1) = 1^2 + 1 = 2 into something seemingly more complicated for reasons that are difficult to discern for me as a reader and no doubt difficult to describe as an expert writer. I have the same difficulty with your last paragraph.

griffzhowl 1y ago
The idea is that it's a set of basic rules that can be used to model any computation (lambda calculus is Turing-complete). So think of it as a programming language with a very minimal set of primitive/builtin operations, which is really what it is. The reason things can seem more complicated than they need to be is that this set of primitive operations is so minimal; and the reason it's so minimal is that Alonzo Church came up with it in the 1930s when they were trying to get to the very bare bones of the concept of computation. Lambda calculus is the grandfather of all functional programming languages. Lisp was a more or less direct implementation of it