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::: Lambda terms are mathematical objects in their own right, just like sets (for example), and lambda calculus is its own mathematical theory. The "data types" and "conversions" you are talking about are further considerations, and not relevant to what is true or false in lambda calculus. In this particular discussion, when we talk about finding the fixed point to a function, the function we mean ''is'' a lambda term; it is ''not'' a function in a different theory which has been "converted" to a lambda term. Such a "converted function" question is a very different question, more along the lines of lambda definability. Finally, because the "fixed point question" is a question about lambda terms (and nothing else), normal form is not relevant. [[User:Haklo|Haklo]] ([[User talk:Haklo|talk]]) 22:50, 14 January 2014 (UTC)
:::: Hmmm interesting perspective. I dont disagree very much. But we start by defining the y combinator in mathematics, so we must give a mathematical value for the fixed point. From the readers point of view this is what they expect. If you were only talking about a lambda calculus fixed point function only then things would be different. But then you could not talk about "value" or "exists" or "solving". I dont think the Y combinator gives a solution in any sense that I can think of. It is a function that satisfies the properties of the equation, but it is not a solution, because it is not a value. You are saying a normal form is not necessarily a value, which I agree with. Do you have a reference for this? We desperately need references. I would love to have a reference that says any of,
:::: * The value of two expressions is the same iff the two expressions are equal.
:::: * A normal form is not necessarily a value.
:::: * 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)
==Its not magic==
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