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> So long as bare metal looks more like a Turing machine than a Church calculus This will always be the case. The Turing machine is simply a much better model

> So long as bare metal looks more like a Turing machine than a Church calculus This will always be the case. The Turing machine is simply a much better model for implementing a machine capable of executing programs. The Lambda calculus (and math in general) are obviously better tools for _reasoning_, but the reason that reasoning in them is so powerful is precisely because you don't have to consider the execution cost of certain operations to reason about them. Think about all of the common set theory operations. It is trivial to write: PrimeNumbers ⊆ NaturalNumbers, however, think about _computing_ the result of this expression. Generating prime numbers is not a simple computational task, and even if it were, you can only ever verify it for a subset of the natural numbers since computation is inherently finite. It's all fun and games until you need to execute the program. The functional style is great in terms of expressivity, but you want a Turing machine at the bottom executing it if you ever want the program to finish in your lifetime.

kaba0 5y ago
I may not get your point - but a mathematical expression in itself is not functional - as far as I know. You have to give a definition that will likely be an infinite recursive function - which is strictly equivalent in what it can do to a Turing machine.
- TomSwirly 5y ago
  General recursive function, you mean. The point is that creating hardware that executes a Turing machine or something like it is easy, but constructing hardware that executes a general recursive function is so hard that it has never been done.
  - kaba0 5y ago
    My point was that a random mathematical expression will not be constructive in itself. And you are right, that either general recursive functions or lambda expressions are required to be equivalent to Turing machines. And while I agree that recursive functions are hard to execute on hardware - but certain aspects of it are apparent in CPU design — out-of-order execution is sort of lambda-like.
doctor_eval 5y ago
I think you're a few levels ahead of me in the theory (at least), but it just blew my mind to think about the fact that it's easier to compute all the numbers than it is to just compute the prime numbers. :brain-explode-emoji:

kaba0 5y ago

I may not get your point - but a mathematical expression in itself is not functional - as far as I know. You have to give a definition that will likely be an infinite recursive function - which is strictly equivalent in what it can do to a Turing machine.

TomSwirly 5y ago
General recursive function, you mean. The point is that creating hardware that executes a Turing machine or something like it is easy, but constructing hardware that executes a general recursive function is so hard that it has never been done.
- kaba0 5y ago
  My point was that a random mathematical expression will not be constructive in itself. And you are right, that either general recursive functions or lambda expressions are required to be equivalent to Turing machines. And while I agree that recursive functions are hard to execute on hardware - but certain aspects of it are apparent in CPU design — out-of-order execution is sort of lambda-like.

doctor_eval 5y ago

I think you're a few levels ahead of me in the theory (at least), but it just blew my mind to think about the fact that it's easier to compute all the numbers than it is to just compute the prime numbers. :brain-explode-emoji: