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In other words, was a physical implementation modelling lambda calculus (so not built on top of a Von Neumann machine) ever devised? Even if just on paper?
If there was, what was it? Did we make use of its concepts somewhere practical (where it can be looked into and studied further)?

-- I'm aware of specialised LISP machines. They were equipped with certain hardware components that made them better but eventually they were still the same at their core.

If there isn't such thing, what stops it from being relevant or worth the effort? Is it just a silly thought to diverge so greatly from the current hardware and still manage to create a general-purpose computer?

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  • $\begingroup$ What do you mean? Something like a Krivine machine? Or the Categorical Abstract Machine? $\endgroup$ – Gilles 'SO- stop being evil' Mar 22 at 20:52
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    $\begingroup$ I think you mean: If we view a von Neumann architecture as a transformation of a Turing machine into practical form that allows more efficient computing, is there an analogous translation of lambda calculus into a practical form that allows more efficient computing? Since you're not requiring that this has been implemented in hardware, I wonder whether @Gilles'SO-stopbeingevil''s comment does answer your question. $\endgroup$ – Mars Mar 23 at 2:47
  • $\begingroup$ MothMan, you might want to think about how to answer the questions in your last paragraph: What are the mappings from a Turing machine to v.N. architecture that makes the latter a more efficient version of the former? (Part of the answer will be mapping of the tape to addressable memory.) Now, what would you need to implement an efficient analogue of lambda calculus? Maybe a stack, for starters, to allow recursion. Next, where will functions' code be stored, and what is its relationship to the stack? How will function's values be passed to calling functions? $\endgroup$ – Mars Mar 23 at 2:51
  • $\begingroup$ what I am looking for is a named physical computer architecture model that maps to lambda calculus in a way analogous to how Von Neumann's architecture maps to a Turing machine. I am not requiring it to be implemented in hardware, true, but it should be physically implementable with circuitry, so not a vm. $\endgroup$ – MothMan Mar 23 at 22:14

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