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It is quite possible to build models of the Turing machine that work (of cause you have to ignore the requirement for unlimited tape). What I am curious is is it possible to implement a model of lambda calculus more or less directly.

Just to head off the trivial answer building a Turing machine (or any other computer) that emulates lambda calculus isn't what I'm looking for.

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    $\begingroup$ Like this? dl.acm.org/doi/10.1145/319838.319864 $\endgroup$ Commented Oct 7, 2024 at 5:08
  • $\begingroup$ what do you mean in implement? building hardware? otherwise if you consider imperative languages like C++ or C, they are turing-complete and they are based on state-like idea of Turing machines, while functional languages like ML are based on the lambda calculus. $\endgroup$ Commented Oct 9, 2024 at 20:20
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    $\begingroup$ Does Lisp machine count? $\endgroup$ Commented Mar 7 at 6:49

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I'm not exactly sure exactly what you have in mind when you say "implement a model of lambda calculus more or less directly" and without "building a Turing machine or any other computer that emulates lambda calculus"

Would you be interested in creating your own lamda-calculus-inspired computer architecture? If yes, I'd begin by creating a way to encode lambda calculus expressions in binary.

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  • $\begingroup$ I think they meant building a physical machine for it, like a physical Turing machine would work with a physical tape and use a camera to read it or something. $\endgroup$ Commented 12 hours ago

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