Now we can see that Church was associated with the Simply Typed Lambda Calculus. Indeed, it seems he explained the Simply Typed Lambda Calculus in order to reduce misunderstanding about the Lambda Calculus.

Now when John McCarthy created Lisp - he based it on the Lambda Calculus. This is by his own admission when he published "Recursive functions of symbolic expressions and their computation by machine, Part I". You can read it here.

Now we know that at the core of Mathematica is a Lisp-like system, but instead of being based purely on the Lambda Calculus, it is based on a term-rewriting system.

Here the author states state:

Mathematica is fundamentally a term rewriting system... a more general concept than the Lambda Calculus behind Lisp.

My question is: Why did the Mathematica Language choose term rewriting instead of the Lambda Calculus as its basis?

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    $\begingroup$ I don't think this is ontopic here. You are asking about historical design decisions behind a proprietary piece of software, which is not a computer science question. Chances are nobody knows, or it was down to Wolfram's whims. $\endgroup$ – Raphael Jul 3 '16 at 9:56
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    $\begingroup$ Note: I asked in their chat if this would be welcome on Mathematica. If there is a positive answer, I'll migrate there. $\endgroup$ – Raphael Jul 3 '16 at 10:03
  • $\begingroup$ They've changed their mind - they'd like to migrate it back... $\endgroup$ – hawkeye Jul 4 '16 at 4:20
  • $\begingroup$ Here's the link to the M.SE version. There's an answer there. @hawkeye Well, crowds don't have a single mind to change ... $\endgroup$ – Szabolcs Jul 4 '16 at 8:45
  • $\begingroup$ *throws arms in the air* I don't know what we can do besides getting the okay of mods... but then, a mod expressed disagreement with the community votes, and the answer seems to be good; hope it helps you. $\endgroup$ – Raphael Jul 4 '16 at 8:47