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.
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?