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Operator precedence is documented. Operators without built-in meanings are documented. The word "associative" apparently does not appear in either page. It's easy enough to do an experiment to observe the associativity of an operator. For example, \[CircleMinus] is left-associative and \[CirclePlus] is not:

ClearAll[CirclePlus, CircleMinus];
CircleMinus[a_, b_] := a[b];
CirclePlus[a_, b_] := a[b];

a⊖b⊖c
a⊕b⊕c
(a⊕b)⊕c
a[b][c]
a⊕b⊕c
a[b][c]

But it would be nicer to discover associativity without an experiment. Neither operator has Attributes, let alone attributes that reveal associativity.

In[534]:= ClearAll[CirclePlus, CircleMinus];
Attributes[CircleMinus]
Attributes[CirclePlus]
{}
{}
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1 Answer 1

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There is some relevant documentation here:

http://reference.wolframcloud.com/language/tutorial/OperatorInputForms.html

enter image description here

What we see is that a difference between CirclePlus and CircleMinus is that CirclePlus takes multiple inputs while CircleMinus takes only two. For example:

CirclePlus[f1, f2, f3, f4]

evaluates nicely while

CircleMinus[f1, f2, f3]

does not (the third argument is red and the command is ignored). So I suspect that what you are perceiving as associativity is a result of the difference in the allowable inputs to the two expressions.

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