Converting prefix to infix

Question

Is there a way in Mathematica to convert prefix to infix notation (where precedence order is preserved)?

For example, how would I convert S[a, S[b, c]] to a ~ S ~ (b ~ S ~ c)?

I checked the cookbook and also on line for "prefix to infix transformation". but did not find this topic.

I noted that Infix[S[Infix[S[a, b]], c]] produces (a ~ S ~ b) ~ S ~ c So it's a matter of nesting the Infix operation in this way. Not sure how to achieve it in Mathematica. — ExpressionCoder, Commented Feb 11, 2019 at 21:43
Perhaps via MapAll? But then only applied to non atomic (non leaf) parts? — ExpressionCoder, Commented Feb 11, 2019 at 21:49
MapAll[Infix, S[a, S[b, c]]] gives Infix[a] ~ S ~ (Infix[b] ~ S ~ Infix[c]) so my remaining question is how to not apply Infix to a, b and c. — ExpressionCoder, Commented Feb 11, 2019 at 21:54

kglr · Accepted Answer · 2019-02-11 21:56:27Z

7

With[{S = Infix[S[##]] &}, S[a, S[b, c]] ]

a ~S~ (b ~S~ c)

Also

S[a, S[b, c]] /. S -> (Infix[S[##]] &)

a ~S~ (b ~S~ c)

answered Feb 11, 2019 at 21:49

kglr

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$\begingroup$ Thank you, that's helpful. I will go with the second option. $\endgroup$
– ExpressionCoder
Commented Feb 11, 2019 at 22:02
2

$\begingroup$ Slightly neater is S -> Infix @* S. $\endgroup$
– Carl Woll
Commented Feb 13, 2019 at 18:11
$\begingroup$ @CarlWoll, yes!! Thank you. $\endgroup$
– kglr
Commented Feb 14, 2019 at 18:54

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Carl Woll · Accepted Answer · 2019-02-12 18:11:53Z

4

You could just give S a format:

MakeBoxes[S[a_, b_], StandardForm] ^:= MakeBoxes[Infix[S[a, b]], StandardForm]

Then:

S[a, S[b, c]]

a ~S~ (b ~S~ c)

answered Feb 12, 2019 at 18:11

Carl Woll

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$\begingroup$ Thanks much appreciated. $\endgroup$
– ExpressionCoder
Commented Feb 13, 2019 at 13:04

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2 Answers 2