Differentiating between ReplaceAll and Division (Times [ , Power])

[rocky]

In mathics/Mathics#989 it was noticed that 1/.2 Is comes out ReplaceAll[1,2] rather than Times[1,Power[.2,-1]].

The fix there was to add a lookahead pattern for a number to distinguish these.

ANTLR4 has such a notion too which I think is called a semantic predicate or {...}? which might help the parser here.

[rljacobson]

The rules for how . is parsed are arcane. Here are my private notes on the subject from last summer:

1//..9 is ReplaceRepeated[1, 0.9`]
1//.9 is ReplaceRepeated[1, 9] should be 0.9[1]
1/.9 is Times[1, Power[0.9`, -1]]
1...9 is 9 ((1)...) or Hold[Times[RepeatedNull[1], 9]]
7//.9 is ReplaceRepeated[7, 9]
7// .9 is 0.9`[7]
1/.1->2 is 10. -> 2

7// .9 is 0.9`[7]

b; 7`b is 7. b
_.1 is Times[Optional[Blank[]], 1]

Rule: If . can be interpreted as part of an operator, it will be. The only exceptions are:

	b=.1
	a/:b=.1
	a/.1
	a.b (* The Dot operator. *)

This places the precedence of the decimal point between //. and /.—excepting for the Dot operator itself.

[rljacobson]

Pingback to #2 for reference, which references the edge case x_.. discussed here.