Add precedence test tool (#104)

* add a WL module with functions to test relative precedences of operators.

* begin and end package

* longer explanation

test/testprecedence.m

@@ -0,0 +1,82 @@
+
+
+(**************************************************************)
+(*
+   Tools for check the consistency of precedence data.
+ 
+   Functions on this package takes strings representing 
+   operators.
+   For example,
+   ``` 
+   PrecedenceOrderByParsing["+","*"]
+   ```
+   compares how the expressions `a+b*c` and `a*b+c` are parsed
+   to determine the precedence of `+` relative to `*`, without using
+   `Precedence` explicitly.
+
+   On the other hand, `CheckPrecedenceOutput["+"]` checks that
+   the OutputForm of expressions of the form 
+   `Infix[{s,a+b},"~", prec, None]` is formatted adding parenthesis
+   in the right place, for prec around the value reported
+   by `Precedence[Head[a+b]]`.
+
+*)
+(**************************************************************)
+
+BeginPackage["testprecedences`"];
+
+
+PrecedenceOrderByParsing::usage="`PrecedenceOrderByParsing[op1, op2]`  \
+Evaluates the precedence ordering of two operators, according the way they are parsed. 1 if op1 has lower precedence than op2,
+0 if they are equal and -1 if op2 has lower precedence than op1. If order cannot be determined, return None.
+"
+
+CheckPrecedenceOutput::usage="`CheckPrecedenceOutput[op]`\ checks if the Precedence value reported by `Precedence[op]` is \
+consistent with the way in which expressions involving `op` are formatted when are inside an `Infix` expression."
+
+
+Begin["`Private`"]
+(*Check the order of the precedence for two operators
+by looking how are they parsed.
+*)
+
+
+
+PrecedenceOrderByParsing[op1_String, op2_String] := 
+ Module[{a, b, c, h1, h2, hl, hr, testexpr},
+  h1 = ToExpression["a" <> op1 <> "b"][[0]]; 
+  h2 = ToExpression["a" <> op2 <> "b"][[0]];
+  hl = Head[ToExpression["a" <> op1 <> "b" <> op2 <> "c"]];
+  hr = Head[ToExpression["a" <> op2 <> "b" <> op1 <> "c"]];
+  If[hl === hr, Return[If[hl === h1, 1, If[hl === h2, -1, None]]], 
+   Return[0]]
+  ]
+
+
+(*Check if the OutputForm is consistent with the precedence*)
+CheckPrecedenceOutput[op_String] := 
+ Module[{a, b, c, precedence, testexpr, test, lesseq, largeeq},
+  testexpr = ToExpression["b" <> op <> "c"]; 
+  precedence = IntegerPart[Precedence[Head[testexpr]]];
+  test = ToString[Infix[{a, testexpr}, "~", precedence - 1, None], 
+    OutputForm];
+  If[StringPart[test, -1] == ")", Return[False]];
+  test = ToString[Infix[{a, testexpr}, "~", precedence, None], 
+    OutputForm];
+  If[StringPart[test, -1] != ")", Return[False]];
+  test = ToString[Infix[{a, testexpr}, "~", precedence + 1, None], 
+    OutputForm];
+  If[StringPart[test, -1] != ")", Return[False]];
+  test = ToString[Infix[{testexpr, a}, "~", precedence - 1, None], 
+    OutputForm];
+  If[StringPart[test, 1] == "(", Return[False]];
+  test = ToString[Infix[{testexpr, a}, "~", precedence, None], 
+    OutputForm];
+  If[StringPart[test, 1] != "(", Return[False]];
+  test = ToString[Infix[{testexpr, a}, "~", precedence + 1, None], 
+    OutputForm];
+  If[StringPart[test, 1] != "(", Return[False]];
+  True
+  ]
+End[]
+EndPackage[]