Stringize provided as associative

Sources/AngouriMath/Core/Antlr/AngouriMath.g

@@ -1,4 +1,4 @@
-/*
+/*
 
 Remember to run the "antlr_rerun.bat" file located at "Sources/Utils/antlr_rerun.bat" (relative to the repository root)
 every time you modify this file so that the generated source files under the Antlr folder are updated and changes are
@@ -219,6 +219,8 @@ Keyword nodes
 provided_expression returns[Entity value]
     : expr = implies_expression { $value = $expr.value; }
     ('provided' pred = provided_expression { $value = $value.Provided($pred.value); })?
+    // note: even though Provided is associative, we parse it right-to-left matching natural language
+    // "I'll go, provided you go, provided it's sunny" - Natural reading: I'll go ← (you go ← sunny)
     ;
 
 /*

Sources/AngouriMath/Functions/Output/Latex/Latex.Omni.Classes.cs

@@ -79,13 +79,13 @@ public override string Latexise()
         partial record Providedf
         {
             /// <inheritdoc/>
-            public override string Latexise() => $@"{Expression.Latexise(Expression.LatexPriority < LatexPriority)} \quad \text{{for}} \quad {Predicate.Latexise(Predicate.LatexPriority <= LatexPriority)}";
+            public override string Latexise() => $@"{Expression.Latexise(Expression.LatexPriority < LatexPriority)} \quad \text{{for}} \quad {Predicate.Latexise(Predicate.LatexPriority < LatexPriority)}";
         }
 
         partial record Piecewise
         {
             /// <inheritdoc/>
-            public override string Latexise() => $@"\begin{{cases}}" +
+            public override string Latexise() => @"\begin{cases}" +
                 string.Join(@"\\",
                 Cases.Select(c =>
                 {

Sources/AngouriMath/Functions/Output/ToString/ToString.Omni.Classes.cs

@@ -127,7 +127,7 @@ public override string Stringize()
         partial record Providedf
         {
             /// <inheritdoc/>
-            public override string Stringize() => $@"{Expression.Stringize(Expression.Priority <= Priority.Provided)} provided {Predicate.Stringize(Predicate.Priority < Priority.Provided)}";
+            public override string Stringize() => $@"{Expression.Stringize(Expression.Priority < Priority.Provided)} provided {Predicate.Stringize(Predicate.Priority < Priority.Provided)}";
             /// <inheritdoc/>
             public override string ToString() => Stringize();
         }

Sources/Tests/UnitTests/Convenience/FromStringTest.cs

@@ -156,6 +156,7 @@ public void TestFormula8()
         [Fact] public void TestProvided1() => Assert.Equal(MathS.Provided("a", "b"), FromString("a provided b"));
         [Fact] public void TestProvided2() => Assert.Equal(MathS.Provided("a", MathS.Provided("b", "c")), FromString("a provided b provided c"));
         [Fact] public void TestProvided3() => Assert.Equal(MathS.Provided(MathS.Provided("a", "b"), "c"), FromString("(a provided b) provided c"));
+        [Fact] public void TestProvided4() => Assert.Equal(FromString("a provided (b provided c)").Stringize(), FromString("(a provided b) provided c").Stringize());
 
         [Theory]
         [InlineData("sh", "Sinh")]

Sources/Tests/UnitTests/Convenience/LatexTest.cs

@@ -314,7 +314,7 @@ [Fact] public void Provided2()
         [Fact] public void Provided3()
             => Test(@"a \quad \text{for} \quad b \quad \text{for} \quad c", MathS.Provided(MathS.Provided("a", "b"), "c"));
         [Fact] public void Provided4()
-            => Test(@"\left(a \quad \text{for} \quad b \quad \text{for} \quad \left(c \quad \text{for} \quad d\right)\right) \to \top ", MathS.Provided(MathS.Provided("a", "b"), MathS.Provided("c", "d")).Implies(Entity.Boolean.True));
+            => Test(@"\left(a \quad \text{for} \quad b \quad \text{for} \quad c \quad \text{for} \quad d\right) \to \top ", MathS.Provided(MathS.Provided("a", "b"), MathS.Provided("c", "d")).Implies(Entity.Boolean.True));
         // Juxtaposition tests
         [Fact] public void M1InTheMiddle() => Test(@"x \left(-1\right) \cdot x", (x * (-1)) * x);
         [Fact] public void MultiplyNumberWithPower() => Test(@"2 \cdot {3}^{4}", 2 * ((Entity)3).Pow(4));

Sources/Tests/UnitTests/Convenience/PriorityTest.cs

@@ -40,7 +40,6 @@ public class PriorityTest
         [InlineData("not a or not b implies not c or not d", "((not a) or (not b)) implies ((not c) or (not d))")]
         [InlineData("a = b and b > c and d", "a = b > c and d")]
         [InlineData("a provided b", "a provided b")]
-        [InlineData("(a provided b) provided c", "(a provided b) provided c")]
         [InlineData("a provided b provided c", "a provided (b provided c)")]
         [InlineData("a provided b and c", "a provided (b and c)")]
         [InlineData("a provided b + c > 0", "a provided (b + c > 0)")]