FormatValues (#1303)

This PR adds `FormatValues` to access the format values of Symbols.

Author: mmatera

CHANGES.rst

@@ -8,6 +8,7 @@ New Builtins
 * ``Between``
 * ``CheckAbort``
 * ``FileNameDrop``
+* ``FormatValues``
 * ``SetEnvironment``
 * ``SequenceForm``
 

mathics/builtin/atomic/symbols.py

@@ -400,6 +400,29 @@ def eval(self, symbol, evaluation):
         return get_symbol_values(symbol, "DownValues", "downvalues", evaluation)
 
 
+# In Mathematica 5, this appears under "Types of Values".
+class FormatValues(Builtin):
+    """
+    <url>:WMA link:https://reference.wolfram.com/language/tutorial/PatternsAndTransformationRules.html#6025</url>
+    <dl>
+      <dt>'FormatValues[$symbol$]'
+      <dd>gives the list of formatvalues associated with $symbol$.
+    </dl>
+
+    >> Format[F[x_], OutputForm]:= Subscript[x, F]
+    >> FormatValues[F]
+     = {HoldPattern[Format[Subscript[x_, F], OutputForm]] :> Subscript[x, F]}
+    """
+
+    summary_text = (
+        "give a list of formatting transformation rules associated with a symbol."
+    )
+
+    def eval(self, symbol, evaluation):
+        """FormatValues[symbol_]"""
+        return get_symbol_values(symbol, "FormatValues", "formatvalues", evaluation)
+
+
 class Information(PrefixOperator):
     """
     <url>:WMA link:

mathics/core/assignment.py

@@ -21,6 +21,7 @@
     SymbolAnd,
     SymbolBlank,
     SymbolCondition,
+    SymbolFormat,
     SymbolHoldPattern,
     SymbolOptionValue,
     SymbolPart,
@@ -116,6 +117,46 @@ def get_symbol_values(
         return ListExpression()
 
     elements = []
+
+    if position == "formatvalues":
+        format_rules = definition.formatvalues
+        for key, rules in format_rules.items():
+            if key == "System`MakeBoxes":
+                elements.extend(rules)
+                continue
+            if key:
+                elements.extend(
+                    (
+                        Expression(
+                            SymbolRuleDelayed,
+                            Expression(
+                                SymbolHoldPattern,
+                                Expression(
+                                    SymbolFormat, rule.pattern.expr, Symbol(key)
+                                ),
+                            ),
+                            rule.replace,
+                        )
+                        for rule in rules
+                    )
+                )
+            else:
+                elements.extend(
+                    (
+                        Expression(
+                            SymbolRuleDelayed,
+                            Expression(
+                                SymbolHoldPattern,
+                                Expression(SymbolFormat, rule.pattern.expr),
+                            ),
+                            rule.replace,
+                        )
+                        for rule in rules
+                    )
+                )
+        elements.sort()
+        return ListExpression(*elements)
+
     for rule in definition.get_values_list(position):
         if isinstance(rule, Rule):
             pattern = rule.pattern