improve OneIdentity builtin

mathics/builtin/__init__.py

@@ -20,6 +20,8 @@
     PatternObject,
 )
 
+from mathics.core.pattern import pattern_objects
+
 from mathics.settings import ENABLE_FILES_MODULE
 from mathics.version import __version__  # noqa used in loading to check consistency.
 
@@ -267,7 +269,6 @@ def sanity_check(cls, module):
 mathics_to_python = {}  # here we have: name -> string
 sympy_to_mathics = {}
 
-pattern_objects = {}
 builtins_precedence = {}
 
 new_builtins = _builtins

mathics/builtin/assignments/clear.py

@@ -22,14 +22,20 @@
     Atom,
     Symbol,
     SymbolNull,
-    system_symbols,
+    symbol_set,
 )
 
 from mathics.core.systemsymbols import (
     SymbolContext,
     SymbolContextPath,
+    SymbolDownValues,
     SymbolFailed,
+    SymbolMessages,
+    SymbolNValues,
     SymbolOptions,
+    SymbolOwnValues,
+    SymbolSubValues,
+    SymbolUpValues,
 )
 
 from mathics.core.atoms import String
@@ -320,12 +326,12 @@ def apply(self, expr, evaluation):
         return SymbolNull
 
 
-SYSTEM_SYMBOL_VALUES = system_symbols(
-    "OwnValues",
-    "DownValues",
-    "SubValues",
-    "UpValues",
-    "NValues",
-    "Options",
-    "Messages",
+SYSTEM_SYMBOL_VALUES = symbol_set(
+    SymbolDownValues,
+    SymbolMessages,
+    SymbolNValues,
+    SymbolOptions,
+    SymbolOwnValues,
+    SymbolSubValues,
+    SymbolUpValues,
 )

mathics/builtin/assignments/internals.py

@@ -720,12 +720,7 @@ def process_rhs_conditions(lhs, rhs, condition, evaluation):
 
 
 def process_tags_and_upset_dont_allow_custom(tags, upset, self, lhs, focus, evaluation):
-    # TODO: the following provides a hacky fix for 1259. I know @rocky loves
-    # this kind of things, but otherwise we need to work on rebuild the pattern
-    # matching mechanism...
-    flag_ioi, evaluation.ignore_oneidentity = evaluation.ignore_oneidentity, True
     focus = focus.evaluate_elements(evaluation)
-    evaluation.ignore_oneidentity = flag_ioi
     name = lhs.get_head_name()
     if tags is None and not upset:
         name = focus.get_lookup_name()
@@ -745,14 +740,9 @@ def process_tags_and_upset_dont_allow_custom(tags, upset, self, lhs, focus, eval
 
 
 def process_tags_and_upset_allow_custom(tags, upset, self, lhs, evaluation):
-    # TODO: the following provides a hacky fix for 1259. I know @rocky loves
-    # this kind of things, but otherwise we need to work on rebuild the pattern
-    # matching mechanism...
     name = lhs.get_head_name()
     focus = lhs
-    flag_ioi, evaluation.ignore_oneidentity = evaluation.ignore_oneidentity, True
     focus = focus.evaluate_elements(evaluation)
-    evaluation.ignore_oneidentity = flag_ioi
     if tags is None and not upset:
         name = focus.get_lookup_name()
         if not name:

mathics/builtin/attributes.py

@@ -460,15 +460,24 @@ class OneIdentity(Predefined):
 
     <dl>
       <dt>'OneIdentity'
-      <dd>is an attribute specifying that '$f$[$x$]' should be treated \
-        as equivalent to $x$ in pattern matching.
+      <dd>is an attribute assigned to a symbol, say $f$, indicating that '$f$[$x$]', $f$[$f$[$x$]], etc. are all \
+          equivalent to $x$ in pattern matching.
     </dl>
 
-    'OneIdentity' affects pattern matching:
+    >> a /. f[x_:0, u_] -> {u}
+     = a
+
+    Here is how 'OneIdentity' changes the pattern matched above :
+
     >> SetAttributes[f, OneIdentity]
-    >> a /. f[args___] -> {args}
+    >> a /. f[x_:0, u_] -> {u}
      = {a}
-    It does not affect evaluation:
+
+    However, without a default argument, the pattern does not match:
+    >> a /. f[u_] -> {u}
+     = a
+
+    'OneIdentity' does not change evaluation:
     >> f[a]
      = f[a]
     """

mathics/builtin/files_io/files.py

@@ -296,7 +296,7 @@ class FilePrint(Builtin):
     }
 
     def apply(self, path, evaluation, options):
-        "FilePrint[path_ OptionsPattern[FilePrint]]"
+        "FilePrint[path_, OptionsPattern[FilePrint]]"
         pypath = path.to_python()
         if not (
             isinstance(pypath, str)

mathics/builtin/graphics.py

@@ -47,23 +47,23 @@
 from mathics.core.list import ListExpression
 from mathics.core.symbols import (
     Symbol,
-    system_symbols,
+    symbol_set,
     system_symbols_dict,
     SymbolList,
     SymbolNull,
 )
 from mathics.core.systemsymbols import (
+    SymbolEdgeForm,
+    SymbolFaceForm,
     SymbolMakeBoxes,
+    SymbolRule,
 )
 
 from mathics.core.formatter import lookup_method
 
 from mathics.core.attributes import A_PROTECTED, A_READ_PROTECTED
 
 
-SymbolEdgeForm = Symbol("System`EdgeForm")
-SymbolFaceForm = Symbol("System`FaceForm")
-
 GRAPHICS_OPTIONS = {
     "AspectRatio": "Automatic",
     "Axes": "False",
@@ -1427,26 +1427,26 @@ class Tiny(Builtin):
 
 
 element_heads = frozenset(
-    system_symbols(
-        "Arrow",
-        "BezierCurve",
-        "Circle",
-        "Cone",
-        "Cuboid",
-        "Cylinder",
-        "Disk",
-        "FilledCurve",
-        "Inset",
-        "Line",
-        "Point",
-        "Polygon",
-        "Rectangle",
-        "RegularPolygon",
-        "Sphere",
-        "Style",
-        "Text",
-        "Tube",
-        "UniformPolyhedron",
+    symbol_set(
+        Symbol("System`Arrow"),
+        Symbol("System`BezierCurve"),
+        Symbol("System`Circle"),
+        Symbol("System`Cone"),
+        Symbol("System`Cuboid"),
+        Symbol("System`Cylinder"),
+        Symbol("System`Disk"),
+        Symbol("System`FilledCurve"),
+        Symbol("System`Inset"),
+        Symbol("System`Line"),
+        Symbol("System`Point"),
+        Symbol("System`Polygon"),
+        Symbol("System`Rectangle"),
+        Symbol("System`RegularPolygon"),
+        Symbol("System`Sphere"),
+        Symbol("System`Style"),
+        Symbol("System`Text"),
+        Symbol("System`Tube"),
+        Symbol("System`UniformPolyhedron"),
     )
 )
 
@@ -1477,7 +1477,7 @@ class Tiny(Builtin):
 style_heads = frozenset(styles.keys())
 
 style_and_form_heads = frozenset(
-    style_heads.union(system_symbols("System`EdgeForm", "System`FaceForm"))
+    style_heads.union(symbol_set(SymbolEdgeForm, SymbolFaceForm))
 )
 
 GLOBALS.update(
@@ -1497,8 +1497,8 @@ class Tiny(Builtin):
 GLOBALS.update(styles)
 
 GRAPHICS_SYMBOLS = {
-    Symbol("System`List"),
-    Symbol("System`Rule"),
+    SymbolList,
+    SymbolRule,
     Symbol("System`VertexColors"),
     *element_heads,
     *[Symbol(element.name + "Box") for element in element_heads],

mathics/builtin/options.py

@@ -79,11 +79,11 @@ def eval(self, f, i, evaluation):
         i = [index.get_int_value() for index in i]
         for index in i:
             if index is None or index < 1:
-                evaluation.message(SymbolDefault, "intp")
+                evaluation.message(SymbolDefault.name, "intp")
                 return
         name = f.get_name()
         if not name:
-            evaluation.message(SymbolDefault, "sym", f, 1)
+            evaluation.message(SymbolDefault.name, "sym", f, 1)
             return
         result = get_default_value(name, evaluation, *i)
         return result

mathics/core/atoms.py

@@ -24,9 +24,9 @@
     Symbol,
     SymbolNull,
     SymbolTrue,
-    system_symbols,
+    symbol_set,
 )
-from mathics.core.systemsymbols import SymbolInfinity
+from mathics.core.systemsymbols import SymbolInfinity, SymbolInputForm, SymbolFullForm
 
 # Imperical number that seems to work.
 # We have to be able to match mpmath values with sympy values
@@ -35,7 +35,7 @@
 SymbolI = Symbol("I")
 SymbolString = Symbol("String")
 
-SYSTEM_SYMBOLS_INPUT_OR_FULL_FORM = system_symbols("InputForm", "FullForm")
+SYSTEM_SYMBOLS_INPUT_OR_FULL_FORM = symbol_set(SymbolInputForm, SymbolFullForm)
 
 
 class Number(Atom, ImmutableValueMixin, NumericOperators):

mathics/core/evaluation.py

@@ -262,9 +262,6 @@ def __init__(
         # status of last evaluate
         self.exc_result = self.SymbolNull
         self.last_eval = None
-        # Necesary to handle OneIdentity on
-        # lhs in assignment
-        self.ignore_oneidentity = False
         # Used in ``mathics.builtin.numbers.constants.get_constant`` and
         # ``mathics.builtin.numeric.N``.
         self._preferred_n_method = []

mathics/core/evaluators.py

@@ -21,10 +21,11 @@
 )
 from mathics.core.convert.sympy import from_sympy
 from mathics.core.definitions import PyMathicsLoadException
+from mathics.core.element import BaseElement
 from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression
 from mathics.core.number import PrecisionValueError, get_precision
-from mathics.core.symbols import Atom, BaseElement
+from mathics.core.symbols import Atom
 from mathics.core.systemsymbols import SymbolMachinePrecision, SymbolN
 
 

mathics/core/expression.py

@@ -37,11 +37,14 @@
     Monomial,
     NumericOperators,
     Symbol,
+    SymbolAbs,
+    SymbolDivide,
     SymbolList,
     SymbolN,
+    SymbolPlus,
     SymbolTimes,
     SymbolTrue,
-    system_symbols,
+    symbol_set,
 )
 from mathics.core.systemsymbols import (
     SymbolAborted,
@@ -50,9 +53,14 @@
     SymbolCondition,
     SymbolDirectedInfinity,
     SymbolFunction,
+    SymbolMinus,
     SymbolPattern,
+    SymbolPower,
     SymbolSequence,
+    SymbolSin,
     SymbolSlot,
+    SymbolSqrt,
+    SymbolSubtract,
     SymbolUnevaluated,
 )
 
@@ -70,16 +78,16 @@
 SymbolVerbatim = Symbol("Verbatim")
 
 
-symbols_arithmetic_operations = system_symbols(
-    "Sqrt",
-    "Times",
-    "Plus",
-    "Subtract",
-    "Minus",
-    "Power",
-    "Abs",
-    "Divide",
-    "Sin",
+symbols_arithmetic_operations = symbol_set(
+    SymbolAbs,
+    SymbolDivide,
+    SymbolMinus,
+    SymbolPlus,
+    SymbolPower,
+    SymbolSin,
+    SymbolSqrt,
+    SymbolSubtract,
+    SymbolTimes,
 )
 
 

mathics/core/list.py

@@ -41,7 +41,7 @@ def __init__(
         #     call_frame = inspect.getouterframes(curframe, 2)
         #     print("caller name:", call_frame[1][3])
 
-        # from mathics.core.symbols import BaseElement
+        # from mathics.core.element import BaseElement
         # for element in elements:
         #     if not isinstance(element, BaseElement):
         #          from trepan.api import debug; debug()