Starting to tidy up mathics.core.pattern (#1086)

In line with the last changes proposed by @rocky, I was doing a pass
over mathics.core.pattern and fixing some issues reported by the linter.

---------

Co-authored-by: R. Bernstein <[email protected]>

mathics/builtin/exp_structure/general.py

@@ -8,7 +8,7 @@
 from mathics.core.exceptions import InvalidLevelspecError
 from mathics.core.expression import Evaluation, Expression
 from mathics.core.list import ListExpression
-from mathics.core.rules import Pattern
+from mathics.core.rules import BasePattern
 from mathics.core.symbols import Atom, SymbolFalse, SymbolTrue
 from mathics.core.systemsymbols import SymbolMap
 from mathics.eval.parts import python_levelspec, walk_levels
@@ -114,7 +114,7 @@ class FreeQ(Builtin):
     def eval(self, expr, form, evaluation: Evaluation):
         "FreeQ[expr_, form_]"
 
-        form = Pattern.create(form)
+        form = BasePattern.create(form)
         if expr.is_free(form, evaluation):
             return SymbolTrue
         else:

mathics/builtin/list/constructing.py

@@ -13,7 +13,7 @@
 from mathics.builtin.box.layout import RowBox
 from mathics.core.atoms import Integer, is_integer_rational_or_real
 from mathics.core.attributes import A_HOLD_FIRST, A_LISTABLE, A_LOCKED, A_PROTECTED
-from mathics.core.builtin import Builtin, IterationFunction, Pattern
+from mathics.core.builtin import BasePattern, Builtin, IterationFunction
 from mathics.core.convert.expression import to_expression
 from mathics.core.convert.sympy import from_sympy
 from mathics.core.element import ElementsProperties
@@ -431,7 +431,7 @@ def eval(self, expr, patterns, f, evaluation: Evaluation):
         "Reap[expr_, {patterns___}, f_]"
 
         patterns = patterns.get_sequence()
-        sown = [(Pattern.create(pattern), []) for pattern in patterns]
+        sown = [(BasePattern.create(pattern), []) for pattern in patterns]
 
         def listener(e, tag):
             result = False

mathics/builtin/numbers/algebra.py

@@ -33,7 +33,7 @@
     MATHICS3_NEG_INFINITY,
 )
 from mathics.core.list import ListExpression
-from mathics.core.rules import Pattern
+from mathics.core.rules import BasePattern
 from mathics.core.symbols import (
     Atom,
     Symbol,
@@ -549,11 +549,11 @@ def coeff_power_internal(
             else:
                 return [([], expr)]
         if len(var_exprs) == 1:
-            target_pat = Pattern.create(var_exprs[0])
+            target_pat = BasePattern.create(var_exprs[0])
             var_pats = [target_pat]
         else:
-            target_pat = Pattern.create(Expression(SymbolAlternatives, *var_exprs))
-            var_pats = [Pattern.create(var) for var in var_exprs]
+            target_pat = BasePattern.create(Expression(SymbolAlternatives, *var_exprs))
+            var_pats = [BasePattern.create(var) for var in var_exprs]
 
         # ###### Auxiliary functions #########
         def key_powers(lst: list) -> Union[int, float]:
@@ -1172,7 +1172,7 @@ def eval_patt(self, expr, target, evaluation: Evaluation, options: dict):
             return
 
         if target:
-            kwargs["pattern"] = Pattern.create(target)
+            kwargs["pattern"] = BasePattern.create(target)
         kwargs["evaluation"] = evaluation
         return expand(expr, True, False, **kwargs)
 
@@ -1235,7 +1235,7 @@ def eval_patt(self, expr, target, evaluation: Evaluation, options: dict):
             return
 
         if target:
-            kwargs["pattern"] = Pattern.create(target)
+            kwargs["pattern"] = BasePattern.create(target)
         kwargs["evaluation"] = evaluation
         return expand(expr, numer=True, denom=True, deep=True, **kwargs)
 

mathics/builtin/numbers/calculus.py

@@ -46,7 +46,7 @@
 from mathics.core.expression import Expression
 from mathics.core.list import ListExpression
 from mathics.core.number import MACHINE_EPSILON, dps
-from mathics.core.rules import Pattern
+from mathics.core.rules import BasePattern
 from mathics.core.symbols import (
     BaseElement,
     Symbol,
@@ -228,7 +228,7 @@ def eval(self, f, x, evaluation: Evaluation):
         if f == x:
             return Integer1
 
-        x_pattern = Pattern.create(x)
+        x_pattern = BasePattern.create(x)
         if f.is_free(x_pattern, evaluation):
             return Integer0
 
@@ -1917,7 +1917,7 @@ def eval_times(
             nummax.get_int_value(),
             den.get_int_value(),
         )
-        x_pattern = Pattern.create(x)
+        x_pattern = BasePattern.create(x)
         incompat_series = []
         max_exponent = Integer(int(series[2] / series[3] + 1))
         if coeff.get_head() is SymbolSequence:
@@ -2263,7 +2263,7 @@ def eval(self, eqs, vars, evaluation: Evaluation):
         vars = []
         vars_sympy = []
         for var, var_sympy in zip(all_vars, all_vars_sympy):
-            pattern = Pattern.create(var)
+            pattern = BasePattern.create(var)
             if not eqs.is_free(pattern, evaluation):
                 vars.append(var)
                 vars_sympy.append(var_sympy)

mathics/builtin/patterns.py

@@ -37,9 +37,6 @@
 The attributes 'Flat', 'Orderless', and 'OneIdentity' affect pattern matching.
 """
 
-# This tells documentation how to sort this module
-sort_order = "mathics.builtin.rules-and-patterns"
-
 from typing import Callable, List, Optional as OptionalType, Tuple, Union
 
 from mathics.core.atoms import Integer, Number, Rational, Real, String
@@ -63,12 +60,15 @@
 from mathics.core.exceptions import InvalidLevelspecError
 from mathics.core.expression import Expression, SymbolVerbatim
 from mathics.core.list import ListExpression
-from mathics.core.pattern import Pattern, StopGenerator
+from mathics.core.pattern import BasePattern, StopGenerator
 from mathics.core.rules import Rule
 from mathics.core.symbols import Atom, Symbol, SymbolList, SymbolTrue
 from mathics.core.systemsymbols import SymbolBlank, SymbolDefault, SymbolDispatch
 from mathics.eval.parts import python_levelspec
 
+# This tells documentation how to sort this module
+sort_order = "mathics.builtin.rules-and-patterns"
+
 
 class Rule_(BinaryOperator):
     """
@@ -159,7 +159,7 @@ def create_rules(
     if any_lists:
         all_lists = True
         for item in rules:
-            if not item.get_head() is SymbolList:
+            if item.get_head() is not SymbolList:
                 all_lists = False
                 break
 
@@ -568,7 +568,7 @@ def init(
             "System`NonNegative": self.match_nonnegative,
         }
 
-        self.pattern = Pattern.create(expr.elements[0], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[0], evaluation=evaluation)
         self.test = expr.elements[1]
         testname = self.test.get_name()
         self.test_name = testname
@@ -765,7 +765,8 @@ def init(
     ) -> None:
         super(Alternatives, self).init(expr, evaluation=evaluation)
         self.alternatives = [
-            Pattern.create(element, evaluation=evaluation) for element in expr.elements
+            BasePattern.create(element, evaluation=evaluation)
+            for element in expr.elements
         ]
 
     def match(self, yield_func, expression, vars, evaluation, **kwargs):
@@ -826,11 +827,11 @@ def init(
         self, expr: Expression, evaluation: OptionalType[Evaluation] = None
     ) -> None:
         super(Except, self).init(expr, evaluation=evaluation)
-        self.c = Pattern.create(expr.elements[0])
+        self.c = BasePattern.create(expr.elements[0])
         if len(expr.elements) == 2:
-            self.p = Pattern.create(expr.elements[1], evaluation=evaluation)
+            self.p = BasePattern.create(expr.elements[1], evaluation=evaluation)
         else:
-            self.p = Pattern.create(Expression(SymbolBlank), evaluation=evaluation)
+            self.p = BasePattern.create(Expression(SymbolBlank), evaluation=evaluation)
 
     def match(self, yield_func, expression, vars, evaluation, **kwargs):
         def except_yield_func(vars, rest):
@@ -910,7 +911,7 @@ def init(
         self, expr: Expression, evaluation: OptionalType[Evaluation] = None
     ) -> None:
         super(HoldPattern, self).init(expr, evaluation=evaluation)
-        self.pattern = Pattern.create(expr.elements[0], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[0], evaluation=evaluation)
 
     def match(self, yield_func, expression, vars, evaluation, **kwargs):
         # for new_vars, rest in self.pattern.match(
@@ -919,7 +920,7 @@ def match(self, yield_func, expression, vars, evaluation, **kwargs):
         self.pattern.match(yield_func, expression, vars, evaluation)
 
 
-class Pattern_(PatternObject):
+class Pattern(PatternObject):
     """
     <url>:WMA link:https://reference.wolfram.com/language/ref/Pattern.html</url>
 
@@ -995,20 +996,20 @@ def init(
         varname = expr.elements[0].get_name()
         if varname is None or varname == "":
             self.error("patvar", expr)
-        super(Pattern_, self).init(expr, evaluation=evaluation)
+        super(Pattern, self).init(expr, evaluation=evaluation)
         self.varname = varname
-        self.pattern = Pattern.create(expr.elements[1], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[1], evaluation=evaluation)
 
     def __repr__(self):
         return "<Pattern: %s>" % repr(self.pattern)
 
     def get_match_count(self, vars={}):
         return self.pattern.get_match_count(vars)
 
-    def match(self, yield_func, expression, vars, evaluation, **kwargs):
-        existing = vars.get(self.varname, None)
+    def match(self, yield_func, expression, vars_dict, evaluation, **kwargs):
+        existing = vars_dict.get(self.varname, None)
         if existing is None:
-            new_vars = vars.copy()
+            new_vars = vars_dict.copy()
             new_vars[self.varname] = expression
             # for vars_2, rest in self.pattern.match(
             #    expression, new_vars, evaluation):
@@ -1021,22 +1022,24 @@ def match(self, yield_func, expression, vars, evaluation, **kwargs):
                 self.pattern.match(yield_func, expression, new_vars, evaluation)
         else:
             if existing.sameQ(expression):
-                yield_func(vars, None)
+                yield_func(vars_dict, None)
 
     def get_match_candidates(
-        self, elements: tuple, expression, attributes, evaluation, vars={}
+        self, elements: tuple, expression, attributes, evaluation, vars_dict=None
     ):
-        existing = vars.get(self.varname, None)
+        if vars_dict is None:
+            vars_dict = {}
+        existing = vars_dict.get(self.varname, None)
         if existing is None:
             return self.pattern.get_match_candidates(
-                elements, expression, attributes, evaluation, vars
+                elements, expression, attributes, evaluation, vars_dict
             )
         else:
             # Treat existing variable as verbatim
             verbatim_expr = Expression(SymbolVerbatim, existing)
             verbatim = Verbatim(verbatim_expr)
             return verbatim.get_match_candidates(
-                elements, expression, attributes, evaluation, vars
+                elements, expression, attributes, evaluation, vars_dict
             )
 
 
@@ -1097,7 +1100,7 @@ def init(
         self, expr: Expression, evaluation: OptionalType[Evaluation] = None
     ) -> None:
         super(Optional, self).init(expr, evaluation=evaluation)
-        self.pattern = Pattern.create(expr.elements[0], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[0], evaluation=evaluation)
         if len(expr.elements) == 2:
             self.default = expr.elements[1]
         else:
@@ -1398,7 +1401,7 @@ def init(
         min: int = 1,
         evaluation: OptionalType[Evaluation] = None,
     ):
-        self.pattern = Pattern.create(expr.elements[0], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[0], evaluation=evaluation)
         self.max = None
         self.min = min
         if len(expr.elements) == 2:
@@ -1550,9 +1553,9 @@ def init(
         # if (expr.elements[0].get_head_name() == "System`Condition" and
         #    len(expr.elements[0].elements) == 2):
         #    self.test = Expression(SymbolAnd, self.test, expr.elements[0].elements[1])
-        #    self.pattern = Pattern.create(expr.elements[0].elements[0])
+        #    self.pattern = BasePattern.create(expr.elements[0].elements[0])
         # else:
-        self.pattern = Pattern.create(expr.elements[0], evaluation=evaluation)
+        self.pattern = BasePattern.create(expr.elements[0], evaluation=evaluation)
 
     def match(
         self,

mathics/core/builtin.py

@@ -54,7 +54,7 @@
 from mathics.core.list import ListExpression
 from mathics.core.number import PrecisionValueError, dps, get_precision, min_prec
 from mathics.core.parser.util import PyMathicsDefinitions, SystemDefinitions
-from mathics.core.pattern import Pattern
+from mathics.core.pattern import BasePattern
 from mathics.core.rules import FunctionApplyRule, Rule
 from mathics.core.symbols import (
     BaseElement,
@@ -1131,7 +1131,7 @@ def __init__(self, name, count, expected):
         super().__init__(name, "argr", count, expected)
 
 
-class PatternObject(BuiltinElement, Pattern):
+class PatternObject(BuiltinElement, BasePattern):
     needs_verbatim = True
 
     arg_counts: List[int] = []
@@ -1142,9 +1142,10 @@ def init(self, expr, evaluation: Optional[Evaluation] = None):
             if len(expr.elements) not in self.arg_counts:
                 self.error_args(len(expr.elements), *self.arg_counts)
         self.expr = expr
-        self.head = Pattern.create(expr.head, evaluation=evaluation)
+        self.head = BasePattern.create(expr.head, evaluation=evaluation)
         self.elements = [
-            Pattern.create(element, evaluation=evaluation) for element in expr.elements
+            BasePattern.create(element, evaluation=evaluation)
+            for element in expr.elements
         ]
 
     def error(self, tag, *args):