Speedups for Position[], Cases[], DeleteCases[]

mathics/builtin/lists.py

@@ -1381,10 +1381,19 @@ class Cases(Builtin):
      = {2 I, 4 - I}
     """
     rules = {
-        'Cases[list_, pattern_]': 'Select[list, MatchQ[#, pattern]&]',
         'Cases[pattern_][list_]': 'Cases[list, pattern]',
     }
 
+    def apply(self, items, pattern, evaluation):
+        'Cases[items_, pattern_]'
+        if items.is_atom():
+            evaluation.message('Select', 'normal')
+            return
+
+        from mathics.builtin.patterns import Matcher
+        match = Matcher(pattern).match
+        return Expression('List', *[leaf for leaf in items.leaves if match(leaf, evaluation)])
+
 
 class DeleteCases(Builtin):
     """
@@ -1400,9 +1409,15 @@ class DeleteCases(Builtin):
      = {1, 2, 3}
     """
 
-    rules = {
-        'DeleteCases[list_, pattern_]': 'Select[list, ! MatchQ[#, pattern]&]',
-    }
+    def apply(self, items, pattern, evaluation):
+        'DeleteCases[items_, pattern_]'
+        if items.is_atom():
+            evaluation.message('Select', 'normal')
+            return
+
+        from mathics.builtin.patterns import Matcher
+        match = Matcher(pattern).match
+        return Expression('List', *[leaf for leaf in items.leaves if not match(leaf, evaluation)])
 
 
 class Position(Builtin):
@@ -1452,10 +1467,13 @@ def apply_level(self, expr, patt, ls, evaluation, options={}):
         except InvalidLevelspecError:
             return evaluation.message('Position', 'level', ls)
 
+        from mathics.builtin.patterns import Matcher
+
+        match = Matcher(patt).match
         result = []
+
         def callback(level, pos):
-            expr = Expression('MatchQ', level, patt)
-            if expr.evaluate(evaluation).is_true():
+            if match(level, evaluation):
                 result.append(pos)
             return level
 

mathics/builtin/patterns.py

@@ -572,19 +572,26 @@ def except_yield_func(vars, rest):
             self.p.match(yield_func, expression, vars, evaluation)
 
 
+class Matcher(object):
+    def __init__(self, form):
+        self.form = Pattern.create(form)
+
+    def match(self, expr, evaluation):
+        class StopGenerator_MatchQ(StopGenerator):
+            pass
+
+        def yield_func(vars, rest):
+            raise StopGenerator_MatchQ(Symbol("True"))
+
+        try:
+            self.form.match(yield_func, expr, {}, evaluation)
+        except StopGenerator_MatchQ:
+            return True
+        return False
+
+
 def match(expr, form, evaluation):
-    class StopGenerator_MatchQ(StopGenerator):
-        pass
-
-    form = Pattern.create(form)
-
-    def yield_func(vars, rest):
-        raise StopGenerator_MatchQ(Symbol("True"))
-    try:
-        form.match(yield_func, expr, {}, evaluation)
-    except StopGenerator_MatchQ:
-        return True
-    return False
+    return Matcher(form).match(expr, evaluation)
 
 
 class MatchQ(Builtin):