Fix mypy errors (#1145)

I've been going through fixing mypy errors, and have gotten through
about half of them. In the process I've added some extra error handling
that fixes some exceptions I've seen due to methods being called on the
wrong types.

Current master:

> Found 1718 errors in 183 files (checked 443 source files)

This branch:

> Found 872 errors in 155 files (checked 443 source files)

Feel free to squash all these commits, the only reason I've left them
separate is that I made sure the test suite was passing after each one.

mathics/builtin/atomic/numbers.py

@@ -668,7 +668,7 @@ class MaxPrecision(Predefined):
      = 3.141592654
     """
 
-    is_numeric = False
+    _is_numeric = False
     messages = {
         "precset": "Cannot set `1` to `2`; value must be a positive number or Infinity.",
         "preccon": "Cannot set `1` such that $MaxPrecision < $MinPrecision.",
@@ -702,7 +702,7 @@ class MachineEpsilon_(Predefined):
      = {0., 0., 2.22045×10^-16}
     """
 
-    is_numeric = True
+    _is_numeric = True
     name = "$MachineEpsilon"
 
     summary_text = "the difference between 1.0 and the next-nearest number representable as a machine-precision number"
@@ -729,7 +729,7 @@ class MachinePrecision_(Predefined):
     summary_text = (
         "the number of decimal digits of precision for machine-precision numbers"
     )
-    is_numeric = True
+    _is_numeric = True
     rules = {
         "$MachinePrecision": "N[MachinePrecision]",
     }
@@ -749,7 +749,7 @@ class MachinePrecision(Predefined):
      = 15.9545897701910033463281614204
     """
 
-    is_numeric = True
+    _is_numeric = True
     rules = {
         "N[MachinePrecision, prec_]": (
             "N[Log[10, 2] * %i, prec]" % FP_MANTISA_BINARY_DIGITS
@@ -786,7 +786,7 @@ class MinPrecision(Builtin):
     }
 
     name = "$MinPrecision"
-    is_numeric = True
+    _is_numeric = True
     rules = {
         "$MinPrecision": "0",
     }

mathics/builtin/box/expression.py

@@ -1,6 +1,8 @@
 # This is never intended to go in Mathics3 docs
 no_doc = True
 
+from typing import Optional, Sequence, Union
+
 from mathics.core.attributes import A_PROTECTED, A_READ_PROTECTED
 from mathics.core.builtin import BuiltinElement
 from mathics.core.element import BoxElementMixin
@@ -109,8 +111,8 @@ def get_head_name(self):
     def get_lookup_name(self):
         return self.get_name()
 
-    def get_sort_key(self) -> tuple:
-        return self.to_expression().get_sort_key()
+    def get_sort_key(self, pattern_sort=False) -> tuple:
+        return self.to_expression().get_sort_key(pattern_sort)
 
     def get_string_value(self):
         return "-@" + self.get_head_name() + "@-"
@@ -119,7 +121,13 @@ def get_string_value(self):
     def head(self):
         return self.get_head()
 
-    def has_form(self, heads, *element_counts):
+    @head.setter
+    def head(self, value):
+        raise ValueError("BoxExpression.head is write protected.")
+
+    def has_form(
+        self, heads: Union[Sequence[str], str], *element_counts: Optional[int]
+    ) -> bool:
         """
         element_counts:
             (,):        no elements allowed
@@ -133,9 +141,13 @@ def has_form(self, heads, *element_counts):
         if isinstance(heads, (tuple, list, set)):
             if head_name not in [ensure_context(h) for h in heads]:
                 return False
-        else:
+        elif isinstance(heads, str):
             if head_name != ensure_context(heads):
                 return False
+        else:
+            raise TypeError(
+                f"Heads must be a string or a sequence of strings, not {type(heads)}"
+            )
         if not element_counts:
             return False
         if element_counts and element_counts[0] is not None:
@@ -151,10 +163,6 @@ def has_form(self, heads, *element_counts):
                     return False
         return True
 
-    @head.setter
-    def head(self, value):
-        raise ValueError("BoxExpression.head is write protected.")
-
     @property
     def is_literal(self) -> bool:
         """

mathics/builtin/list/constructing.py

@@ -8,7 +8,9 @@
 See also Constructing Vectors.
 """
 
+import typing
 from itertools import permutations
+from typing import Optional, Tuple
 
 from mathics.builtin.box.layout import RowBox
 from mathics.core.atoms import Integer, is_integer_rational_or_real
@@ -20,7 +22,7 @@
 from mathics.core.evaluation import Evaluation
 from mathics.core.expression import Expression, structure
 from mathics.core.list import ListExpression
-from mathics.core.symbols import Atom
+from mathics.core.symbols import Atom, Symbol
 from mathics.core.systemsymbols import SymbolNormal
 from mathics.eval.lists import get_tuples, list_boxes
 
@@ -268,9 +270,9 @@ def eval(self, imin, imax, di, evaluation: Evaluation):
             and isinstance(di, Integer)
         ):
             pm = 1 if di.value >= 0 else -1
-            result = [Integer(i) for i in range(imin.value, imax.value + pm, di.value)]
             return ListExpression(
-                *result, elements_properties=range_list_elements_properties
+                *[Integer(i) for i in range(imin.value, imax.value + pm, di.value)],
+                elements_properties=range_list_elements_properties,
             )
 
         imin = imin.to_sympy()
@@ -344,7 +346,7 @@ def eval(self, li, evaluation: Evaluation):
     def eval_n(self, li, n, evaluation: Evaluation):
         "Permutations[li_List, n_]"
 
-        rs = None
+        rs: Optional[Tuple[int, ...]] = None
         if isinstance(n, Integer):
             py_n = min(n.get_int_value(), len(li.elements))
         elif n.has_form("List", 1) and isinstance(n.elements[0], Integer):
@@ -359,12 +361,12 @@ def eval_n(self, li, n, evaluation: Evaluation):
 
         if py_n is None or py_n < 0:
             evaluation.message(
-                self.get_name(), "nninfseq", Expression(self.get_name(), li, n)
+                self.get_name(), "nninfseq", Expression(Symbol(self.get_name()), li, n)
             )
             return
 
         if rs is None:
-            rs = range(py_n + 1)
+            rs = tuple(range(py_n + 1))
 
         inner = structure("List", li, evaluation)
         outer = structure("List", inner, evaluation)
@@ -431,7 +433,7 @@ def eval(self, expr, patterns, f, evaluation: Evaluation):
         "Reap[expr_, {patterns___}, f_]"
 
         patterns = patterns.get_sequence()
-        sown = [
+        sown: typing.List[typing.Tuple[BasePattern, list]] = [
             (BasePattern.create(pattern, evaluation=evaluation), [])
             for pattern in patterns
         ]

mathics/builtin/list/rearrange.py

@@ -232,7 +232,7 @@ def eval_zero(self, element, n, evaluation: Evaluation):
             Integer0,
             Integer0,
             evaluation,
-            lambda: Expression(self.get_name(), element, n),
+            lambda: Expression(Symbol(self.get_name()), element, n),
         )
 
     def eval(self, element, n, x, evaluation: Evaluation):
@@ -243,7 +243,7 @@ def eval(self, element, n, x, evaluation: Evaluation):
             x,
             Integer0,
             evaluation,
-            lambda: Expression(self.get_name(), element, n, x),
+            lambda: Expression(Symbol(self.get_name()), element, n, x),
         )
 
     def eval_margin(self, element, n, x, m, evaluation: Evaluation):
@@ -254,7 +254,7 @@ def eval_margin(self, element, n, x, m, evaluation: Evaluation):
             x,
             m,
             evaluation,
-            lambda: Expression(self.get_name(), element, n, x, m),
+            lambda: Expression(Symbol(self.get_name()), element, n, x, m),
         )
 
 
@@ -354,6 +354,8 @@ def _gather(self, keys, values, equivalence):
 class _Rotate(Builtin):
     messages = {"rspec": "`` should be an integer or a list of integers."}
 
+    _sign: int
+
     def _rotate(self, expr, n, evaluation: Evaluation):
         if not isinstance(expr, Expression):
             return expr
@@ -363,12 +365,12 @@ def _rotate(self, expr, n, evaluation: Evaluation):
             return expr
 
         index = (self._sign * n[0]) % len(elements)  # with Python's modulo: index >= 1
-        new_elements = chain(elements[index:], elements[:index])
+        new_elements = tuple(chain(elements[index:], elements[:index]))
 
         if len(n) > 1:
-            new_elements = [
+            new_elements = tuple(
                 self._rotate(item, n[1:], evaluation) for item in new_elements
-            ]
+            )
 
         return expr.restructure(expr.head, new_elements, evaluation)
 

mathics/builtin/numbers/algebra.py

@@ -438,7 +438,9 @@ def eval(self, expr, evaluation):
 
 
 # Get a coefficient of form in an expression
-def _coefficient(name, expr, form, n, evaluation):
+def _coefficient(
+    name: str, expr: Expression, form: Expression, n: Integer, evaluation: Evaluation
+) -> BaseElement:
     if expr is SymbolNull or form is SymbolNull or n is SymbolNull:
         return Integer0
 
@@ -450,18 +452,11 @@ def _coefficient(name, expr, form, n, evaluation):
     sympy_var = form.to_sympy()
     sympy_n = n.to_sympy()
 
-    def combine_exprs(exprs):
-        result = 0
-        for e in exprs:
-            result += e
-        return result
-
     # expand sub expressions if they contain variables
-    sympy_exprs = [
+    sympy_expr: sympy.Expr = sum(
         sympy.expand(e) if sympy_var.free_symbols.issubset(e.free_symbols) else e
         for e in sympy_exprs
-    ]
-    sympy_expr = combine_exprs(sympy_exprs)
+    )
     sympy_result = sympy_expr.coeff(sympy_var, sympy_n)
     return from_sympy(sympy_result)
 
@@ -519,16 +514,18 @@ class Coefficient(Builtin):
 
     summary_text = "coefficient of a monomial in a polynomial expression"
 
-    def eval_noform(self, expr, evaluation):
+    def eval_noform(self, expr: Expression, evaluation: Evaluation):
         "Coefficient[expr_]"
         evaluation.message("Coefficient", "argtu")
 
-    def eval(self, expr, form, evaluation):
+    def eval(self, expr: Expression, form: Expression, evaluation: Evaluation):
         "Coefficient[expr_, form_]"
         return _coefficient(self.__class__.__name__, expr, form, Integer1, evaluation)
 
-    def eval_n(self, expr, form, n, evaluation):
-        "Coefficient[expr_, form_, n_]"
+    def eval_n(
+        self, expr: Expression, form: Expression, n: Integer, evaluation: Evaluation
+    ):
+        "Coefficient[expr_, form_, n_Integer]"
         return _coefficient(self.__class__.__name__, expr, form, n, evaluation)
 
 
@@ -559,9 +556,8 @@ def coeff_power_internal(
 
         # ###### Auxiliary functions #########
         def key_powers(lst: list) -> Union[int, float]:
-            key = Expression(SymbolPlus, *lst)
-            key = key.evaluate(evaluation)
-            if key.is_numeric(evaluation):
+            key = Expression(SymbolPlus, *lst).evaluate(evaluation)
+            if key is not None and key.is_numeric(evaluation):
                 return key.to_python()
             return 0