diff --git a/artiq/py2llvm/types.py b/artiq/py2llvm/types.py
index 97aff58ca..19ad56d48 100644
--- a/artiq/py2llvm/types.py
+++ b/artiq/py2llvm/types.py
@@ -163,13 +163,14 @@ class TValue(Type):
 def is_var(typ):
     return isinstance(typ.find(), TVar)
 
-def is_mono(typ, name, **params):
+def is_mono(typ, name=None, **params):
     typ = typ.find()
     params_match = True
     for param in params:
-        params_match = params_match and typ.params[param] == params[param]
+        params_match = params_match and \
+            typ.params[param].find() == params[param].find()
     return isinstance(typ, TMono) and \
-        typ.name == name and params_match
+        (name is None or (typ.name == name and params_match))
 
 def is_tuple(typ, elts=None):
     typ = typ.find()
diff --git a/artiq/py2llvm/typing.py b/artiq/py2llvm/typing.py
index ec4991eb7..875920df3 100644
--- a/artiq/py2llvm/typing.py
+++ b/artiq/py2llvm/typing.py
@@ -283,7 +283,6 @@ class ASTTypedRewriter(algorithm.Transformer):
 
     # expr
     visit_Call = visit_unsupported
-    visit_Compare = visit_unsupported
     visit_Dict = visit_unsupported
     visit_DictComp = visit_unsupported
     visit_Ellipsis = visit_unsupported
@@ -393,11 +392,14 @@ class Inferencer(algorithm.Visitor):
                     node.attr_loc, [node.value.loc])
                 self.engine.process(diag)
 
+    def _unify_collection(self, element, collection):
+        # TODO: support more than just lists
+        self._unify(builtins.TList(element.type), collection.type,
+                    element.loc, collection.loc)
+
     def visit_SubscriptT(self, node):
         self.generic_visit(node)
-        # TODO: support more than just lists
-        self._unify(builtins.TList(node.type), node.value.type,
-                    node.loc, node.value.loc)
+        self._unify_collection(element=node, collection=node.value)
 
     def visit_IfExpT(self, node):
         self.generic_visit(node)
@@ -455,43 +457,39 @@ class Inferencer(algorithm.Visitor):
     def _coerce_one(self, typ, coerced_node, other_node):
         if coerced_node.type.find() == typ.find():
             return coerced_node
+        elif isinstance(coerced_node, asttyped.CoerceT):
+            node.type, node.other_expr = typ, other_node
         else:
             node = asttyped.CoerceT(type=typ, expr=coerced_node, other_expr=other_node,
                                     loc=coerced_node.loc)
-            self.visit(node)
-            return node
+        self.visit(node)
+        return node
 
-    def _coerce_numeric(self, left, right):
-        # Implements the coercion protocol.
+    def _coerce_numeric(self, nodes, map_return=lambda typ: typ):
         # See https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex.
-        if builtins.is_float(left.type) or builtins.is_float(right.type):
-            typ = builtins.TFloat()
-        elif builtins.is_int(left.type) or builtins.is_int(right.type):
-            left_width, right_width = \
-                builtins.get_int_width(left.type), builtins.get_int_width(left.type)
-            if left_width and right_width:
-                typ = builtins.TInt(types.TValue(max(left_width, right_width)))
-            else:
-                typ = builtins.TInt()
-        elif types.is_var(left.type) or types.is_var(right.type): # not enough info yet
+        node_types = [node.type for node in nodes]
+        if any(map(types.is_var, node_types)): # not enough info yet
             return
-        else: # conflicting types
-            printer = types.TypePrinter()
-            note1 = diagnostic.Diagnostic("note",
-                "expression of type {typea}", {"typea": printer.name(left.type)},
-                left.loc)
-            note2 = diagnostic.Diagnostic("note",
-                "expression of type {typeb}", {"typeb": printer.name(right.type)},
-                right.loc)
+        elif not all(map(builtins.is_numeric, node_types)):
+            err_node = next(filter(lambda node: not builtins.is_numeric(node.type), nodes))
             diag = diagnostic.Diagnostic("error",
-                "cannot coerce {typea} and {typeb} to a common numeric type",
-                {"typea": printer.name(left.type), "typeb": printer.name(right.type)},
-                left.loc, [right.loc],
-                [note1, note2])
+                "cannot coerce {type} to a numeric type",
+                {"type": types.TypePrinter().name(err_node.type)},
+                err_node.loc, [])
             self.engine.process(diag)
             return
+        elif any(map(builtins.is_float, node_types)):
+            typ = builtins.TFloat()
+        elif any(map(builtins.is_int, node_types)):
+            widths = map(builtins.get_int_width, node_types)
+            if all(widths):
+                typ = builtins.TInt(types.TValue(max(widths)))
+            else:
+                typ = builtins.TInt()
+        else:
+            assert False
 
-        return typ, typ, typ
+        return map_return(typ)
 
     def _order_by_pred(self, pred, left, right):
         if pred(left.type):
@@ -503,7 +501,7 @@ class Inferencer(algorithm.Visitor):
 
     def _coerce_binop(self, op, left, right):
         if isinstance(op, (ast.BitAnd, ast.BitOr, ast.BitXor,
-                                ast.LShift, ast.RShift)):
+                           ast.LShift, ast.RShift)):
             # bitwise operators require integers
             for operand in (left, right):
                 if not types.is_var(operand.type) and not builtins.is_int(operand.type):
@@ -515,7 +513,7 @@ class Inferencer(algorithm.Visitor):
                     self.engine.process(diag)
                     return
 
-            return self._coerce_numeric(left, right)
+            return self._coerce_numeric((left, right), lambda typ: (typ, typ, typ))
         elif isinstance(op, ast.Add):
             # add works on numbers and also collections
             if builtins.is_collection(left.type) or builtins.is_collection(right.type):
@@ -554,7 +552,7 @@ class Inferencer(algorithm.Visitor):
                                 left.loc, right.loc)
                     return left.type, left.type, right.type
             else:
-                return self._coerce_numeric(left, right)
+                return self._coerce_numeric((left, right), lambda typ: (typ, typ, typ))
         elif isinstance(op, ast.Mult):
             # mult works on numbers and also number & collection
             if types.is_tuple(left.type) or types.is_tuple(right.type):
@@ -585,10 +583,10 @@ class Inferencer(algorithm.Visitor):
 
                 return list_.type, left.type, right.type
             else:
-                return self._coerce_numeric(left, right)
+                return self._coerce_numeric((left, right), lambda typ: (typ, typ, typ))
         elif isinstance(op, (ast.Div, ast.FloorDiv, ast.Mod, ast.Pow, ast.Sub)):
             # numeric operators work on any kind of number
-            return self._coerce_numeric(left, right)
+            return self._coerce_numeric((left, right), lambda typ: (typ, typ, typ))
         else: # MatMult
             diag = diagnostic.Diagnostic("error",
                 "operator '{op}' is not supported", {"op": op.loc.source()},
@@ -605,6 +603,42 @@ class Inferencer(algorithm.Visitor):
             node.right = self._coerce_one(right_type, node.right, other_node=node.left)
             node.type.unify(return_type) # should never fail
 
+    def visit_CompareT(self, node):
+        self.generic_visit(node)
+        pairs = zip([node.left] + node.comparators, node.comparators)
+        if all(map(lambda op: isinstance(op, (ast.Is, ast.IsNot)), node.ops)):
+            for left, right in pairs:
+                self._unify(left.type, right.type,
+                            left.loc, right.loc)
+        elif all(map(lambda op: isinstance(op, (ast.In, ast.NotIn)), node.ops)):
+            for left, right in pairs:
+                self._unify_collection(element=left, collection=right)
+        else: # Eq, NotEq, Lt, LtE, Gt, GtE
+            operands = [node.left] + node.comparators
+            operand_types = [operand.type for operand in operands]
+            if any(map(builtins.is_collection, operand_types)):
+                for left, right in pairs:
+                    self._unify(left.type, right.type,
+                                left.loc, right.loc)
+            else:
+                typ = self._coerce_numeric(operands)
+                if typ:
+                    try:
+                        other_node = next(filter(lambda operand: operand.type.find() == typ.find(),
+                                                 operands))
+                    except StopIteration:
+                        # can't find an argument with an exact type, meaning
+                        # the return value is more generic than any of the inputs, meaning
+                        # the type is known (typ is not None), but its width is not
+                        def wide_enough(opreand):
+                            return types.is_mono(opreand.type) and \
+                                opreand.type.find().name == typ.find().name
+                        other_node = next(filter(wide_enough, operands))
+                    print(typ, other_node)
+                    node.left, *node.comparators = \
+                        [self._coerce_one(typ, operand, other_node) for operand in operands]
+        node.type.unify(builtins.TBool())
+
     def visit_Assign(self, node):
         self.generic_visit(node)
         if len(node.targets) > 1:
diff --git a/lit-test/py2llvm/typing/coerce.py b/lit-test/py2llvm/typing/coerce.py
index 786f3e81a..34df20e7e 100644
--- a/lit-test/py2llvm/typing/coerce.py
+++ b/lit-test/py2llvm/typing/coerce.py
@@ -27,3 +27,15 @@
 
 a = []; a += [1]
 # CHECK-L: a:list(elt=int(width='r)) = []:list(elt=int(width='r)); a:list(elt=int(width='r)) += [1:int(width='r)]:list(elt=int(width='r))
+
+[] is [1]
+# CHECK-L: []:list(elt=int(width='s)) is [1:int(width='s)]:list(elt=int(width='s)):bool
+
+1 in [1]
+# CHECK-L: 1:int(width='t) in [1:int(width='t)]:list(elt=int(width='t)):bool
+
+[] < [1]
+# CHECK-L: []:list(elt=int(width='u)) < [1:int(width='u)]:list(elt=int(width='u)):bool
+
+1.0 < 1
+# CHECK-L: 1.0:float < 1:int(width='v):float:bool
diff --git a/lit-test/py2llvm/typing/error_coerce.py b/lit-test/py2llvm/typing/error_coerce.py
index ad8416577..0ac65724f 100644
--- a/lit-test/py2llvm/typing/error_coerce.py
+++ b/lit-test/py2llvm/typing/error_coerce.py
@@ -25,13 +25,7 @@
 # CHECK-L: ${LINE:+1}: note: operand of type list(elt='b), which is not a valid repetition amount
 [1] * []
 
-# CHECK-L: ${LINE:+3}: error: cannot coerce list(elt='a) and NoneType to a common numeric type
-# CHECK-L: ${LINE:+2}: note: expression of type list(elt='a)
-# CHECK-L: ${LINE:+1}: note: expression of type NoneType
-[] - None
-
-# CHECK-L: ${LINE:+2}: error: cannot coerce list(elt='a) to float
-# CHECK-L: ${LINE:+1}: note: expression that required coercion to float
+# CHECK-L: ${LINE:+1}: error: cannot coerce list(elt='a) to a numeric type
 [] - 1.0
 
 # CHECK-L: ${LINE:+2}: error: expression of type int(width='a) has to be coerced to float, which makes assignment invalid