diff --git a/lib/cretonne/meta/build.py b/lib/cretonne/meta/build.py
index cfda7ae862..1554b6a54c 100644
--- a/lib/cretonne/meta/build.py
+++ b/lib/cretonne/meta/build.py
@@ -15,7 +15,7 @@ parser = argparse.ArgumentParser(description='Generate sources for Cretonne.')
 parser.add_argument('--out-dir', help='set output directory')
 
 args = parser.parse_args()
-out_dir = args.out_dir
+out_dir = args.out_dir  # type: ignore
 
 isas = isa.all_isas()
 
diff --git a/lib/cretonne/meta/cretonne/__init__.py b/lib/cretonne/meta/cretonne/__init__.py
index d9005d6572..e8a82f650e 100644
--- a/lib/cretonne/meta/cretonne/__init__.py
+++ b/lib/cretonne/meta/cretonne/__init__.py
@@ -9,14 +9,23 @@ import re
 import math
 import importlib
 from collections import OrderedDict
-from .predicates import And
-from .ast import Apply
+from .predicates import And, Predicate, FieldPredicate  # noqa
+
+# The typing module is only required by mypy, and we don't use these imports
+# outside type comments.
+try:
+    from typing import Tuple, Union, Any, Iterable, Sequence  # noqa
+    MaybeBoundInst = Union['Instruction', 'BoundInstruction']
+    AnyPredicate = Union['Predicate', 'FieldPredicate']
+except ImportError:
+    pass
 
 
 camel_re = re.compile('(^|_)([a-z])')
 
 
 def camel_case(s):
+    # type: (str) -> str
     """Convert the string s to CamelCase"""
     return camel_re.sub(lambda m: m.group(2).upper(), s)
 
@@ -133,7 +142,7 @@ class SettingGroup(object):
     """
 
     # The currently open setting group.
-    _current = None
+    _current = None  # type: SettingGroup
 
     def __init__(self, name, parent=None):
         self.name = name
@@ -175,7 +184,6 @@ class SettingGroup(object):
                 .format(self, SettingGroup._current))
         SettingGroup._current = None
         if globs:
-            from .predicates import Predicate
             for name, obj in globs.iteritems():
                 if isinstance(obj, Setting):
                     assert obj.name is None, obj.name
@@ -381,10 +389,10 @@ class ValueType(object):
     """
 
     # Map name -> ValueType.
-    _registry = dict()
+    _registry = dict()  # type: Dict[str, ValueType]
 
     # List of all the scalar types.
-    all_scalars = list()
+    all_scalars = list()  # type: List[ValueType]
 
     def __init__(self, name, membytes, doc):
         self.name = name
@@ -534,7 +542,7 @@ class InstructionGroup(object):
     """
 
     # The currently open instruction group.
-    _current = None
+    _current = None  # type: InstructionGroup
 
     def open(self):
         """
@@ -644,15 +652,17 @@ class InstructionFormat(object):
     """
 
     # Map (multiple_results, kind, kind, ...) -> InstructionFormat
-    _registry = dict()
+    _registry = dict()  # type: Dict[Tuple, InstructionFormat]
 
     # All existing formats.
-    all_formats = list()
+    all_formats = list()  # type: List[InstructionFormat]
 
     def __init__(self, *kinds, **kwargs):
-        self.name = kwargs.get('name', None)
+        # type: (*Union[OperandKind, Tuple[str, OperandKind]], **Any) -> None # noqa
+        self.name = kwargs.get('name', None)  # type: str
         self.multiple_results = kwargs.get('multiple_results', False)
         self.boxed_storage = kwargs.get('boxed_storage', False)
+        self.members = list()  # type: List[str]
         self.kinds = tuple(self._process_member_names(kinds))
 
         # Which of self.kinds are `value`?
@@ -660,7 +670,7 @@ class InstructionFormat(object):
                 i for i, k in enumerate(self.kinds) if k is value)
 
         # The typevar_operand argument must point to a 'value' operand.
-        self.typevar_operand = kwargs.get('typevar_operand', None)
+        self.typevar_operand = kwargs.get('typevar_operand', None)  # type: int
         if self.typevar_operand is not None:
             assert self.kinds[self.typevar_operand] is value, \
                     "typevar_operand must indicate a 'value' operand"
@@ -678,6 +688,7 @@ class InstructionFormat(object):
         InstructionFormat.all_formats.append(self)
 
     def _process_member_names(self, kinds):
+        # type: (Sequence[Union[OperandKind, Tuple[str, OperandKind]]]) -> Iterable[OperandKind] # noqa
         """
         Extract names of all the immediate operands in the kinds tuple.
 
@@ -687,14 +698,14 @@ class InstructionFormat(object):
 
         Yields the operand kinds.
         """
-        self.members = list()
-        for i, k in enumerate(kinds):
-            if isinstance(k, tuple):
-                member, k = k
+        for arg in kinds:
+            if isinstance(arg, OperandKind):
+                member = arg.default_member
+                k = arg
             else:
-                member = k.default_member
-            yield k
+                member, k = arg
             self.members.append(member)
+            yield k
 
             # Create `FormatField` instances for the immediates.
             if isinstance(k, ImmediateKind):
@@ -704,6 +715,7 @@ class InstructionFormat(object):
 
     @staticmethod
     def lookup(ins, outs):
+        # type: (Sequence[Operand], Sequence[Operand]) -> InstructionFormat
         """
         Find an existing instruction format that matches the given lists of
         instruction inputs and outputs.
@@ -750,6 +762,7 @@ class FormatField(object):
     """
 
     def __init__(self, format, operand, name):
+        # type: (InstructionFormat, int, str) -> None
         self.format = format
         self.operand = operand
         self.name = name
@@ -758,6 +771,7 @@ class FormatField(object):
         return '{}.{}'.format(self.format.name, self.name)
 
     def rust_name(self):
+        # type: () -> str
         if self.format.boxed_storage:
             return 'data.' + self.name
         else:
@@ -782,6 +796,7 @@ class Instruction(object):
     """
 
     def __init__(self, name, doc, ins=(), outs=(), **kwargs):
+        # type: (str, str, Union[Sequence[Operand], Operand], Union[Sequence[Operand], Operand], **Any) -> None # noqa
         self.name = name
         self.camel_name = camel_case(name)
         self.__doc__ = doc
@@ -898,6 +913,7 @@ class Instruction(object):
 
     @staticmethod
     def _to_operand_tuple(x):
+        # type: (Union[Sequence[Operand], Operand]) -> Tuple[Operand, ...]
         # Allow a single Operand instance instead of the awkward singleton
         # tuple syntax.
         if isinstance(x, Operand):
@@ -909,6 +925,7 @@ class Instruction(object):
         return x
 
     def bind(self, *args):
+        # type: (*ValueType) -> BoundInstruction
         """
         Bind a polymorphic instruction to a concrete list of type variable
         values.
@@ -917,6 +934,7 @@ class Instruction(object):
         return BoundInstruction(self, args)
 
     def __getattr__(self, name):
+        # type: (str) -> BoundInstruction
         """
         Bind a polymorphic instruction to a single type variable with dot
         syntax:
@@ -926,6 +944,7 @@ class Instruction(object):
         return self.bind(ValueType.by_name(name))
 
     def fully_bound(self):
+        # type: () -> Tuple[Instruction, Tuple[ValueType, ...]]
         """
         Verify that all typevars have been bound, and return a
         `(inst, typevars)` pair.
@@ -941,6 +960,7 @@ class Instruction(object):
         Create an `ast.Apply` AST node representing the application of this
         instruction to the arguments.
         """
+        from .ast import Apply
         return Apply(self, args)
 
 
@@ -950,6 +970,7 @@ class BoundInstruction(object):
     """
 
     def __init__(self, inst, typevars):
+        # type: (Instruction, Tuple[ValueType, ...]) -> None
         self.inst = inst
         self.typevars = typevars
         assert len(typevars) <= 1 + len(inst.other_typevars)
@@ -958,12 +979,14 @@ class BoundInstruction(object):
         return '.'.join([self.inst.name, ] + list(map(str, self.typevars)))
 
     def bind(self, *args):
+        # type: (*ValueType) -> BoundInstruction
         """
         Bind additional typevars.
         """
         return BoundInstruction(self.inst, self.typevars + args)
 
     def __getattr__(self, name):
+        # type: (str) -> BoundInstruction
         """
         Bind an additional typevar dot syntax:
 
@@ -972,6 +995,7 @@ class BoundInstruction(object):
         return self.bind(ValueType.by_name(name))
 
     def fully_bound(self):
+        # type: () -> Tuple[Instruction, Tuple[ValueType, ...]]
         """
         Verify that all typevars have been bound, and return a
         `(inst, typevars)` pair.
@@ -989,6 +1013,7 @@ class BoundInstruction(object):
         Create an `ast.Apply` AST node representing the application of this
         instruction to the arguments.
         """
+        from .ast import Apply
         return Apply(self, args)
 
 
@@ -1139,6 +1164,7 @@ class Encoding(object):
     """
 
     def __init__(self, cpumode, inst, recipe, encbits, instp=None, isap=None):
+        # type: (CPUMode, MaybeBoundInst, EncRecipe, int, AnyPredicate, AnyPredicate) -> None # noqa
         assert isinstance(cpumode, CPUMode)
         assert isinstance(recipe, EncRecipe)
         self.inst, self.typevars = inst.fully_bound()
diff --git a/lib/cretonne/meta/cretonne/ast.py b/lib/cretonne/meta/cretonne/ast.py
index 8c9c8576cb..693a0b5a2b 100644
--- a/lib/cretonne/meta/cretonne/ast.py
+++ b/lib/cretonne/meta/cretonne/ast.py
@@ -5,6 +5,12 @@ This module defines classes that can be used to create abstract syntax trees
 for patern matching an rewriting of cretonne instructions.
 """
 from __future__ import absolute_import
+from . import Instruction, BoundInstruction
+
+try:
+    from typing import Union, Tuple  # noqa
+except ImportError:
+    pass
 
 
 class Def(object):
@@ -29,10 +35,12 @@ class Def(object):
     """
 
     def __init__(self, defs, expr):
+        # type: (Union[Var, Tuple[Var, ...]], Apply) -> None
         if not isinstance(defs, tuple):
-            defs = (defs,)
-        assert isinstance(expr, Expr)
-        self.defs = defs
+            self.defs = (defs,)  # type: Tuple[Var, ...]
+        else:
+            self.defs = defs
+        assert isinstance(expr, Apply)
         self.expr = expr
 
     def __repr__(self):
@@ -42,7 +50,18 @@ class Def(object):
         if len(self.defs) == 1:
             return "{!s} << {!s}".format(self.defs[0], self.expr)
         else:
-            return "({}) << {!s}".format(", ".join(self.defs), self.expr)
+            return "({}) << {!s}".format(
+                    ', '.join(map(str, self.defs)), self.expr)
+
+    def root_inst(self):
+        # type: () -> Instruction
+        """Get the instruction at the root of this tree."""
+        return self.expr.root_inst()
+
+    def defs_expr(self):
+        # type: () -> Tuple[Tuple[Var, ...], Apply]
+        """Split into a defs tuple and an Apply expr."""
+        return (self.defs, self.expr)
 
 
 class Expr(object):
@@ -50,12 +69,6 @@ class Expr(object):
     An AST expression.
     """
 
-    def __rlshift__(self, other):
-        """
-        Define variables using `var << expr` or `(v1, v2) << expr`.
-        """
-        return Def(other, self)
-
 
 class Var(Expr):
     """
@@ -63,6 +76,7 @@ class Var(Expr):
     """
 
     def __init__(self, name):
+        # type: (str) -> None
         self.name = name
         # Bitmask of contexts where this variable is defined.
         # See XForm._rewrite_defs().
@@ -98,16 +112,24 @@ class Apply(Expr):
     """
 
     def __init__(self, inst, args):
-        from . import BoundInstruction
+        # type: (Union[Instruction, BoundInstruction], Tuple[Expr, ...]) -> None  # noqa
         if isinstance(inst, BoundInstruction):
             self.inst = inst.inst
             self.typevars = inst.typevars
         else:
+            assert isinstance(inst, Instruction)
             self.inst = inst
             self.typevars = ()
         self.args = args
         assert len(self.inst.ins) == len(args)
 
+    def __rlshift__(self, other):
+        # type: (Union[Var, Tuple[Var, ...]]) -> Def
+        """
+        Define variables using `var << expr` or `(v1, v2) << expr`.
+        """
+        return Def(other, self)
+
     def instname(self):
         i = self.inst.name
         for t in self.typevars:
@@ -120,3 +142,13 @@ class Apply(Expr):
     def __str__(self):
         args = ', '.join(map(str, self.args))
         return '{}({})'.format(self.instname(), args)
+
+    def root_inst(self):
+        # type: () -> Instruction
+        """Get the instruction at the root of this tree."""
+        return self.inst
+
+    def defs_expr(self):
+        # type: () -> Tuple[Tuple[Var, ...], Apply]
+        """Split into a defs tuple and an Apply expr."""
+        return ((), self)
diff --git a/lib/cretonne/meta/cretonne/legalize.py b/lib/cretonne/meta/cretonne/legalize.py
index 9d7b218755..21073d0aec 100644
--- a/lib/cretonne/meta/cretonne/legalize.py
+++ b/lib/cretonne/meta/cretonne/legalize.py
@@ -15,7 +15,7 @@ from .ast import Var
 from .xform import Rtl, XFormGroup
 
 
-narrow = XFormGroup("""
+narrow = XFormGroup('narrow', """
         Legalize instructions by narrowing.
 
         The transformations in the 'narrow' group work by expressing
@@ -24,7 +24,7 @@ narrow = XFormGroup("""
         operations are expressed in terms of smaller integer types.
         """)
 
-expand = XFormGroup("""
+expand = XFormGroup('expand', """
         Legalize instructions by expansion.
 
         Rewrite instructions in terms of other instructions, generally
@@ -114,5 +114,5 @@ expand.legalize(
         Rtl(
             (a1, b1) << isub_bout(x, y),
             (a, b2) << isub_bout(a1, b_in),
-            c << bor(c1, c2)
+            c << bor(b1, b2)
         ))
diff --git a/lib/cretonne/meta/cretonne/xform.py b/lib/cretonne/meta/cretonne/xform.py
index 8015ee04b0..1100e4721f 100644
--- a/lib/cretonne/meta/cretonne/xform.py
+++ b/lib/cretonne/meta/cretonne/xform.py
@@ -2,7 +2,13 @@
 Instruction transformations.
 """
 from __future__ import absolute_import
-from .ast import Def, Var, Apply
+from .ast import Def, Var, Apply, Expr  # noqa
+
+try:
+    from typing import Union, Iterator, Sequence, Iterable  # noqa
+    DefApply = Union[Def, Apply]
+except ImportError:
+    pass
 
 
 SRCCTX = 1
@@ -21,9 +27,11 @@ class Rtl(object):
     """
 
     def __init__(self, *args):
+        # type: (*DefApply) -> None
         self.rtl = args
 
     def __iter__(self):
+        # type: () -> Iterator[DefApply]
         return iter(self.rtl)
 
 
@@ -55,16 +63,17 @@ class XForm(object):
     """
 
     def __init__(self, src, dst):
+        # type: (Rtl, Rtl) -> None
         self.src = src
         self.dst = dst
         # Variables that are inputs to the source pattern.
-        self.inputs = list()
+        self.inputs = list()  # type: List[Var]
         # Variables defined in either src or dst.
-        self.defs = list()
+        self.defs = list()  # type: List[Var]
 
         # Rewrite variables in src and dst RTL lists to our own copies.
         # Map name -> private Var.
-        symtab = dict()
+        symtab = dict()  # type: Dict[str, Var]
         self._rewrite_rtl(src, symtab, SRCCTX)
         num_src_inputs = len(self.inputs)
         self._rewrite_rtl(dst, symtab, DSTCTX)
@@ -90,7 +99,8 @@ class XForm(object):
         return s
 
     def _rewrite_rtl(self, rtl, symtab, context):
-        for line in rtl:
+        # type: (Rtl, Dict[str, Var], int) -> None
+        for line in rtl.rtl:
             if isinstance(line, Def):
                 line.defs = tuple(
                         self._rewrite_defs(line.defs, symtab, context))
@@ -100,6 +110,7 @@ class XForm(object):
             self._rewrite_expr(expr, symtab, context)
 
     def _rewrite_expr(self, expr, symtab, context):
+        # type: (Apply, Dict[str, Var], int) -> None
         """
         Find all uses of variables in `expr` and replace them with our own
         local symbols.
@@ -113,6 +124,7 @@ class XForm(object):
                     self._rewrite_uses(expr, stack, symtab, context))
 
     def _rewrite_defs(self, defs, symtab, context):
+        # type: (Sequence[Var], Dict[str, Var], int) -> Iterable[Var]
         """
         Given a tuple of symbols defined in a Def, rewrite them to local
         symbols. Yield the new locals.
@@ -131,6 +143,7 @@ class XForm(object):
             yield var
 
     def _rewrite_uses(self, expr, stack, symtab, context):
+        # type: (Apply, List[Apply], Dict[str, Var], int) -> Iterable[Expr]
         """
         Given an `Apply` expr, rewrite all uses in its arguments to local
         variables. Yield a sequence of new arguments.
@@ -140,7 +153,7 @@ class XForm(object):
         for arg, operand in zip(expr.args, expr.inst.ins):
             # Nested instructions are allowed. Visit recursively.
             if isinstance(arg, Apply):
-                stack.push(arg)
+                stack.append(arg)
                 yield arg
                 continue
             if not isinstance(arg, Var):
@@ -169,11 +182,14 @@ class XFormGroup(object):
     A group of related transformations.
     """
 
-    def __init__(self, doc):
-        self.xforms = list()
+    def __init__(self, name, doc):
+        # type: (str, str) -> None
+        self.xforms = list()  # type: List[XForm]
+        self.name = name
         self.__doc__ = doc
 
     def legalize(self, src, dst):
+        # type: (Union[Def, Apply], Rtl) -> None
         """
         Add a legalization pattern to this group.
 
diff --git a/lib/cretonne/meta/isa/__init__.py b/lib/cretonne/meta/isa/__init__.py
index addc70b8a9..9412f6502c 100644
--- a/lib/cretonne/meta/isa/__init__.py
+++ b/lib/cretonne/meta/isa/__init__.py
@@ -7,9 +7,11 @@ architecture supported by Cretonne.
 """
 from __future__ import absolute_import
 from . import riscv
+from cretonne import TargetISA  # noqa
 
 
 def all_isas():
+    # type: () -> List[TargetISA]
     """
     Get a list of all the supported target ISAs. Each target ISA is represented
     as a :py:class:`cretonne.TargetISA` instance.
diff --git a/lib/cretonne/meta/isa/riscv/recipes.py b/lib/cretonne/meta/isa/riscv/recipes.py
index db6d7021c8..375b0e2150 100644
--- a/lib/cretonne/meta/isa/riscv/recipes.py
+++ b/lib/cretonne/meta/isa/riscv/recipes.py
@@ -22,37 +22,44 @@ from cretonne.predicates import IsSignedInt
 
 
 def LOAD(funct3):
+    # type: (int) -> int
     assert funct3 <= 0b111
     return 0b00000 | (funct3 << 5)
 
 
 def STORE(funct3):
+    # type: (int) -> int
     assert funct3 <= 0b111
     return 0b01000 | (funct3 << 5)
 
 
 def BRANCH(funct3):
+    # type: (int) -> int
     assert funct3 <= 0b111
     return 0b11000 | (funct3 << 5)
 
 
 def OPIMM(funct3, funct7=0):
+    # type: (int, int) -> int
     assert funct3 <= 0b111
     return 0b00100 | (funct3 << 5) | (funct7 << 8)
 
 
 def OPIMM32(funct3, funct7=0):
+    # type: (int, int) -> int
     assert funct3 <= 0b111
     return 0b00110 | (funct3 << 5) | (funct7 << 8)
 
 
 def OP(funct3, funct7):
+    # type: (int, int) -> int
     assert funct3 <= 0b111
     assert funct7 <= 0b1111111
     return 0b01100 | (funct3 << 5) | (funct7 << 8)
 
 
 def OP32(funct3, funct7):
+    # type: (int, int) -> int
     assert funct3 <= 0b111
     assert funct7 <= 0b1111111
     return 0b01110 | (funct3 << 5) | (funct7 << 8)
diff --git a/lib/cretonne/meta/srcgen.py b/lib/cretonne/meta/srcgen.py
index 962a881436..75b102f534 100644
--- a/lib/cretonne/meta/srcgen.py
+++ b/lib/cretonne/meta/srcgen.py
@@ -10,6 +10,11 @@ import sys
 import os
 import re
 
+try:
+    from typing import Any  # noqa
+except ImportError:
+    pass
+
 
 class Formatter(object):
     """
@@ -38,19 +43,23 @@ class Formatter(object):
     shiftwidth = 4
 
     def __init__(self):
+        # type: () -> None
         self.indent = ''
-        self.lines = []
+        self.lines = []  # type: List[str]
 
     def indent_push(self):
+        # type: () -> None
         """Increase current indentation level by one."""
         self.indent += ' ' * self.shiftwidth
 
     def indent_pop(self):
+        # type: () -> None
         """Decrease indentation by one level."""
         assert self.indent != '', 'Already at top level indentation'
         self.indent = self.indent[0:-self.shiftwidth]
 
     def line(self, s=None):
+        # type: (str) -> None
         """Add an indented line."""
         if s:
             self.lines.append('{}{}\n'.format(self.indent, s))
@@ -58,6 +67,7 @@ class Formatter(object):
             self.lines.append('\n')
 
     def outdented_line(self, s):
+        # type: (str) -> None
         """
         Emit a line outdented one level.
 
@@ -67,12 +77,14 @@ class Formatter(object):
         self.lines.append('{}{}\n'.format(self.indent[0:-self.shiftwidth], s))
 
     def writelines(self, f=None):
+        # type: (Any) -> None
         """Write all lines to `f`."""
         if not f:
             f = sys.stdout
         f.writelines(self.lines)
 
     def update_file(self, filename, directory):
+        # type: (str, str) -> None
         if directory is not None:
             filename = os.path.join(directory, filename)
         with open(filename, 'w') as f:
@@ -80,10 +92,12 @@ class Formatter(object):
 
     class _IndentedScope(object):
         def __init__(self, fmt, after):
+            # type: (Formatter, str) -> None
             self.fmt = fmt
             self.after = after
 
         def __enter__(self):
+            # type: () -> None
             self.fmt.indent_push()
 
         def __exit__(self, t, v, tb):
@@ -92,6 +106,7 @@ class Formatter(object):
                 self.fmt.line(self.after)
 
     def indented(self, before=None, after=None):
+        # type: (str, str) -> Formatter._IndentedScope
         """
         Return a scope object for use with a `with` statement:
 
@@ -108,7 +123,7 @@ class Formatter(object):
         """
         if before:
             self.line(before)
-        return self._IndentedScope(self, after)
+        return Formatter._IndentedScope(self, after)
 
     def format(self, fmt, *args):
         self.line(fmt.format(*args))