diff --git a/meta/cretonne/__init__.py b/meta/cretonne/__init__.py
index d318b27ef3..a5fe761bce 100644
--- a/meta/cretonne/__init__.py
+++ b/meta/cretonne/__init__.py
@@ -10,6 +10,7 @@ import math
 import importlib
 from collections import OrderedDict
 from .predicates import And
+from .ast import Apply
 
 
 camel_re = re.compile('(^|_)([a-z])')
@@ -603,6 +604,12 @@ class Operand(object):
     def __str__(self):
         return "`{}`".format(self.name)
 
+    def is_value(self):
+        """
+        Is this an SSA value operand?
+        """
+        return self.kind is value
+
 
 class InstructionFormat(object):
     """
@@ -779,10 +786,13 @@ class Instruction(object):
         self.format = InstructionFormat.lookup(self.ins, self.outs)
         # Indexes into outs for value results. Others are `variable_args`.
         self.value_results = tuple(
-                i for i, o in enumerate(self.outs) if o.kind is value)
+                i for i, o in enumerate(self.outs) if o.is_value())
         self._verify_polymorphic()
         InstructionGroup.append(self)
 
+    def __str__(self):
+        return self.name
+
     def _verify_polymorphic(self):
         """
         Check if this instruction is polymorphic, and verify its use of type
@@ -910,6 +920,13 @@ class Instruction(object):
         assert not self.is_polymorphic, self
         return (self, ())
 
+    def __call__(self, *args):
+        """
+        Create an `ast.Apply` AST node representing the application of this
+        instruction to the arguments.
+        """
+        return Apply(self, args)
+
 
 class BoundInstruction(object):
     """
@@ -951,6 +968,13 @@ class BoundInstruction(object):
         assert len(self.typevars) == 1 + len(self.inst.other_typevars)
         return (self.inst, self.typevars)
 
+    def __call__(self, *args):
+        """
+        Create an `ast.Apply` AST node representing the application of this
+        instruction to the arguments.
+        """
+        return Apply(self, args)
+
 
 # Defining target ISAs.
 
diff --git a/meta/cretonne/ast.py b/meta/cretonne/ast.py
new file mode 100644
index 0000000000..8c9c8576cb
--- /dev/null
+++ b/meta/cretonne/ast.py
@@ -0,0 +1,122 @@
+"""
+Abstract syntax trees.
+
+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
+
+
+class Def(object):
+    """
+    An AST definition associates a set of variables with the values produced by
+    an expression.
+
+    Example:
+
+    >>> from .base import iadd_cout, iconst
+    >>> x = Var('x')
+    >>> y = Var('y')
+    >>> x << iconst(4)
+    (Var(x),) << Apply(iconst, (4,))
+    >>> (x, y) << iadd_cout(4, 5)
+    (Var(x), Var(y)) << Apply(iadd_cout, (4, 5))
+
+    The `<<` operator is used to create variable definitions.
+
+    :param defs: Single variable or tuple of variables to be defined.
+    :param expr: Expression generating the values.
+    """
+
+    def __init__(self, defs, expr):
+        if not isinstance(defs, tuple):
+            defs = (defs,)
+        assert isinstance(expr, Expr)
+        self.defs = defs
+        self.expr = expr
+
+    def __repr__(self):
+        return "{} << {!r}".format(self.defs, self.expr)
+
+    def __str__(self):
+        if len(self.defs) == 1:
+            return "{!s} << {!s}".format(self.defs[0], self.expr)
+        else:
+            return "({}) << {!s}".format(", ".join(self.defs), self.expr)
+
+
+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):
+    """
+    A free variable.
+    """
+
+    def __init__(self, name):
+        self.name = name
+        # Bitmask of contexts where this variable is defined.
+        # See XForm._rewrite_defs().
+        self.defctx = 0
+
+    def __str__(self):
+        return self.name
+
+    def __repr__(self):
+        s = self.name
+        if self.defctx:
+            s += ", d={:02b}".format(self.defctx)
+        return "Var({})".format(s)
+
+
+class Apply(Expr):
+    """
+    Apply an instruction to arguments.
+
+    An `Apply` AST expression is created by using function call syntax on
+    instructions. This applies to both bound and unbound polymorphic
+    instructions:
+
+    >>> from .base import jump, iadd
+    >>> jump('next', ())
+    Apply(jump, ('next', ()))
+    >>> iadd.i32('x', 'y')
+    Apply(iadd.i32, ('x', 'y'))
+
+    :param inst: The instruction being applied, an `Instruction` or
+                 `BoundInstruction` instance.
+    :param args: Tuple of arguments.
+    """
+
+    def __init__(self, inst, args):
+        from . import BoundInstruction
+        if isinstance(inst, BoundInstruction):
+            self.inst = inst.inst
+            self.typevars = inst.typevars
+        else:
+            self.inst = inst
+            self.typevars = ()
+        self.args = args
+        assert len(self.inst.ins) == len(args)
+
+    def instname(self):
+        i = self.inst.name
+        for t in self.typevars:
+            i += '.{}'.format(t)
+        return i
+
+    def __repr__(self):
+        return "Apply({}, {})".format(self.instname(), self.args)
+
+    def __str__(self):
+        args = ', '.join(map(str, self.args))
+        return '{}({})'.format(self.instname(), args)
diff --git a/meta/cretonne/test_ast.py b/meta/cretonne/test_ast.py
new file mode 100644
index 0000000000..71791db3f6
--- /dev/null
+++ b/meta/cretonne/test_ast.py
@@ -0,0 +1,28 @@
+from __future__ import absolute_import
+from unittest import TestCase
+from doctest import DocTestSuite
+from . import ast
+from .base import jump, iadd
+
+
+def load_tests(loader, tests, ignore):
+    tests.addTests(DocTestSuite(ast))
+    return tests
+
+
+x = 'x'
+y = 'y'
+a = 'a'
+
+
+class TestPatterns(TestCase):
+    def test_apply(self):
+        i = jump(x, y)
+        self.assertEqual(repr(i), "Apply(jump, ('x', 'y'))")
+
+        i = iadd.i32(x, y)
+        self.assertEqual(repr(i), "Apply(iadd.i32, ('x', 'y'))")
+
+    def test_single_ins(self):
+        pat = a << iadd.i32(x, y)
+        self.assertEqual(repr(pat), "('a',) << Apply(iadd.i32, ('x', 'y'))")
diff --git a/meta/cretonne/test_xform.py b/meta/cretonne/test_xform.py
new file mode 100644
index 0000000000..b472a8f458
--- /dev/null
+++ b/meta/cretonne/test_xform.py
@@ -0,0 +1,59 @@
+from __future__ import absolute_import
+from unittest import TestCase
+from doctest import DocTestSuite
+from . import xform
+from .base import iadd, iadd_imm, iconst
+from .ast import Var
+from .xform import Rtl, XForm
+
+
+def load_tests(loader, tests, ignore):
+    tests.addTests(DocTestSuite(xform))
+    return tests
+
+
+x = Var('x')
+y = Var('y')
+a = Var('a')
+c = Var('c')
+
+
+class TestXForm(TestCase):
+    def test_macro_pattern(self):
+        src = Rtl(a << iadd_imm(x, y))
+        dst = Rtl(
+                c << iconst(y),
+                a << iadd(x, c))
+        XForm(src, dst)
+
+    def test_def_input(self):
+        # Src pattern has a def which is an input in dst.
+        src = Rtl(a << iadd_imm(x, 1))
+        dst = Rtl(y << iadd_imm(a, 1))
+        with self.assertRaisesRegexp(
+                AssertionError,
+                "'a' used as both input and def"):
+            XForm(src, dst)
+
+    def test_input_def(self):
+        # Converse of the above.
+        src = Rtl(y << iadd_imm(a, 1))
+        dst = Rtl(a << iadd_imm(x, 1))
+        with self.assertRaisesRegexp(
+                AssertionError,
+                "'a' used as both input and def"):
+            XForm(src, dst)
+
+    def test_extra_input(self):
+        src = Rtl(a << iadd_imm(x, 1))
+        dst = Rtl(a << iadd(x, y))
+        with self.assertRaisesRegexp(AssertionError, "extra inputs in dst"):
+            XForm(src, dst)
+
+    def test_double_def(self):
+        src = Rtl(
+                a << iadd_imm(x, 1),
+                a << iadd(x, y))
+        dst = Rtl(a << iadd(x, y))
+        with self.assertRaisesRegexp(AssertionError, "'a' multiply defined"):
+            XForm(src, dst)
diff --git a/meta/cretonne/xform.py b/meta/cretonne/xform.py
new file mode 100644
index 0000000000..16a9eae870
--- /dev/null
+++ b/meta/cretonne/xform.py
@@ -0,0 +1,182 @@
+"""
+Instruction transformations.
+"""
+from __future__ import absolute_import
+from .ast import Def, Var, Apply
+
+
+SRCCTX = 1
+DSTCTX = 2
+
+
+class Rtl(object):
+    """
+    Register Transfer Language list.
+
+    An RTL object contains a list of register assignments in the form of `Def`
+    objects and/or Apply objects for side-effecting instructions.
+
+    An RTL list can represent both a source pattern to be matched, or a
+    destination pattern to be inserted.
+    """
+
+    def __init__(self, *args):
+        self.rtl = args
+
+    def __iter__(self):
+        return iter(self.rtl)
+
+
+class XForm(object):
+    """
+    An instruction transformation consists of a source and destination pattern.
+
+    Patterns are expressed in *register transfer language* as tuples of
+    `ast.Def` or `ast.Expr` nodes.
+
+    A legalization pattern must have a source pattern containing only a single
+    instruction.
+
+    >>> from .base import iconst, iadd, iadd_imm
+    >>> a = Var('a')
+    >>> c = Var('c')
+    >>> v = Var('v')
+    >>> x = Var('x')
+    >>> XForm(
+    ...     Rtl(c << iconst(v),
+    ...         a << iadd(x, c)),
+    ...     Rtl(a << iadd_imm(x, v)))
+    XForm(inputs=[Var(v), Var(x)], defs=[Var(c, d=01), Var(a, d=11)],
+      c << iconst(v)
+      a << iadd(x, c)
+    =>
+      a << iadd_imm(x, v)
+    )
+    """
+
+    def __init__(self, src, dst):
+        self.src = src
+        self.dst = dst
+        # Variables that are inputs to the source pattern.
+        self.inputs = list()
+        # Variables defined in either src or dst.
+        self.defs = list()
+
+        # Rewrite variables in src and dst RTL lists to our own copies.
+        # Map name -> private Var.
+        symtab = dict()
+        self._rewrite_rtl(src, symtab, SRCCTX)
+        num_src_inputs = len(self.inputs)
+        self._rewrite_rtl(dst, symtab, DSTCTX)
+
+        # Check for inconsistently used inputs.
+        for i in self.inputs:
+            if i.defctx:
+                raise AssertionError(
+                        "'{}' used as both input and def".format(i))
+
+        # Check for spurious inputs in dst.
+        if len(self.inputs) > num_src_inputs:
+            raise AssertionError(
+                    "extra inputs in dst RTL: {}".format(
+                        self.inputs[num_src_inputs:]))
+
+    def __repr__(self):
+        s = "XForm(inputs={}, defs={},\n  ".format(self.inputs, self.defs)
+        s += '\n  '.join(str(n) for n in self.src)
+        s += '\n=>\n  '
+        s += '\n  '.join(str(n) for n in self.dst)
+        s += '\n)'
+        return s
+
+    def _rewrite_rtl(self, rtl, symtab, context):
+        for line in rtl:
+            if isinstance(line, Def):
+                line.defs = tuple(
+                        self._rewrite_defs(line.defs, symtab, context))
+                expr = line.expr
+            else:
+                expr = line
+            self._rewrite_expr(expr, symtab, context)
+
+    def _rewrite_expr(self, expr, symtab, context):
+        """
+        Find all uses of variables in `expr` and replace them with our own
+        local symbols.
+        """
+
+        # Accept a whole expression tree.
+        stack = [expr]
+        while len(stack) > 0:
+            expr = stack.pop()
+            expr.args = tuple(
+                    self._rewrite_uses(expr, stack, symtab, context))
+
+    def _rewrite_defs(self, defs, symtab, context):
+        """
+        Given a tuple of symbols defined in a Def, rewrite them to local
+        symbols. Yield the new locals.
+        """
+        for sym in defs:
+            name = str(sym)
+            if name in symtab:
+                var = symtab[name]
+                if var.defctx & context:
+                    raise AssertionError("'{}' multiply defined".format(name))
+            else:
+                var = Var(name)
+                symtab[name] = var
+                self.defs.append(var)
+            var.defctx |= context
+            yield var
+
+    def _rewrite_uses(self, expr, stack, symtab, context):
+        """
+        Given an `Apply` expr, rewrite all uses in its arguments to local
+        variables. Yield a sequence of new arguments.
+
+        Append any `Apply` arguments to `stack`.
+        """
+        for arg, operand in zip(expr.args, expr.inst.ins):
+            # Nested instructions are allowed. Visit recursively.
+            if isinstance(arg, Apply):
+                stack.push(arg)
+                yield arg
+                continue
+            if not isinstance(arg, Var):
+                assert not operand.is_value(), "Value arg must be `Var`"
+                yield arg
+                continue
+            # This is supposed to be a symbolic value reference.
+            name = str(arg)
+            if name in symtab:
+                var = symtab[name]
+                # The variable must be used consistenty as a def or input.
+                if var.defctx and (var.defctx & context) == 0:
+                    raise AssertionError(
+                            "'{}' used as both input and def"
+                            .format(name))
+            else:
+                # First time use of variable.
+                var = Var(name)
+                symtab[name] = var
+                self.inputs.append(var)
+            yield var
+
+
+class XFormGroup(object):
+    """
+    A group of related transformations.
+    """
+
+    def __init__(self):
+        self.xforms = list()
+
+    def legalize(self, src, dst):
+        """
+        Add a legalization pattern to this group.
+
+        :param src: Single `Def` or `Apply` to be legalized.
+        :param dst: `Rtl` list of replacement instructions.
+        """
+        self.xforms.append(XForm(Rtl(src), dst))