Cleanup for PR #123 (#129)

* Fix bextend semantics; Change smtlib.py to use z3 python bindings for query building instead of raw strings

* Forgot the mypy stubs for z3

lib/cretonne/meta/base/semantics.py

@@ -1,6 +1,6 @@
 from __future__ import absolute_import
 from semantics.primitives import prim_to_bv, prim_from_bv, bvsplit, bvconcat,\
-    bvadd, bvult, bvzeroext
+    bvadd, bvult, bvzeroext, bvsignext
 from .instructions import vsplit, vconcat, iadd, iadd_cout, icmp, bextend, \
     isplit, iconcat, iadd_cin, iadd_carry
 from .immediates import intcc
@@ -116,7 +116,7 @@ bextend.set_semantics(
     a << bextend(x),
     (Rtl(
         bvx << prim_to_bv(x),
-        bvy << bvzeroext(bvx),
+        bvy << bvsignext(bvx),
         a << prim_from_bv(bvy)
     ), [InTypeset(x.get_typevar(), ScalarTS)]),
     Rtl(

lib/cretonne/meta/semantics/primitives.py

@@ -82,4 +82,8 @@ bvzeroext = Instruction(
         'bvzeroext', r"""Unsigned bitvector extension""",
         ins=x, outs=x1, constraints=WiderOrEq(ToBV, BV))
 
+bvsignext = Instruction(
+        'bvsignext', r"""Signed bitvector extension""",
+        ins=x, outs=x1, constraints=WiderOrEq(ToBV, BV))
+
 GROUP.close()

lib/cretonne/meta/semantics/smtlib.py

@@ -3,64 +3,74 @@ Tools to emit SMTLIB bitvector queries encoding concrete RTLs containing only
 primitive instructions.
 """
 from .primitives import GROUP as PRIMITIVES, prim_from_bv, prim_to_bv, bvadd,\
-    bvult, bvzeroext, bvsplit, bvconcat
+    bvult, bvzeroext, bvsplit, bvconcat, bvsignext
 from cdsl.ast import Var
 from cdsl.types import BVType
 from .elaborate import elaborate
+from z3 import BitVec, ZeroExt, SignExt, And, Extract, Concat, Not, Solver,\
+    unsat, BoolRef, BitVecVal, If
+from z3.z3core import Z3_mk_eq
 
 try:
-    from typing import TYPE_CHECKING, Tuple # noqa
+    from typing import TYPE_CHECKING, Tuple, Dict, List # noqa
     from cdsl.xform import Rtl, XForm # noqa
     from cdsl.ast import VarMap # noqa
     from cdsl.ti import VarTyping # noqa
+    if TYPE_CHECKING:
+        from z3 import ExprRef, BitVecRef # noqa
+        Z3VarMap = Dict[Var, BitVecRef]
 except ImportError:
     TYPE_CHECKING = False
 
 
-def bvtype_to_sort(typ):
+# Use this for constructing a == b instead of == since MyPy doesn't
-    # type: (BVType) -> str
+# accept overloading of __eq__ that doesn't return bool
-    """Return the BitVec sort corresponding to a BVType"""
+def mk_eq(e1, e2):
-    return "(_ BitVec {})".format(typ.bits)
+    # type: (ExprRef, ExprRef) -> ExprRef
+    """Return a z3 expression equivalent to e1 == e2"""
+    return BoolRef(Z3_mk_eq(e1.ctx_ref(), e1.as_ast(), e2.as_ast()), e1.ctx)
 
 
 def to_smt(r):
-    # type: (Rtl) -> Tuple[str, VarMap]
+    # type: (Rtl) -> Tuple[List[ExprRef], Z3VarMap]
     """
-    Encode a concrete primitive Rtl r sa SMTLIB 2.0 query.
+    Encode a concrete primitive Rtl r sa z3 query.
     Returns a tuple (query, var_m) where:
-        - query is the resulting query.
+        - query is a list of z3 expressions
-        - var_m is a map from Vars v with non-BVType to their Vars v' with
+        - var_m is a map from Vars v with non-BVType to their correspodning z3
-          BVType s.t. v' holds the flattend bitvector value of v.
+          bitvector variable.
     """
     assert r.is_concrete()
     # Should contain only primitives
     primitives = set(PRIMITIVES.instructions)
     assert set(d.expr.inst for d in r.rtl).issubset(primitives)
 
-    q = ""
+    q = []  # type: List[ExprRef]
-    m = {}  # type: VarMap
+    m = {}  # type: Z3VarMap
 
     # Build declarations for any bitvector Vars
+    var_to_bv = {}  # type: Z3VarMap
     for v in r.vars():
         typ = v.get_typevar().singleton_type()
         if not isinstance(typ, BVType):
             continue
 
-        q += "(declare-fun {} () {})\n".format(v.name, bvtype_to_sort(typ))
+        var_to_bv[v] = BitVec(v.name, typ.bits)
 
     # Encode each instruction as a equality assertion
     for d in r.rtl:
         inst = d.expr.inst
 
+        exp = None  # type: ExprRef
         # For prim_to_bv/prim_from_bv just update var_m. No assertion needed
         if inst == prim_to_bv:
             assert isinstance(d.expr.args[0], Var)
-            m[d.expr.args[0]] = d.defs[0]
+            m[d.expr.args[0]] = var_to_bv[d.defs[0]]
             continue
 
         if inst == prim_from_bv:
             assert isinstance(d.expr.args[0], Var)
-            m[d.defs[0]] = d.expr.args[0]
+            m[d.defs[0]] = var_to_bv[d.expr.args[0]]
             continue
 
         if inst in [bvadd, bvult]:  # Binary instructions
@@ -70,12 +80,15 @@ def to_smt(r):
             df = d.defs[0]
             assert isinstance(lhs, Var) and isinstance(rhs, Var)
 
-            if inst in [bvadd]:  # Normal binary - output type same as args
+            if inst == bvadd:  # Normal binary - output type same as args
-                exp = "(= {} ({} {} {}))".format(df, inst.name, lhs, rhs)
+                exp = (var_to_bv[lhs] + var_to_bv[rhs])
             else:
+                assert inst == bvult
+                exp = (var_to_bv[lhs] < var_to_bv[rhs])
                 # Comparison binary - need to convert bool to BitVec 1
-                exp = "(= {} (ite ({} {} {}) #b1 #b0))"\
+                exp = If(exp, BitVecVal(1, 1), BitVecVal(0, 1))
-                      .format(df, inst.name, lhs, rhs)
+
+            exp = mk_eq(var_to_bv[df], exp)
         elif inst == bvzeroext:
             arg = d.expr.args[0]
             df = d.defs[0]
@@ -83,8 +96,15 @@ def to_smt(r):
             fromW = arg.get_typevar().singleton_type().width()
             toW = df.get_typevar().singleton_type().width()
 
-            exp = "(= {} ((_ zero_extend {}) {}))"\
+            exp = mk_eq(var_to_bv[df], ZeroExt(toW-fromW, var_to_bv[arg]))
-                  .format(df, toW-fromW, arg)
+        elif inst == bvsignext:
+            arg = d.expr.args[0]
+            df = d.defs[0]
+            assert isinstance(arg, Var)
+            fromW = arg.get_typevar().singleton_type().width()
+            toW = df.get_typevar().singleton_type().width()
+
+            exp = mk_eq(var_to_bv[df], SignExt(toW-fromW, var_to_bv[arg]))
         elif inst == bvsplit:
             arg = d.expr.args[0]
             assert isinstance(arg, Var)
@@ -95,12 +115,10 @@ def to_smt(r):
             lo = d.defs[0]
             hi = d.defs[1]
 
-            exp = "(and "
+            exp = And(mk_eq(var_to_bv[lo],
-            exp += "(= {} ((_ extract {} {}) {})) "\
+                      Extract(width//2-1, 0, var_to_bv[arg])),
-                   .format(lo, width//2-1, 0, arg)
+                      mk_eq(var_to_bv[hi],
-            exp += "(= {} ((_ extract {} {}) {}))"\
+                      Extract(width-1, width//2, var_to_bv[arg])))
-                   .format(hi, width-1, width//2, arg)
-            exp += ")"
         elif inst == bvconcat:
             assert isinstance(d.expr.args[0], Var) and \
                 isinstance(d.expr.args[1], Var)
@@ -109,18 +127,17 @@ def to_smt(r):
             df = d.defs[0]
 
             # Z3 Concat expects hi bits first, then lo bits
-            exp = "(= {} (concat {} {}))"\
+            exp = mk_eq(var_to_bv[df], Concat(var_to_bv[hi], var_to_bv[lo]))
-                  .format(df, hi, lo)
         else:
             assert False, "Unknown primitive instruction {}".format(inst)
 
-        q += "(assert {})\n".format(exp)
+        q.append(exp)
 
     return (q, m)
 
 
 def equivalent(r1, r2, inp_m, out_m):
-    # type: (Rtl, Rtl, VarMap, VarMap) -> str
+    # type: (Rtl, Rtl, VarMap, VarMap) -> List[ExprRef]
     """
     Given:
         - concrete source Rtl r1
@@ -156,36 +173,25 @@ def equivalent(r1, r2, inp_m, out_m):
     (q2, m2) = to_smt(r2)
 
     # Build an expression for the equality of real Cretone inputs of r1 and r2
-    args_eq_exp = "(and \n"
+    args_eq_exp = []  # type: List[ExprRef]
 
     for v in r1.free_vars():
-        args_eq_exp += "(= {} {})\n".format(m1[v], m2[inp_m[v]])
+        args_eq_exp.append(mk_eq(m1[v], m2[inp_m[v]]))
-    args_eq_exp += ")"
 
     # Build an expression for the equality of real Cretone outputs of r1 and r2
-    results_eq_exp = "(and \n"
+    results_eq_exp = []  # type: List[ExprRef]
     for (v1, v2) in out_m.items():
-        results_eq_exp += "(= {} {})\n".format(m1[v1], m2[v2])
+        results_eq_exp.append(mk_eq(m1[v1], m2[v2]))
-    results_eq_exp += ")"
 
     # Put the whole query toghether
-    q = '; Rtl 1 declarations and assertions\n' + q1
+    return q1 + q2 + args_eq_exp + [Not(And(*results_eq_exp))]
-    q += '; Rtl 2 declarations and assertions\n' + q2
-
-    q += '; Assert that the inputs of Rtl1 and Rtl2 are equal\n' + \
-         '(assert {})\n'.format(args_eq_exp)
-
-    q += '; Assert that the outputs of Rtl1 and Rtl2 are not equal\n' + \
-         '(assert (not {}))\n'.format(results_eq_exp)
-
-    return q
 
 
 def xform_correct(x, typing):
-    # type: (XForm, VarTyping) -> str
+    # type: (XForm, VarTyping) -> bool
     """
-    Given an XForm x and a concrete variable typing for x build the smtlib
+    Given an XForm x and a concrete variable typing for x check whether x is
-    query asserting that x is correct for the given typing.
+    semantically preserving for the concrete typing.
     """
     assert x.ti.permits(typing)
 
@@ -208,4 +214,8 @@ def xform_correct(x, typing):
     # Get the primitive semantic Rtls for src and dst
     prim_src = elaborate(src)
     prim_dst = elaborate(dst)
-    return equivalent(prim_src, prim_dst, inp_m, out_m)
+    asserts = equivalent(prim_src, prim_dst, inp_m, out_m)
+
+    s = Solver()
+    s.add(*asserts)
+    return s.check() == unsat

lib/cretonne/meta/stubs/z3/__init__.pyi

@@ -0,0 +1,151 @@
+from typing import overload, Tuple, Any, List, Iterable, Union, TypeVar
+from .z3types import Ast, ContextObj
+
+TExprRef = TypeVar("TExprRef", bound="ExprRef")
+
+class Context:
+  ...
+
+class Z3PPObject:
+  ...
+
+class AstRef(Z3PPObject):
+  @overload
+  def __init__(self, ast: Ast, ctx: Context) -> None:
+    self.ast: Ast = ...
+    self.ctx: Context= ...
+
+  @overload
+  def __init__(self, ast: Ast) -> None:
+    self.ast: Ast = ...
+    self.ctx: Context= ...
+  def ctx_ref(self) -> ContextObj:  ...
+  def as_ast(self) -> Ast:  ...
+  def children(self) -> List[AstRef]: ...
+
+class SortRef(AstRef):
+  ...
+
+class FuncDeclRef(AstRef):
+  def arity(self) -> int: ...
+  def name(self) -> str:  ...
+
+class ExprRef(AstRef):
+  def eq(self, other: ExprRef) -> ExprRef:  ...
+  def sort(self) -> SortRef:  ...
+  def decl(self) -> FuncDeclRef:  ...
+
+class BoolSortRef(SortRef):
+  ...
+
+class BoolRef(ExprRef):
+  ...
+
+
+def is_true(a: BoolRef) -> bool:  ...
+def is_false(a: BoolRef) -> bool:  ...
+def is_int_value(a: AstRef) -> bool:  ...
+def substitute(a: AstRef, *m: Tuple[AstRef, AstRef]) -> AstRef: ...
+
+
+class ArithSortRef(SortRef):
+  ...
+
+class ArithRef(ExprRef):
+  def __neg__(self) -> ExprRef: ...
+  def __le__(self, other: ArithRef) -> ArithRef:  ...
+  def __lt__(self, other: ArithRef) -> ArithRef:  ...
+  def __ge__(self, other: ArithRef) -> ArithRef:  ...
+  def __gt__(self, other: ArithRef) -> ArithRef:  ...
+  def __add__(self, other: ArithRef) -> ArithRef:  ...
+  def __sub__(self, other: ArithRef) -> ArithRef:  ...
+  def __mul__(self, other: ArithRef) -> ArithRef:  ...
+  def __div__(self, other: ArithRef) -> ArithRef:  ...
+  def __mod__(self, other: ArithRef) -> ArithRef:  ...
+
+class IntNumRef(ArithRef):
+  def as_long(self) -> int: ...
+
+class BitVecRef(ExprRef):
+  def __neg__(self) -> ExprRef: ...
+  def __le__(self, other: BitVecRef) -> ExprRef:  ...
+  def __lt__(self, other: BitVecRef) -> ExprRef:  ...
+  def __ge__(self, other: BitVecRef) -> ExprRef:  ...
+  def __gt__(self, other: BitVecRef) -> ExprRef:  ...
+  def __add__(self, other: BitVecRef) -> BitVecRef:  ...
+  def __sub__(self, other: BitVecRef) -> BitVecRef:  ...
+  def __mul__(self, other: BitVecRef) -> BitVecRef:  ...
+  def __div__(self, other: BitVecRef) -> BitVecRef:  ...
+  def __mod__(self, other: BitVecRef) -> BitVecRef:  ...
+
+class BitVecNumRef(BitVecRef):
+  def as_long(self) -> int: ...
+
+class CheckSatResult: ...
+
+class ModelRef(Z3PPObject):
+  def __getitem__(self, k:  FuncDeclRef) -> IntNumRef:  ...
+  def decls(self) ->  Iterable[FuncDeclRef]:  ...
+
+class Solver(Z3PPObject):
+  @overload
+  def __init__(self) -> None:
+    self.ctx: Context = ...
+  @overload
+  def __init__(self, ctx:Context) -> None:
+    self.ctx: Context = ...
+
+  def add(self, e:ExprRef) -> None: ...
+  def to_smt2(self) -> str: ...
+  def check(self) -> CheckSatResult: ...
+  def push(self) -> None:  ...
+  def pop(self) -> None:  ...
+  def model(self) -> ModelRef:  ...
+
+sat: CheckSatResult = ...
+unsat: CheckSatResult = ...
+
+@overload
+def Int(name: str) -> ArithRef: ...
+@overload
+def Int(name: str, ctx: Context) -> ArithRef: ...
+
+@overload
+def Bool(name: str) -> BoolRef: ...
+@overload
+def Bool(name: str, ctx: Context) -> BoolRef: ...
+
+def BitVec(name: str, width: int) -> BitVecRef: ...
+
+@overload
+def parse_smt2_string(s: str) -> ExprRef: ...
+@overload
+def parse_smt2_string(s: str, ctx: Context) -> ExprRef: ...
+
+# Can't give more precise types here since func signature is
+# a vararg list of ExprRef optionally followed by a Context
+def Or(*args: Union[ExprRef, Context]) -> ExprRef: ...
+def And(*args: Union[ExprRef, Context]) -> ExprRef: ...
+@overload
+def Not(p: ExprRef) -> ExprRef: ...
+@overload
+def Not(p: ExprRef, ctx: Context) -> ExprRef: ...
+def Implies(a: ExprRef, b: ExprRef, ctx:Context) -> ExprRef: ...
+def If(a: ExprRef, b:TExprRef, c:TExprRef) -> TExprRef:  ...
+
+def ZeroExt(width: int, expr: BitVecRef) -> BitVecRef:  ...
+def SignExt(width: int, expr: BitVecRef) -> BitVecRef:  ...
+def Extract(hi: int, lo: int, expr: BitVecRef) -> BitVecRef:  ...
+def Concat(expr1: BitVecRef, expr2: BitVecRef) -> BitVecRef:  ...
+
+def Function(name: str, *sig: Tuple[SortRef,...]) -> FuncDeclRef:  ...
+
+def IntVal(val: int, ctx: Context) -> IntNumRef:  ...
+@overload
+def BoolVal(val: bool, ctx: Context) -> BoolRef:  ...
+@overload
+def BoolVal(val: bool) -> BoolRef:  ...
+@overload
+def BitVecVal(val: int, bits: int, ctx: Context) -> BitVecNumRef:  ...
+@overload
+def BitVecVal(val: int, bits: int) -> BitVecNumRef:  ...

lib/cretonne/meta/stubs/z3/z3core.pyi

@@ -0,0 +1,3 @@
+from .z3types import Ast, ContextObj
+def Z3_mk_eq(ctx: ContextObj, a: Ast, b: Ast) -> Ast: ...
+def Z3_mk_div(ctx: ContextObj, a: Ast, b: Ast) -> Ast: ...

lib/cretonne/meta/stubs/z3/z3types.pyi

@@ -0,0 +1,12 @@
+from typing import Any
+
+class Z3Exception(Exception):
+  def __init__(self, a: Any) -> None:
+    self.value = a
+    ...
+
+class ContextObj:
+  ...
+
+class Ast:
+  ...