typeinfer.py

"""
Type inference base on CPA.
The algorithm guarantees monotonic growth of type-sets for each variable.

Steps:
    1. seed initial types
    2. build constraints
    3. propagate constraints
    4. unify types

Constraint propagation is precise and does not regret (no backtracing).
Constraints push types forward following the dataflow.
"""


import logging
import operator
import contextlib
import itertools
from pprint import pprint
from collections import OrderedDict, defaultdict
from functools import reduce

from numba.core import types, utils, typing, ir, config
from numba.core.typing.templates import Signature
from numba.core.errors import (TypingError, UntypedAttributeError,
                               new_error_context, termcolor, UnsupportedError,
                               ForceLiteralArg, CompilerError, NumbaValueError)
from numba.core.funcdesc import qualifying_prefix
from numba.core.typeconv import Conversion

_logger = logging.getLogger(__name__)


class NOTSET:
    pass


# terminal color markup
_termcolor = termcolor()


class TypeVar(object):
    def __init__(self, context, var):
        self.context = context
        self.var = var
        self.type = None
        self.locked = False
        # Stores source location of first definition
        self.define_loc = None
        # Qualifiers
        self.literal_value = NOTSET

    def add_type(self, tp, loc):
        assert isinstance(tp, types.Type), type(tp)
        # Special case for _undef_var.
        # If the typevar is the _undef_var, use the incoming type directly.
        if self.type is types._undef_var:
            self.type = tp
            return self.type

        if self.locked:
            if tp != self.type:
                if self.context.can_convert(tp, self.type) is None:
                    msg = ("No conversion from %s to %s for '%s', "
                           "defined at %s")
                    raise TypingError(msg % (tp, self.type, self.var,
                                             self.define_loc),
                                      loc=loc)
        else:
            if self.type is not None:
                unified = self.context.unify_pairs(self.type, tp)
                if unified is None:
                    msg = "Cannot unify %s and %s for '%s', defined at %s"
                    raise TypingError(msg % (self.type, tp, self.var,
                                             self.define_loc),
                                      loc=self.define_loc)
            else:
                # First time definition
                unified = tp
                self.define_loc = loc

            self.type = unified

        return self.type

    def lock(self, tp, loc, literal_value=NOTSET):
        assert isinstance(tp, types.Type), type(tp)

        if self.locked:
            msg = ("Invalid reassignment of a type-variable detected, type "
                   "variables are locked according to the user provided "
                   "function signature or from an ir.Const node. This is a "
                   "bug! Type={}. {}").format(tp, self.type)
            raise CompilerError(msg, loc)

        # If there is already a type, ensure we can convert it to the
        # locked type.
        if (self.type is not None and
                self.context.can_convert(self.type, tp) is None):
            raise TypingError("No conversion from %s to %s for "
                              "'%s'" % (tp, self.type, self.var), loc=loc)

        self.type = tp
        self.locked = True
        if self.define_loc is None:
            self.define_loc = loc
        self.literal_value = literal_value

    def union(self, other, loc):
        if other.type is not None:
            self.add_type(other.type, loc=loc)

        return self.type

    def __repr__(self):
        return '%s := %s' % (self.var, self.type or "<undecided>")

    @property
    def defined(self):
        return self.type is not None

    def get(self):
        return (self.type,) if self.type is not None else ()

    def getone(self):
        if self.type is None:
            raise TypingError("Undecided type {}".format(self))
        return self.type

    def __len__(self):
        return 1 if self.type is not None else 0


class ConstraintNetwork(object):
    """
    TODO: It is possible to optimize constraint propagation to consider only
          dirty type variables.
    """

    def __init__(self):
        self.constraints = []

    def append(self, constraint):
        self.constraints.append(constraint)

    def propagate(self, typeinfer):
        """
        Execute all constraints.  Errors are caught and returned as a list.
        This allows progressing even though some constraints may fail
        due to lack of information
        (e.g. imprecise types such as List(undefined)).
        """
        errors = []
        for constraint in self.constraints:
            loc = constraint.loc
            with typeinfer.warnings.catch_warnings(filename=loc.filename,
                                                   lineno=loc.line):
                try:
                    constraint(typeinfer)
                except ForceLiteralArg as e:
                    errors.append(e)
                except TypingError as e:
                    _logger.debug("captured error", exc_info=e)
                    new_exc = TypingError(
                        str(e), loc=constraint.loc,
                        highlighting=False,
                    )
                    errors.append(utils.chain_exception(new_exc, e))
                except Exception as e:
                    if utils.use_old_style_errors():
                        _logger.debug("captured error", exc_info=e)
                        msg = ("Internal error at {con}.\n{err}\n"
                               "Enable logging at debug level for details.")
                        new_exc = TypingError(
                            msg.format(con=constraint, err=str(e)),
                            loc=constraint.loc,
                            highlighting=False,
                        )
                        errors.append(utils.chain_exception(new_exc, e))
                    elif utils.use_new_style_errors():
                        raise e
                    else:
                        msg = ("Unknown CAPTURED_ERRORS style: "
                               f"'{config.CAPTURED_ERRORS}'.")
                        assert 0, msg

        return errors


class Propagate(object):
    """
    A simple constraint for direct propagation of types for assignments.
    """

    def __init__(self, dst, src, loc):
        self.dst = dst
        self.src = src
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of assignment at {0}", self.loc,
                               loc=self.loc):
            typeinfer.copy_type(self.src, self.dst, loc=self.loc)
            # If `dst` is refined, notify us
            typeinfer.refine_map[self.dst] = self

    def refine(self, typeinfer, target_type):
        # Do not back-propagate to locked variables (e.g. constants)
        assert target_type.is_precise()
        typeinfer.add_type(self.src, target_type, unless_locked=True,
                           loc=self.loc)


class ArgConstraint(object):

    def __init__(self, dst, src, loc):
        self.dst = dst
        self.src = src
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of argument at {0}", self.loc):
            typevars = typeinfer.typevars
            src = typevars[self.src]
            if not src.defined:
                return
            ty = src.getone()
            if isinstance(ty, types.Omitted):
                ty = typeinfer.context.resolve_value_type_prefer_literal(
                    ty.value,
                )
            if not ty.is_precise():
                raise TypingError('non-precise type {}'.format(ty))
            typeinfer.add_type(self.dst, ty, loc=self.loc)


class BuildTupleConstraint(object):
    def __init__(self, target, items, loc):
        self.target = target
        self.items = items
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of tuple at {0}", self.loc):
            typevars = typeinfer.typevars
            tsets = [typevars[i.name].get() for i in self.items]
            for vals in itertools.product(*tsets):
                if vals and all(vals[0] == v for v in vals):
                    tup = types.UniTuple(dtype=vals[0], count=len(vals))
                else:
                    # empty tuples fall here as well
                    tup = types.Tuple(vals)
                assert tup.is_precise()
                typeinfer.add_type(self.target, tup, loc=self.loc)


class _BuildContainerConstraint(object):

    def __init__(self, target, items, loc):
        self.target = target
        self.items = items
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of {0} at {1}",
                               self.container_type, self.loc):
            typevars = typeinfer.typevars
            tsets = [typevars[i.name].get() for i in self.items]
            if not tsets:
                typeinfer.add_type(self.target,
                                   self.container_type(types.undefined),
                                   loc=self.loc)
            else:
                for typs in itertools.product(*tsets):
                    unified = typeinfer.context.unify_types(*typs)
                    if unified is not None:
                        typeinfer.add_type(self.target,
                                           self.container_type(unified),
                                           loc=self.loc)


class BuildListConstraint(_BuildContainerConstraint):

    def __init__(self, target, items, loc):
        self.target = target
        self.items = items
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of {0} at {1}",
                               types.List, self.loc):
            typevars = typeinfer.typevars
            tsets = [typevars[i.name].get() for i in self.items]
            if not tsets:
                typeinfer.add_type(self.target,
                                   types.List(types.undefined),
                                   loc=self.loc)
            else:
                for typs in itertools.product(*tsets):
                    unified = typeinfer.context.unify_types(*typs)
                    if unified is not None:
                        # pull out literals if available
                        islit = [isinstance(x, types.Literal) for x in typs]
                        iv = None
                        if all(islit):
                            iv = [x.literal_value for x in typs]
                        typeinfer.add_type(self.target,
                                           types.List(unified,
                                                      initial_value=iv),
                                           loc=self.loc)
                    else:
                        typeinfer.add_type(self.target,
                                           types.LiteralList(typs),
                                           loc=self.loc)


class BuildSetConstraint(_BuildContainerConstraint):
    container_type = types.Set


class BuildMapConstraint(object):

    def __init__(self, target, items, special_value, value_indexes, loc):
        self.target = target
        self.items = items
        self.special_value = special_value
        self.value_indexes = value_indexes
        self.loc = loc

    def __call__(self, typeinfer):

        with new_error_context("typing of dict at {0}", self.loc):
            typevars = typeinfer.typevars

            # figure out what sort of dict is being dealt with
            tsets = [(typevars[k.name].getone(), typevars[v.name].getone())
                     for k, v in self.items]

            if not tsets:
                typeinfer.add_type(self.target,
                                   types.DictType(types.undefined,
                                                  types.undefined,
                                                  self.special_value),
                                   loc=self.loc)
            else:
                # all the info is known about the dict, if its
                # str keys -> random heterogeneous values treat as literalstrkey
                ktys = [x[0] for x in tsets]
                vtys = [x[1] for x in tsets]
                strkey = all([isinstance(x, types.StringLiteral) for x in ktys])
                literalvty = all([isinstance(x, types.Literal) for x in vtys])
                vt0 = types.unliteral(vtys[0])

                # homogeneous values comes in the form of being able to cast
                # all the other values in the ctor to the type of the first.
                # The order is important as `typed.Dict` takes it's type from
                # the first element.
                def check(other):
                    conv = typeinfer.context.can_convert(other, vt0)
                    return conv is not None and conv < Conversion.unsafe
                homogeneous = all([check(types.unliteral(x)) for x in vtys])

                # Special cases:
                # Single key:value in ctor, key is str, value is an otherwise
                # illegal container type, e.g. LiteralStrKeyDict or
                # List, there's no way to put this into a typed.Dict, so make it
                # a LiteralStrKeyDict, same goes for LiteralList.
                if len(vtys) == 1:
                    valty = vtys[0]
                    if isinstance(valty, (types.LiteralStrKeyDict,
                                          types.List,
                                          types.LiteralList)):
                        homogeneous = False

                if strkey and not homogeneous:
                    resolved_dict = {x: y for x, y in zip(ktys, vtys)}
                    ty = types.LiteralStrKeyDict(resolved_dict,
                                                 self.value_indexes)
                    typeinfer.add_type(self.target, ty, loc=self.loc)
                else:
                    init_value = self.special_value if literalvty else None
                    key_type, value_type = tsets[0]
                    typeinfer.add_type(self.target,
                                       types.DictType(key_type,
                                                      value_type,
                                                      init_value),
                                       loc=self.loc)


class ExhaustIterConstraint(object):
    def __init__(self, target, count, iterator, loc):
        self.target = target
        self.count = count
        self.iterator = iterator
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of exhaust iter at {0}", self.loc):
            typevars = typeinfer.typevars
            for tp in typevars[self.iterator.name].get():
                # unpack optional
                tp = tp.type if isinstance(tp, types.Optional) else tp
                if isinstance(tp, types.BaseTuple):
                    if len(tp) == self.count:
                        assert tp.is_precise()
                        typeinfer.add_type(self.target, tp, loc=self.loc)
                        break
                    else:
                        msg = (f"wrong tuple length for {self.iterator.name}: ",
                               f"expected {self.count}, got {len(tp)}")
                        raise NumbaValueError(msg)
                elif isinstance(tp, types.IterableType):
                    tup = types.UniTuple(dtype=tp.iterator_type.yield_type,
                                         count=self.count)
                    assert tup.is_precise()
                    typeinfer.add_type(self.target, tup, loc=self.loc)
                    break
                else:
                    raise TypingError("failed to unpack {}".format(tp),
                                      loc=self.loc)


class PairFirstConstraint(object):
    def __init__(self, target, pair, loc):
        self.target = target
        self.pair = pair
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of pair-first at {0}", self.loc):
            typevars = typeinfer.typevars
            for tp in typevars[self.pair.name].get():
                if not isinstance(tp, types.Pair):
                    # XXX is this an error?
                    continue
                assert (isinstance(tp.first_type, types.UndefinedFunctionType)
                        or tp.first_type.is_precise())
                typeinfer.add_type(self.target, tp.first_type, loc=self.loc)


class PairSecondConstraint(object):
    def __init__(self, target, pair, loc):
        self.target = target
        self.pair = pair
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of pair-second at {0}", self.loc):
            typevars = typeinfer.typevars
            for tp in typevars[self.pair.name].get():
                if not isinstance(tp, types.Pair):
                    # XXX is this an error?
                    continue
                assert tp.second_type.is_precise()
                typeinfer.add_type(self.target, tp.second_type, loc=self.loc)


class StaticGetItemConstraint(object):
    def __init__(self, target, value, index, index_var, loc):
        self.target = target
        self.value = value
        self.index = index
        if index_var is not None:
            self.fallback = IntrinsicCallConstraint(target, operator.getitem,
                                                    (value, index_var), {},
                                                    None, loc)
        else:
            self.fallback = None
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of static-get-item at {0}", self.loc):
            typevars = typeinfer.typevars
            for ty in typevars[self.value.name].get():
                sig = typeinfer.context.resolve_static_getitem(
                    value=ty, index=self.index,
                )

                if sig is not None:
                    itemty = sig.return_type
                    # if the itemty is not precise, let it through, unification
                    # will catch it and produce a better error message
                    typeinfer.add_type(self.target, itemty, loc=self.loc)
                elif self.fallback is not None:
                    self.fallback(typeinfer)

    def get_call_signature(self):
        # The signature is only needed for the fallback case in lowering
        return self.fallback and self.fallback.get_call_signature()


class TypedGetItemConstraint(object):
    def __init__(self, target, value, dtype, index, loc):
        self.target = target
        self.value = value
        self.dtype = dtype
        self.index = index
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of typed-get-item at {0}", self.loc):
            typevars = typeinfer.typevars
            idx_ty = typevars[self.index.name].get()
            ty = typevars[self.value.name].get()
            self.signature = Signature(self.dtype, ty + idx_ty, None)
            typeinfer.add_type(self.target, self.dtype, loc=self.loc)

    def get_call_signature(self):
        return self.signature


def fold_arg_vars(typevars, args, vararg, kws):
    """
    Fold and resolve the argument variables of a function call.
    """
    # Fetch all argument types, bail if any is unknown
    n_pos_args = len(args)
    kwds = [kw for (kw, var) in kws]
    argtypes = [typevars[a.name] for a in args]
    argtypes += [typevars[var.name] for (kw, var) in kws]
    if vararg is not None:
        argtypes.append(typevars[vararg.name])

    if not all(a.defined for a in argtypes):
        return

    args = tuple(a.getone() for a in argtypes)

    pos_args = args[:n_pos_args]
    if vararg is not None:
        errmsg = "*args in function call should be a tuple, got %s"
        # Handle constant literal used for `*args`
        if isinstance(args[-1], types.Literal):
            const_val = args[-1].literal_value
            # Is the constant value a tuple?
            if not isinstance(const_val, tuple):
                raise TypeError(errmsg % (args[-1],))
            # Append the elements in the const tuple to the positional args
            pos_args += const_val
        # Handle non-constant
        elif not isinstance(args[-1], types.BaseTuple):
            # Unsuitable for *args
            # (Python is more lenient and accepts all iterables)
            raise TypeError(errmsg % (args[-1],))
        else:
            # Append the elements in the tuple to the positional args
            pos_args += args[-1].types
        # Drop the last arg
        args = args[:-1]
    kw_args = dict(zip(kwds, args[n_pos_args:]))
    return pos_args, kw_args


def _is_array_not_precise(arrty):
    """Check type is array and it is not precise
    """
    return isinstance(arrty, types.Array) and not arrty.is_precise()


class CallConstraint(object):
    """Constraint for calling functions.
    Perform case analysis foreach combinations of argument types.
    """
    signature = None

    def __init__(self, target, func, args, kws, vararg, loc):
        self.target = target
        self.func = func
        self.args = args
        self.kws = kws or {}
        self.vararg = vararg
        self.loc = loc

    def __call__(self, typeinfer):
        msg = "typing of call at {0}\n".format(self.loc)
        with new_error_context(msg):
            typevars = typeinfer.typevars
            with new_error_context(
                    "resolving caller type: {}".format(self.func)):
                fnty = typevars[self.func].getone()
            with new_error_context("resolving callee type: {0}", fnty):
                self.resolve(typeinfer, typevars, fnty)

    def resolve(self, typeinfer, typevars, fnty):
        assert fnty
        context = typeinfer.context

        r = fold_arg_vars(typevars, self.args, self.vararg, self.kws)
        if r is None:
            # Cannot resolve call type until all argument types are known
            return
        pos_args, kw_args = r

        # Check argument to be precise
        for a in itertools.chain(pos_args, kw_args.values()):
            # Forbids imprecise type except array of undefined dtype
            if not a.is_precise() and not isinstance(a, types.Array):
                return

        # Resolve call type
        if isinstance(fnty, types.TypeRef):
            # Unwrap TypeRef
            fnty = fnty.instance_type
        try:
            sig = typeinfer.resolve_call(fnty, pos_args, kw_args)
        except ForceLiteralArg as e:
            # Adjust for bound methods
            folding_args = ((fnty.this,) + tuple(self.args)
                            if isinstance(fnty, types.BoundFunction)
                            else self.args)
            folded = e.fold_arguments(folding_args, self.kws)
            requested = set()
            unsatisfied = set()
            for idx in e.requested_args:
                maybe_arg = typeinfer.func_ir.get_definition(folded[idx])
                if isinstance(maybe_arg, ir.Arg):
                    requested.add(maybe_arg.index)
                else:
                    unsatisfied.add(idx)
            if unsatisfied:
                raise TypingError("Cannot request literal type.", loc=self.loc)
            elif requested:
                raise ForceLiteralArg(requested, loc=self.loc)
        if sig is None:
            # Note: duplicated error checking.
            #       See types.BaseFunction.get_call_type
            # Arguments are invalid => explain why
            headtemp = "Invalid use of {0} with parameters ({1})"
            args = [str(a) for a in pos_args]
            args += ["%s=%s" % (k, v) for k, v in sorted(kw_args.items())]
            head = headtemp.format(fnty, ', '.join(map(str, args)))
            desc = context.explain_function_type(fnty)
            msg = '\n'.join([head, desc])
            raise TypingError(msg)

        typeinfer.add_type(self.target, sig.return_type, loc=self.loc)

        # If the function is a bound function and its receiver type
        # was refined, propagate it.
        if (isinstance(fnty, types.BoundFunction)
                and sig.recvr is not None
                and sig.recvr != fnty.this):
            refined_this = context.unify_pairs(sig.recvr, fnty.this)
            if (refined_this is None and
                    fnty.this.is_precise() and
                    sig.recvr.is_precise()):
                msg = "Cannot refine type {} to {}".format(
                    sig.recvr, fnty.this,
                )
                raise TypingError(msg, loc=self.loc)
            if refined_this is not None and refined_this.is_precise():
                refined_fnty = fnty.copy(this=refined_this)
                typeinfer.propagate_refined_type(self.func, refined_fnty)

        # If the return type is imprecise but can be unified with the
        # target variable's inferred type, use the latter.
        # Useful for code such as::
        #    s = set()
        #    s.add(1)
        # (the set() call must be typed as int64(), not undefined())
        if not sig.return_type.is_precise():
            target = typevars[self.target]
            if target.defined:
                targetty = target.getone()
                if context.unify_pairs(targetty, sig.return_type) == targetty:
                    sig = sig.replace(return_type=targetty)

        self.signature = sig
        self._add_refine_map(typeinfer, typevars, sig)

    def _add_refine_map(self, typeinfer, typevars, sig):
        """Add this expression to the refine_map base on the type of target_type
        """
        target_type = typevars[self.target].getone()
        # Array
        if (isinstance(target_type, types.Array)
                and isinstance(sig.return_type.dtype, types.Undefined)):
            typeinfer.refine_map[self.target] = self
        # DictType
        if (isinstance(target_type, types.DictType) and
                not target_type.is_precise()):
            typeinfer.refine_map[self.target] = self

    def refine(self, typeinfer, updated_type):
        # Is getitem?
        if self.func == operator.getitem:
            aryty = typeinfer.typevars[self.args[0].name].getone()
            # is array not precise?
            if _is_array_not_precise(aryty):
                # allow refinement of dtype
                assert updated_type.is_precise()
                newtype = aryty.copy(dtype=updated_type.dtype)
                typeinfer.add_type(self.args[0].name, newtype, loc=self.loc)
        else:
            m = 'no type refinement implemented for function {} updating to {}'
            raise TypingError(m.format(self.func, updated_type))

    def get_call_signature(self):
        return self.signature


class IntrinsicCallConstraint(CallConstraint):
    def __call__(self, typeinfer):
        with new_error_context("typing of intrinsic-call at {0}", self.loc):
            fnty = self.func
            if fnty in utils.OPERATORS_TO_BUILTINS:
                fnty = typeinfer.resolve_value_type(None, fnty)
            self.resolve(typeinfer, typeinfer.typevars, fnty=fnty)


class GetAttrConstraint(object):
    def __init__(self, target, attr, value, loc, inst):
        self.target = target
        self.attr = attr
        self.value = value
        self.loc = loc
        self.inst = inst

    def __call__(self, typeinfer):
        with new_error_context("typing of get attribute at {0}", self.loc):
            typevars = typeinfer.typevars
            valtys = typevars[self.value.name].get()
            for ty in valtys:
                attrty = typeinfer.context.resolve_getattr(ty, self.attr)
                if attrty is None:
                    raise UntypedAttributeError(ty, self.attr,
                                                loc=self.inst.loc)
                else:
                    assert attrty.is_precise()
                    typeinfer.add_type(self.target, attrty, loc=self.loc)
            typeinfer.refine_map[self.target] = self

    def refine(self, typeinfer, target_type):
        if isinstance(target_type, types.BoundFunction):
            recvr = target_type.this
            assert recvr.is_precise()
            typeinfer.add_type(self.value.name, recvr, loc=self.loc)
            source_constraint = typeinfer.refine_map.get(self.value.name)
            if source_constraint is not None:
                source_constraint.refine(typeinfer, recvr)

    def __repr__(self):
        return 'resolving type of attribute "{attr}" of "{value}"'.format(
            value=self.value, attr=self.attr)


class SetItemRefinement(object):
    """A mixin class to provide the common refinement logic in setitem
    and static setitem.
    """

    def _refine_target_type(self, typeinfer, targetty, idxty, valty, sig):
        """Refine the target-type given the known index type and value type.
        """
        # For array setitem, refine imprecise array dtype
        if _is_array_not_precise(targetty):
            typeinfer.add_type(self.target.name, sig.args[0], loc=self.loc)
        # For Dict setitem
        if isinstance(targetty, types.DictType):
            if not targetty.is_precise():
                refined = targetty.refine(idxty, valty)
                typeinfer.add_type(
                    self.target.name, refined,
                    loc=self.loc,
                )
            elif isinstance(targetty, types.LiteralStrKeyDict):
                typeinfer.add_type(
                    self.target.name, types.DictType(idxty, valty),
                    loc=self.loc,
                )


class SetItemConstraint(SetItemRefinement):
    def __init__(self, target, index, value, loc):
        self.target = target
        self.index = index
        self.value = value
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of setitem at {0}", self.loc):
            typevars = typeinfer.typevars
            if not all(typevars[var.name].defined
                       for var in (self.target, self.index, self.value)):
                return
            targetty = typevars[self.target.name].getone()
            idxty = typevars[self.index.name].getone()
            valty = typevars[self.value.name].getone()

            sig = typeinfer.context.resolve_setitem(targetty, idxty, valty)
            if sig is None:
                raise TypingError("Cannot resolve setitem: %s[%s] = %s" %
                                  (targetty, idxty, valty), loc=self.loc)

            self.signature = sig
            self._refine_target_type(typeinfer, targetty, idxty, valty, sig)

    def get_call_signature(self):
        return self.signature


class StaticSetItemConstraint(SetItemRefinement):
    def __init__(self, target, index, index_var, value, loc):
        self.target = target
        self.index = index
        self.index_var = index_var
        self.value = value
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of staticsetitem at {0}", self.loc):
            typevars = typeinfer.typevars
            if not all(typevars[var.name].defined
                       for var in (self.target, self.index_var, self.value)):
                return
            targetty = typevars[self.target.name].getone()
            idxty = typevars[self.index_var.name].getone()
            valty = typevars[self.value.name].getone()

            sig = typeinfer.context.resolve_static_setitem(targetty,
                                                           self.index, valty)
            if sig is None:
                sig = typeinfer.context.resolve_setitem(targetty, idxty, valty)
            if sig is None:
                raise TypingError("Cannot resolve setitem: %s[%r] = %s" %
                                  (targetty, self.index, valty), loc=self.loc)
            self.signature = sig
            self._refine_target_type(typeinfer, targetty, idxty, valty, sig)

    def get_call_signature(self):
        return self.signature


class DelItemConstraint(object):
    def __init__(self, target, index, loc):
        self.target = target
        self.index = index
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of delitem at {0}", self.loc):
            typevars = typeinfer.typevars
            if not all(typevars[var.name].defined
                       for var in (self.target, self.index)):
                return
            targetty = typevars[self.target.name].getone()
            idxty = typevars[self.index.name].getone()

            sig = typeinfer.context.resolve_delitem(targetty, idxty)
            if sig is None:
                raise TypingError("Cannot resolve delitem: %s[%s]" %
                                  (targetty, idxty), loc=self.loc)
            self.signature = sig

    def get_call_signature(self):
        return self.signature


class SetAttrConstraint(object):
    def __init__(self, target, attr, value, loc):
        self.target = target
        self.attr = attr
        self.value = value
        self.loc = loc

    def __call__(self, typeinfer):
        with new_error_context("typing of set attribute {0!r} at {1}",
                               self.attr, self.loc):
            typevars = typeinfer.typevars
            if not all(typevars[var.name].defined
                       for var in (self.target, self.value)):
                return
            targetty = typevars[self.target.name].getone()
            valty = typevars[self.value.name].getone()
            sig = typeinfer.context.resolve_setattr(targetty, self.attr,
                                                    valty)
            if sig is None:
                raise TypingError("Cannot resolve setattr: (%s).%s = %s" %
                                  (targetty, self.attr, valty),
                                  loc=self.loc)
            self.signature = sig

    def get_call_signature(self):
        return self.signature


class PrintConstraint(object):
    def __init__(self, args, vararg, loc):
        self.args = args
        self.vararg = vararg
        self.loc = loc

    def __call__(self, typeinfer):
        typevars = typeinfer.typevars

        r = fold_arg_vars(typevars, self.args, self.vararg, {})
        if r is None:
            # Cannot resolve call type until all argument types are known
            return
        pos_args, kw_args = r

        fnty = typeinfer.context.resolve_value_type(print)
        assert fnty is not None
        sig = typeinfer.resolve_call(fnty, pos_args, kw_args)
        self.signature = sig

    def get_call_signature(self):
        return self.signature


class TypeVarMap(dict):
    def set_context(self, context):
        self.context = context

    def __getitem__(self, name):
        if name not in self:
            self[name] = TypeVar(self.context, name)
        return super(TypeVarMap, self).__getitem__(name)

    def __setitem__(self, name, value):
        assert isinstance(name, str)
        if name in self:
            raise KeyError("Cannot redefine typevar %s" % name)
        else:
            super(TypeVarMap, self).__setitem__(name, value)


# A temporary mapping of {function name: dispatcher object}
_temporary_dispatcher_map = {}
# A temporary mapping of {function name: dispatcher object reference count}
# Reference: https://github.com/numba/numba/issues/3658
_temporary_dispatcher_map_ref_count = defaultdict(int)


@contextlib.contextmanager
def register_dispatcher(disp):
    """
    Register a Dispatcher for inference while it is not yet stored
    as global or closure variable (e.g. during execution of the @jit()
    call).  This allows resolution of recursive calls with eager
    compilation.
    """
    assert callable(disp)
    assert callable(disp.py_func)
    name = disp.py_func.__name__
    _temporary_dispatcher_map[name] = disp
    _temporary_dispatcher_map_ref_count[name] += 1
    try:
        yield
    finally:
        _temporary_dispatcher_map_ref_count[name] -= 1
        if not _temporary_dispatcher_map_ref_count[name]:
            del _temporary_dispatcher_map[name]


typeinfer_extensions = {}


class TypeInferer(object):
    """
    Operates on block that shares the same ir.Scope.
    """

    def __init__(self, context, func_ir, warnings):
        self.context = context
        # sort based on label, ensure iteration order!
        self.blocks = OrderedDict()
        for k in sorted(func_ir.blocks.keys()):
            self.blocks[k] = func_ir.blocks[k]
        self.generator_info = func_ir.generator_info
        self.func_id = func_ir.func_id
        self.func_ir = func_ir

        self.typevars = TypeVarMap()
        self.typevars.set_context(context)
        self.constraints = ConstraintNetwork()
        self.warnings = warnings

        # { index: mangled name }
        self.arg_names = {}
        # self.return_type = None
        # Set of assumed immutable globals
        self.assumed_immutables = set()
        # Track all calls and associated constraints
        self.calls = []
        # The inference result of the above calls
        self.calltypes = utils.UniqueDict()
        # Target var -> constraint with refine hook
        self.refine_map = {}

        if config.DEBUG or config.DEBUG_TYPEINFER:
            self.debug = TypeInferDebug(self)
        else:
            self.debug = NullDebug()

        self._skip_recursion = False

    def copy(self, skip_recursion=False):
        clone = TypeInferer(self.context, self.func_ir, self.warnings)
        clone.arg_names = self.arg_names.copy()
        clone._skip_recursion = skip_recursion

        for k, v in self.typevars.items():
            if not v.locked and v.defined:
                clone.typevars[k].add_type(v.getone(), loc=v.define_loc)

        return clone

    def _mangle_arg_name(self, name):
        # Disambiguise argument name
        return "arg.%s" % (name,)

    def _get_return_vars(self):
        rets = []
        for blk in self.blocks.values():
            inst = blk.terminator
            if isinstance(inst, ir.Return):
                rets.append(inst.value)
        return rets

    def get_argument_types(self):
        return [self.typevars[k].getone() for k in self.arg_names.values()]

    def seed_argument(self, name, index, typ):
        name = self._mangle_arg_name(name)
        self.seed_type(name, typ)
        self.arg_names[index] = name

    def seed_type(self, name, typ):
        """All arguments should be seeded.
        """
        self.lock_type(name, typ, loc=None)

    def seed_return(self, typ):
        """Seeding of return value is optional.
        """
        for var in self._get_return_vars():
            self.lock_type(var.name, typ, loc=None)

    def build_constraint(self):
        for blk in self.blocks.values():
            for inst in blk.body:
                self.constrain_statement(inst)

    def return_types_from_partial(self):
        """
        Resume type inference partially to deduce the return type.
        Note: No side-effect to `self`.

        Returns the inferred return type or None if it cannot deduce the return
        type.
        """
        # Clone the typeinferer and disable typing recursive calls
        cloned = self.copy(skip_recursion=True)
        # rebuild constraint network
        cloned.build_constraint()
        # propagate without raising
        cloned.propagate(raise_errors=False)
        # get return types
        rettypes = set()
        for retvar in cloned._get_return_vars():
            if retvar.name in cloned.typevars:
                typevar = cloned.typevars[retvar.name]
                if typevar and typevar.defined:
                    rettypes.add(types.unliteral(typevar.getone()))
        if not rettypes:
            return
        # unify return types
        return cloned._unify_return_types(rettypes)

    def propagate(self, raise_errors=True):
        newtoken = self.get_state_token()
        oldtoken = None
        # Since the number of types are finite, the typesets will eventually
        # stop growing.

        while newtoken != oldtoken:
            self.debug.propagate_started()
            oldtoken = newtoken
            # Errors can appear when the type set is incomplete; only
            # raise them when there is no progress anymore.
            errors = self.constraints.propagate(self)
            newtoken = self.get_state_token()
            self.debug.propagate_finished()
        if errors:
            if raise_errors:
                force_lit_args = [e for e in errors
                                  if isinstance(e, ForceLiteralArg)]
                if not force_lit_args:
                    raise errors[0]
                else:
                    raise reduce(operator.or_, force_lit_args)
            else:
                return errors

    def add_type(self, var, tp, loc, unless_locked=False):
        assert isinstance(var, str), type(var)
        tv = self.typevars[var]
        if unless_locked and tv.locked:
            return
        oldty = tv.type
        unified = tv.add_type(tp, loc=loc)
        if unified != oldty:
            self.propagate_refined_type(var, unified)

    def add_calltype(self, inst, signature):
        assert signature is not None
        self.calltypes[inst] = signature

    def copy_type(self, src_var, dest_var, loc):
        self.typevars[dest_var].union(self.typevars[src_var], loc=loc)

    def lock_type(self, var, tp, loc, literal_value=NOTSET):
        tv = self.typevars[var]
        tv.lock(tp, loc=loc, literal_value=literal_value)

    def propagate_refined_type(self, updated_var, updated_type):
        source_constraint = self.refine_map.get(updated_var)
        if source_constraint is not None:
            source_constraint.refine(self, updated_type)

    def unify(self, raise_errors=True):
        """
        Run the final unification pass over all inferred types, and
        catch imprecise types.
        """
        typdict = utils.UniqueDict()

        def find_offender(name, exhaustive=False):
            # finds the offending variable definition by name
            # if exhaustive is set it will try and trace through temporary
            # variables to find a concrete offending definition.
            offender = None
            for block in self.func_ir.blocks.values():
                offender = block.find_variable_assignment(name)
                if offender is not None:
                    if not exhaustive:
                        break
                    try:  # simple assignment
                        hasattr(offender.value, 'name')
                        offender_value = offender.value.name
                    except (AttributeError, KeyError):
                        break
                    orig_offender = offender
                    if offender_value.startswith('$'):
                        offender = find_offender(offender_value,
                                                 exhaustive=exhaustive)
                        if offender is None:
                            offender = orig_offender
                    break
            return offender

        def diagnose_imprecision(offender):
            # helper for diagnosing imprecise types

            list_msg = """\n
For Numba to be able to compile a list, the list must have a known and
precise type that can be inferred from the other variables. Whilst sometimes
the type of empty lists can be inferred, this is not always the case, see this
documentation for help:

https://numba.readthedocs.io/en/stable/user/troubleshoot.html#my-code-has-an-untyped-list-problem
"""
            if offender is not None:
                # This block deals with imprecise lists
                if hasattr(offender, 'value'):
                    if hasattr(offender.value, 'op'):
                        # might be `foo = []`
                        if offender.value.op == 'build_list':
                            return list_msg
                        # or might be `foo = list()`
                        elif offender.value.op == 'call':
                            try:  # assignment involving a call
                                call_name = offender.value.func.name
                                # find the offender based on the call name
                                offender = find_offender(call_name)
                                if isinstance(offender.value, ir.Global):
                                    if offender.value.name == 'list':
                                        return list_msg
                            except (AttributeError, KeyError):
                                pass
            return ""  # no help possible

        def check_var(name):
            tv = self.typevars[name]
            if not tv.defined:
                if raise_errors:
                    offender = find_offender(name)
                    val = getattr(offender, 'value', 'unknown operation')
                    loc = getattr(offender, 'loc', ir.unknown_loc)
                    msg = ("Type of variable '%s' cannot be determined, "
                           "operation: %s, location: %s")
                    raise TypingError(msg % (var, val, loc), loc)
                else:
                    typdict[var] = types.unknown
                    return
            tp = tv.getone()

            if isinstance(tp, types.UndefinedFunctionType):
                tp = tp.get_precise()

            if not tp.is_precise():
                offender = find_offender(name, exhaustive=True)
                msg = ("Cannot infer the type of variable '%s'%s, "
                       "have imprecise type: %s. %s")
                istmp = " (temporary variable)" if var.startswith('$') else ""
                loc = getattr(offender, 'loc', ir.unknown_loc)
                # is this an untyped list? try and provide help
                extra_msg = diagnose_imprecision(offender)
                if raise_errors:
                    raise TypingError(msg % (var, istmp, tp, extra_msg), loc)
                else:
                    typdict[var] = types.unknown
                    return
            else:  # type is precise, hold it
                typdict[var] = tp

        # For better error display, check first user-visible vars, then
        # temporaries
        temps = set(k for k in self.typevars if not k[0].isalpha())
        others = set(self.typevars) - temps
        for var in sorted(others):
            check_var(var)
        for var in sorted(temps):
            check_var(var)

        try:
            retty = self.get_return_type(typdict)
        except Exception as e:
            # partial type inference may raise e.g. attribute error if a
            # constraint has no computable signature, ignore this as needed
            if raise_errors:
                raise e
            else:
                retty = None
        else:
            typdict = utils.UniqueDict(
                typdict, **{v.name: retty for v in self._get_return_vars()})

        try:
            fntys = self.get_function_types(typdict)
        except Exception as e:
            # partial type inference may raise e.g. attribute error if a
            # constraint has no computable signature, ignore this as needed
            if raise_errors:
                raise e
            else:
                fntys = None

        if self.generator_info:
            retty = self.get_generator_type(typdict, retty,
                                            raise_errors=raise_errors)

        def check_undef_var_in_calls():
            # Check for undefined variables in the call arguments.
            for callnode, calltype in self.calltypes.items():
                if calltype is not None:
                    for i, v in enumerate(calltype.args, start=1):
                        if v is types._undef_var:
                            m = f"undefined variable used in call argument #{i}"
                            raise TypingError(m, loc=callnode.loc)

        check_undef_var_in_calls()

        self.debug.unify_finished(typdict, retty, fntys)

        return typdict, retty, fntys

    def get_generator_type(self, typdict, retty, raise_errors=True):
        gi = self.generator_info
        arg_types = [None] * len(self.arg_names)
        for index, name in self.arg_names.items():
            arg_types[index] = typdict[name]

        state_types = None
        try:
            state_types = [typdict[var_name] for var_name in gi.state_vars]
        except KeyError:
            msg = "Cannot type generator: state variable types cannot be found"
            if raise_errors:
                raise TypingError(msg)
            state_types = [types.unknown for _ in gi.state_vars]

        yield_types = None
        try:
            yield_types = [typdict[y.inst.value.name]
                           for y in gi.get_yield_points()]
        except KeyError:
            msg = "Cannot type generator: yield type cannot be found"
            if raise_errors:
                raise TypingError(msg)
        if not yield_types:
            msg = "Cannot type generator: it does not yield any value"
            if raise_errors:
                raise TypingError(msg)
            yield_types = [types.unknown for _ in gi.get_yield_points()]

        if not yield_types or all(yield_types) == types.unknown:
            # unknown yield, probably partial type inference, escape
            return types.Generator(self.func_id.func, types.unknown, arg_types,
                                   state_types, has_finalizer=True)

        yield_type = self.context.unify_types(*yield_types)
        if yield_type is None or isinstance(yield_type, types.Optional):
            msg = "Cannot type generator: cannot unify yielded types %s"
            yp_highlights = []
            for y in gi.get_yield_points():
                msg = (_termcolor.errmsg("Yield of: IR '%s', type '%s', "
                                         "location: %s"))
                yp_highlights.append(msg % (str(y.inst),
                                            typdict[y.inst.value.name],
                                            y.inst.loc.strformat()))

            explain_ty = set()
            for ty in yield_types:
                if isinstance(ty, types.Optional):
                    explain_ty.add(ty.type)
                    explain_ty.add(types.NoneType('none'))
                else:
                    explain_ty.add(ty)
            if raise_errors:
                raise TypingError("Can't unify yield type from the "
                                  "following types: %s"
                                  % ", ".join(sorted(map(str, explain_ty))) +
                                  "\n\n" + "\n".join(yp_highlights))

        return types.Generator(self.func_id.func, yield_type, arg_types,
                               state_types, has_finalizer=True)

    def get_function_types(self, typemap):
        """
        Fill and return the calltypes map.
        """
        # XXX why can't this be done on the fly?
        calltypes = self.calltypes
        for call, constraint in self.calls:
            calltypes[call] = constraint.get_call_signature()
        return calltypes

    def _unify_return_types(self, rettypes):
        if rettypes:
            unified = self.context.unify_types(*rettypes)
            if isinstance(unified, types.FunctionType):
                # unified is allowed to be UndefinedFunctionType
                # instance (that is imprecise).
                return unified
            if unified is None or not unified.is_precise():
                def check_type(atype):
                    lst = []
                    for k, v in self.typevars.items():
                        if atype == v.type:
                            lst.append(k)
                    returns = {}
                    for x in reversed(lst):
                        for block in self.func_ir.blocks.values():
                            for instr in block.find_insts(ir.Return):
                                value = instr.value
                                if isinstance(value, ir.Var):
                                    name = value.name
                                else:
                                    pass
                                if x == name:
                                    returns[x] = instr
                                    break

                    interped = ""
                    for name, offender in returns.items():
                        loc = getattr(offender, 'loc', ir.unknown_loc)
                        msg = ("Return of: IR name '%s', type '%s', "
                               "location: %s")
                        interped = msg % (name, atype, loc.strformat())
                    return interped

                problem_str = []
                for xtype in rettypes:
                    problem_str.append(_termcolor.errmsg(check_type(xtype)))

                raise TypingError("Can't unify return type from the "
                                  "following types: %s"
                                  % ", ".join(sorted(map(str, rettypes))) +
                                  "\n" + "\n".join(problem_str))
            return unified
        else:
            # Function without a successful return path
            return types.none

    def get_return_type(self, typemap):
        rettypes = set()
        for var in self._get_return_vars():
            rettypes.add(typemap[var.name])
        retty = self._unify_return_types(rettypes)
        # Check return value is not undefined
        if retty is types._undef_var:
            raise TypingError("return value is undefined")
        return retty

    def get_state_token(self):
        """The algorithm is monotonic.  It can only grow or "refine" the
        typevar map.
        """
        return [tv.type for name, tv in sorted(self.typevars.items())]

    def constrain_statement(self, inst):
        if isinstance(inst, ir.Assign):
            self.typeof_assign(inst)
        elif isinstance(inst, ir.SetItem):
            self.typeof_setitem(inst)
        elif isinstance(inst, ir.StaticSetItem):
            self.typeof_static_setitem(inst)
        elif isinstance(inst, ir.DelItem):
            self.typeof_delitem(inst)
        elif isinstance(inst, ir.SetAttr):
            self.typeof_setattr(inst)
        elif isinstance(inst, ir.Print):
            self.typeof_print(inst)
        elif isinstance(inst, ir.StoreMap):
            self.typeof_storemap(inst)
        elif isinstance(inst, (ir.Jump, ir.Branch, ir.Return, ir.Del)):
            pass
        elif isinstance(inst, (ir.DynamicRaise, ir.DynamicTryRaise)):
            pass
        elif isinstance(inst, (ir.StaticRaise, ir.StaticTryRaise)):
            pass
        elif isinstance(inst, ir.PopBlock):
            pass # It's a marker statement
        elif type(inst) in typeinfer_extensions:
            # let external calls handle stmt if type matches
            f = typeinfer_extensions[type(inst)]
            f(inst, self)
        else:
            msg = "Unsupported constraint encountered: %s" % inst
            raise UnsupportedError(msg, loc=inst.loc)

    def typeof_setitem(self, inst):
        constraint = SetItemConstraint(target=inst.target, index=inst.index,
                                       value=inst.value, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_storemap(self, inst):
        constraint = SetItemConstraint(target=inst.dct, index=inst.key,
                                       value=inst.value, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_static_setitem(self, inst):
        constraint = StaticSetItemConstraint(target=inst.target,
                                             index=inst.index,
                                             index_var=inst.index_var,
                                             value=inst.value, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_delitem(self, inst):
        constraint = DelItemConstraint(target=inst.target, index=inst.index,
                                       loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_setattr(self, inst):
        constraint = SetAttrConstraint(target=inst.target, attr=inst.attr,
                                       value=inst.value, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_print(self, inst):
        constraint = PrintConstraint(args=inst.args, vararg=inst.vararg,
                                     loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst, constraint))

    def typeof_assign(self, inst):
        value = inst.value
        if isinstance(value, ir.Const):
            self.typeof_const(inst, inst.target, value.value)
        elif isinstance(value, ir.Var):
            self.constraints.append(Propagate(dst=inst.target.name,
                                              src=value.name, loc=inst.loc))
        elif isinstance(value, (ir.Global, ir.FreeVar)):
            self.typeof_global(inst, inst.target, value)
        elif isinstance(value, ir.Arg):
            self.typeof_arg(inst, inst.target, value)
        elif isinstance(value, ir.Expr):
            self.typeof_expr(inst, inst.target, value)
        elif isinstance(value, ir.Yield):
            self.typeof_yield(inst, inst.target, value)
        else:
            msg = ("Unsupported assignment encountered: %s %s" %
                   (type(value), str(value)))
            raise UnsupportedError(msg, loc=inst.loc)

    def resolve_value_type(self, inst, val):
        """
        Resolve the type of a simple Python value, such as can be
        represented by literals.
        """
        try:
            return self.context.resolve_value_type(val)
        except ValueError as e:
            msg = str(e)
        raise TypingError(msg, loc=inst.loc)

    def typeof_arg(self, inst, target, arg):
        src_name = self._mangle_arg_name(arg.name)
        self.constraints.append(ArgConstraint(dst=target.name,
                                              src=src_name,
                                              loc=inst.loc))

    def typeof_const(self, inst, target, const):
        ty = self.resolve_value_type(inst, const)
        if inst.value.use_literal_type:
            lit = types.maybe_literal(value=const)
        else:
            lit = None
        self.add_type(target.name, lit or ty, loc=inst.loc)

    def typeof_yield(self, inst, target, yield_):
        # Sending values into generators isn't supported.
        self.add_type(target.name, types.none, loc=inst.loc)

    def sentry_modified_builtin(self, inst, gvar):
        """
        Ensure that builtins are not modified.
        """
        if gvar.name == 'range' and gvar.value is not range:
            bad = True
        elif gvar.name == 'slice' and gvar.value is not slice:
            bad = True
        elif gvar.name == 'len' and gvar.value is not len:
            bad = True
        else:
            bad = False

        if bad:
            raise TypingError("Modified builtin '%s'" % gvar.name,
                              loc=inst.loc)

    def resolve_call(self, fnty, pos_args, kw_args):
        """
        Resolve a call to a given function type.  A signature is returned.
        """
        if isinstance(fnty, types.FunctionType):
            return fnty.get_call_type(self, pos_args, kw_args)
        if isinstance(fnty, types.RecursiveCall) and not self._skip_recursion:
            # Recursive call
            disp = fnty.dispatcher_type.dispatcher
            pysig, args = disp.fold_argument_types(pos_args, kw_args)

            frame = self.context.callstack.match(disp.py_func, args)

            # If the signature is not being compiled
            if frame is None:
                sig = self.context.resolve_function_type(fnty.dispatcher_type,
                                                         pos_args, kw_args)
                fndesc = disp.overloads[args].fndesc
                qual = qualifying_prefix(fndesc.modname, fndesc.qualname)
                fnty.add_overloads(args, qual, fndesc.uid)
                return sig

            fnid = frame.func_id
            qual = qualifying_prefix(fnid.modname, fnid.func_qualname)
            fnty.add_overloads(args, qual, fnid.unique_id)
            # Resume propagation in parent frame
            return_type = frame.typeinfer.return_types_from_partial()
            # No known return type
            if return_type is None:
                raise TypingError("cannot type infer runaway recursion")

            sig = typing.signature(return_type, *args)
            sig = sig.replace(pysig=pysig)
            # Keep track of unique return_type
            frame.add_return_type(return_type)
            return sig
        else:
            # Normal non-recursive call
            return self.context.resolve_function_type(fnty, pos_args, kw_args)

    def typeof_global(self, inst, target, gvar):
        try:
            typ = self.resolve_value_type(inst, gvar.value)
        except TypingError as e:
            if (gvar.name == self.func_id.func_name
                    and gvar.name in _temporary_dispatcher_map):
                # Self-recursion case where the dispatcher is not (yet?) known
                # as a global variable
                typ = types.Dispatcher(_temporary_dispatcher_map[gvar.name])
            else:
                from numba.misc import special

                nm = gvar.name
                # check if the problem is actually a name error
                func_glbls = self.func_id.func.__globals__
                if (nm not in func_glbls.keys() and
                        nm not in special.__all__ and
                        nm not in __builtins__.keys() and
                        nm not in self.func_id.code.co_freevars):
                    errstr = "NameError: name '%s' is not defined"
                    msg = _termcolor.errmsg(errstr % nm)
                    e.patch_message(msg)
                    raise
                else:
                    msg = _termcolor.errmsg("Untyped global name '%s':" % nm)
                msg += " %s"  # interps the actual error

                # if the untyped global is a numba internal function then add
                # to the error message asking if it's been imported.

                if nm in special.__all__:
                    tmp = ("\n'%s' looks like a Numba internal function, has "
                           "it been imported (i.e. 'from numba import %s')?\n" %
                           (nm, nm))
                    msg += _termcolor.errmsg(tmp)
                e.patch_message(msg % e)
                raise

        if isinstance(typ, types.Dispatcher) and typ.dispatcher.is_compiling:
            # Recursive call
            callstack = self.context.callstack
            callframe = callstack.findfirst(typ.dispatcher.py_func)
            if callframe is not None:
                typ = types.RecursiveCall(typ)
            else:
                raise NotImplementedError(
                    "call to %s: unsupported recursion"
                    % typ.dispatcher)

        if isinstance(typ, types.Array):
            # Global array in nopython mode is constant
            typ = typ.copy(readonly=True)

        if isinstance(typ, types.BaseAnonymousTuple):
            # if it's a tuple of literal types, swap the type for the more
            # specific literal version
            literaled = [types.maybe_literal(x) for x in gvar.value]
            if all(literaled):
                typ = types.Tuple(literaled)

            # if any of the items in the tuple are arrays, they need to be
            # typed as readonly, mutating an array in a global container
            # is not supported (should be compile time constant etc).
            def mark_array_ro(tup):
                newtup = []
                for item in tup.types:
                    if isinstance(item, types.Array):
                        item = item.copy(readonly=True)
                    elif isinstance(item, types.BaseAnonymousTuple):
                        item = mark_array_ro(item)
                    newtup.append(item)
                return types.BaseTuple.from_types(newtup)
            typ = mark_array_ro(typ)

        self.sentry_modified_builtin(inst, gvar)
        # Setting literal_value for globals because they are handled
        # like const value in numba
        lit = types.maybe_literal(gvar.value)
        # The user may have provided the type for this variable already.
        # In this case, call add_type() to make sure the value type is
        # consistent. See numba.tests.test_array_reductions
        # TestArrayReductions.test_array_cumsum for examples.
        # Variable type locked by using the locals dict.
        tv = self.typevars[target.name]
        if tv.locked:
            tv.add_type(lit or typ, loc=inst.loc)
        else:
            self.lock_type(target.name, lit or typ, loc=inst.loc)
        self.assumed_immutables.add(inst)

    def typeof_expr(self, inst, target, expr):
        if expr.op == 'call':
            self.typeof_call(inst, target, expr)
        elif expr.op in ('getiter', 'iternext'):
            self.typeof_intrinsic_call(inst, target, expr.op, expr.value)
        elif expr.op == 'exhaust_iter':
            constraint = ExhaustIterConstraint(target.name, count=expr.count,
                                               iterator=expr.value,
                                               loc=expr.loc)
            self.constraints.append(constraint)
        elif expr.op == 'pair_first':
            constraint = PairFirstConstraint(target.name, pair=expr.value,
                                             loc=expr.loc)
            self.constraints.append(constraint)
        elif expr.op == 'pair_second':
            constraint = PairSecondConstraint(target.name, pair=expr.value,
                                              loc=expr.loc)
            self.constraints.append(constraint)
        elif expr.op == 'binop':
            self.typeof_intrinsic_call(inst, target, expr.fn, expr.lhs,
                                       expr.rhs)
        elif expr.op == 'inplace_binop':
            self.typeof_intrinsic_call(inst, target, expr.fn,
                                       expr.lhs, expr.rhs)
        elif expr.op == 'unary':
            self.typeof_intrinsic_call(inst, target, expr.fn, expr.value)
        elif expr.op == 'static_getitem':
            constraint = StaticGetItemConstraint(target.name, value=expr.value,
                                                 index=expr.index,
                                                 index_var=expr.index_var,
                                                 loc=expr.loc)
            self.constraints.append(constraint)
            self.calls.append((inst.value, constraint))
        elif expr.op == 'getitem':
            self.typeof_intrinsic_call(inst, target, operator.getitem,
                                       expr.value, expr.index,)
        elif expr.op == 'typed_getitem':
            constraint = TypedGetItemConstraint(target.name, value=expr.value,
                                                dtype=expr.dtype,
                                                index=expr.index,
                                                loc=expr.loc)
            self.constraints.append(constraint)
            self.calls.append((inst.value, constraint))

        elif expr.op == 'getattr':
            constraint = GetAttrConstraint(target.name, attr=expr.attr,
                                           value=expr.value, loc=inst.loc,
                                           inst=inst)
            self.constraints.append(constraint)
        elif expr.op == 'build_tuple':
            constraint = BuildTupleConstraint(target.name, items=expr.items,
                                              loc=inst.loc)
            self.constraints.append(constraint)
        elif expr.op == 'build_list':
            constraint = BuildListConstraint(target.name, items=expr.items,
                                             loc=inst.loc)
            self.constraints.append(constraint)
        elif expr.op == 'build_set':
            constraint = BuildSetConstraint(target.name, items=expr.items,
                                            loc=inst.loc)
            self.constraints.append(constraint)
        elif expr.op == 'build_map':
            constraint = BuildMapConstraint(
                target.name,
                items=expr.items,
                special_value=expr.literal_value,
                value_indexes=expr.value_indexes,
                loc=inst.loc)
            self.constraints.append(constraint)
        elif expr.op == 'cast':
            self.constraints.append(Propagate(dst=target.name,
                                              src=expr.value.name,
                                              loc=inst.loc))
        elif expr.op == 'phi':
            for iv in expr.incoming_values:
                if iv is not ir.UNDEFINED:
                    self.constraints.append(Propagate(dst=target.name,
                                                      src=iv.name,
                                                      loc=inst.loc))
        elif expr.op == 'make_function':
            self.lock_type(target.name, types.MakeFunctionLiteral(expr),
                           loc=inst.loc, literal_value=expr)

        elif expr.op == 'undef':
            self.add_type(target.name, types._undef_var, loc=inst.loc)

        else:
            msg = "Unsupported op-code encountered: %s" % expr
            raise UnsupportedError(msg, loc=inst.loc)

    def typeof_call(self, inst, target, call):
        constraint = CallConstraint(target.name, call.func.name, call.args,
                                    call.kws, call.vararg, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst.value, constraint))

    def typeof_intrinsic_call(self, inst, target, func, *args):
        constraint = IntrinsicCallConstraint(target.name, func, args,
                                             kws=(), vararg=None, loc=inst.loc)
        self.constraints.append(constraint)
        self.calls.append((inst.value, constraint))


class NullDebug(object):

    def propagate_started(self):
        pass

    def propagate_finished(self):
        pass

    def unify_finished(self, typdict, retty, fntys):
        pass


class TypeInferDebug(object):

    def __init__(self, typeinfer):
        self.typeinfer = typeinfer

    def _dump_state(self):
        print('---- type variables ----')
        pprint([v for k, v in sorted(self.typeinfer.typevars.items())])

    def propagate_started(self):
        print("propagate".center(80, '-'))

    def propagate_finished(self):
        self._dump_state()

    def unify_finished(self, typdict, retty, fntys):
        print("Variable types".center(80, "-"))
        pprint(typdict)
        print("Return type".center(80, "-"))
        pprint(retty)
        print("Call types".center(80, "-"))
        pprint(fntys)