typelimits.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
#########################
# limitation parameters #
#########################
const MAX_TYPEUNION_COMPLEXITY = 3
const MAX_TYPEUNION_LENGTH = 3
const MAX_INLINE_CONST_SIZE = 256
#########################
# limitation heuristics #
#########################
# limit the complexity of type `t` to be simpler than the comparison type `compare`
# no new values may be introduced, so the parameter `source` encodes the set of all values already present
# the outermost tuple type is permitted to have up to `allowed_tuplelen` parameters
function limit_type_size(@nospecialize(t), @nospecialize(compare), @nospecialize(source), allowed_tupledepth::Int, allowed_tuplelen::Int)
source = svec(unwrap_unionall(compare), unwrap_unionall(source))
source[1] === source[2] && (source = svec(source[1]))
type_more_complex(t, compare, source, 1, allowed_tupledepth, allowed_tuplelen) || return t
r = _limit_type_size(t, compare, source, 1, allowed_tuplelen)
#@assert t <: r # this may fail if t contains a typevar in invariant and multiple times
# in covariant position and r looses the occurrence in invariant position (see #36407)
if !(t <: r) # ideally, this should never happen
# widen to minimum complexity to obtain a valid result
r = _limit_type_size(t, Any, source, 1, allowed_tuplelen)
t <: r || (r = Any) # final escape hatch
end
#@assert r === _limit_type_size(r, t, source) # this monotonicity constraint is slightly stronger than actually required,
# since we only actually need to demonstrate that repeated application would reaches a fixed point,
#not that it is already at the fixed point
return r
end
# try to find `type` somewhere in `comparison` type
# at a minimum nesting depth of `mindepth`
function is_derived_type(@nospecialize(t), @nospecialize(c), mindepth::Int)
if t === c
return mindepth <= 1
end
isvarargtype(t) && (t = unwrapva(t))
isvarargtype(c) && (c = unwrapva(c))
if isa(c, Union)
# see if it is one of the elements of the union
return is_derived_type(t, c.a, mindepth) || is_derived_type(t, c.b, mindepth)
elseif isa(c, UnionAll)
# see if it is derived from the body
# also handle the var here, since this construct bounds the mindepth to the smallest possible value
return is_derived_type(t, c.var.ub, mindepth) || is_derived_type(t, c.body, mindepth)
elseif isa(c, DataType)
if mindepth > 0
mindepth -= 1
end
if isa(t, DataType)
# see if it is one of the supertypes of a parameter
super = supertype(c)
while super !== Any
t === super && return true
super = supertype(super)
end
end
# see if it was extracted from a type parameter
cP = c.parameters
for p in cP
is_derived_type(t, p, mindepth) && return true
end
end
return false
end
function is_derived_type_from_any(@nospecialize(t), sources::SimpleVector, mindepth::Int)
for s in sources
is_derived_type(t, s, mindepth) && return true
end
return false
end
# The goal of this function is to return a type of greater "size" and less "complexity" than
# both `t` or `c` over the lattice defined by `sources`, `depth`, and `allowed_tuplelen`.
function _limit_type_size(@nospecialize(t), @nospecialize(c), sources::SimpleVector, depth::Int, allowed_tuplelen::Int)
@assert isa(t, Type) && isa(c, Type) "unhandled TypeVar / Vararg"
if t === c
return t # quick egal test
elseif t === Union{}
return t # easy case
elseif isa(t, DataType) && isempty(t.parameters)
return t # fast path: unparameterized are always simple
else
ut = unwrap_unionall(t)
if isa(ut, DataType) && isa(c, Type) && c !== Union{} && c <: t
# TODO: need to check that the UnionAll bounds on t are limited enough too
return t # t is already wider than the comparison in the type lattice
elseif is_derived_type_from_any(ut, sources, depth)
return t # t isn't something new
end
end
# peel off (and ignore) wrappers - they contribute no useful information, so we don't need to consider their size
# first attempt to turn `c` into a type that contributes meaningful information
# by peeling off meaningless non-matching wrappers of comparison one at a time
# then unwrap `t`
# NOTE that `TypeVar` / `Vararg` are handled separately to catch the logic errors
if isa(c, UnionAll)
return __limit_type_size(t, c.body, sources, depth, allowed_tuplelen)::Type
end
if isa(t, UnionAll)
tbody = __limit_type_size(t.body, c, sources, depth, allowed_tuplelen)
tbody === t.body && return t
return UnionAll(t.var, tbody)::Type
elseif isa(t, Union)
if isa(c, Union)
a = __limit_type_size(t.a, c.a, sources, depth, allowed_tuplelen)
b = __limit_type_size(t.b, c.b, sources, depth, allowed_tuplelen)
return Union{a, b}
end
elseif isa(t, DataType)
if isType(t) # see equivalent case in type_more_complex
tt = unwrap_unionall(t.parameters[1])
if isa(tt, Union) || isa(tt, TypeVar) || isType(tt)
is_derived_type_from_any(tt, sources, depth + 1) && return t
else
isType(c) && (c = unwrap_unionall(c.parameters[1]))
type_more_complex(tt, c, sources, depth, 0, 0) || return t
end
return Type
elseif isa(c, DataType)
tP = t.parameters
cP = c.parameters
if t.name === c.name && !isempty(cP)
if t.name === Tuple.name
# for covariant datatypes (Tuple),
# apply type-size limit element-wise
ltP = length(tP)
lcP = length(cP)
np = min(ltP, max(lcP, allowed_tuplelen))
Q = Any[ tP[i] for i in 1:np ]
if ltP > np
# combine tp[np:end] into tP[np] using Vararg
Q[np] = tuple_tail_elem(Bottom, Any[ tP[i] for i in np:ltP ])
end
for i = 1:np
# now apply limit element-wise to Q
# padding out the comparison as needed to allowed_tuplelen elements
if i <= lcP
cPi = cP[i]
elseif isvarargtype(cP[lcP])
cPi = cP[lcP]
else
cPi = Any
end
Q[i] = __limit_type_size(Q[i], cPi, sources, depth + 1, 0)
end
return Tuple{Q...}
end
end
end
if allowed_tuplelen < 1 && t.name === Tuple.name
return Any
end
widert = t.name.wrapper
if !(t <: widert)
# This can happen when a typevar has bounds too wide for its context, e.g.
# `Complex{T} where T` is not a subtype of `Complex`. In that case widen even
# faster to something safe to ensure the result is a supertype of the input.
return Any
end
return widert
end
return Any
end
# helper function of `_limit_type_size`, which has the right to take and return `TypeVar` / `Vararg`
function __limit_type_size(@nospecialize(t), @nospecialize(c), sources::SimpleVector, depth::Int, allowed_tuplelen::Int)
cN = 0
if isvarargtype(c) # Tuple{Vararg{T}} --> Tuple{T} is OK
isdefined(c, :N) && (cN = c.N)
c = unwrapva(c)
end
if isa(c, TypeVar)
if isa(t, TypeVar) && t.ub === c.ub && (t.lb === Union{} || t.lb === c.lb)
return t # it's ok to change the name, or widen `lb` to Union{}, so we can handle this immediately here
end
return __limit_type_size(t, c.ub, sources, depth, allowed_tuplelen)
elseif isa(t, TypeVar)
# don't have a matching TypeVar in comparison, so we keep just the upper bound
return __limit_type_size(t.ub, c, sources, depth, allowed_tuplelen)
elseif isvarargtype(t)
# Tuple{Vararg{T,N}} --> Tuple{Vararg{S,M}} is OK
# Tuple{T} --> Tuple{Vararg{T}} is OK
# but S must be more limited than T, and must not introduce a new number for M
VaT = __limit_type_size(unwrapva(t), c, sources, depth + 1, 0)
if isdefined(t, :N)
tN = t.N
if isa(tN, TypeVar) || tN === cN
return Vararg{VaT, tN}
end
end
return Vararg{VaT}
else
return _limit_type_size(t, c, sources, depth, allowed_tuplelen)
end
end
function type_more_complex(@nospecialize(t), @nospecialize(c), sources::SimpleVector, depth::Int, tupledepth::Int, allowed_tuplelen::Int)
# detect cases where the comparison is trivial
if t === c
return false
elseif t === Union{}
return false # Bottom is as simple as they come
elseif isa(t, DataType) && isempty(t.parameters)
return false # fastpath: unparameterized types are always finite
elseif tupledepth > 0 && isa(unwrap_unionall(t), DataType) && isa(c, Type) && c !== Union{} && c <: t
# TODO: need to check that the UnionAll bounds on t are limited enough too
return false # t is already wider than the comparison in the type lattice
elseif tupledepth > 0 && is_derived_type_from_any(unwrap_unionall(t), sources, depth)
return false # t isn't something new
end
# peel off wrappers
isvarargtype(t) && (t = unwrapva(t))
isvarargtype(c) && (c = unwrapva(c))
if isa(c, UnionAll)
# allow wrapping type with fewer UnionAlls than comparison if in a covariant context
if !isa(t, UnionAll) && tupledepth == 0
return true
end
t = unwrap_unionall(t)
c = unwrap_unionall(c)
end
# rules for various comparison types
if isa(c, TypeVar)
tupledepth = 1 # allow replacing a TypeVar with a concrete value (since we know the UnionAll must be in covariant position)
if isa(t, TypeVar)
return !(t.lb === Union{} || t.lb === c.lb) || # simplify lb towards Union{}
type_more_complex(t.ub, c.ub, sources, depth + 1, tupledepth, 0)
end
c.lb === Union{} || return true
return type_more_complex(t, c.ub, sources, depth, tupledepth, 0)
elseif isa(c, Union)
if isa(t, Union)
return type_more_complex(t.a, c.a, sources, depth, tupledepth, allowed_tuplelen) ||
type_more_complex(t.b, c.b, sources, depth, tupledepth, allowed_tuplelen)
end
return type_more_complex(t, c.a, sources, depth, tupledepth, allowed_tuplelen) &&
type_more_complex(t, c.b, sources, depth, tupledepth, allowed_tuplelen)
elseif isa(t, Int) && isa(c, Int)
return t !== 1 && !(0 <= t < c) # alternatively, could use !(abs(t) <= abs(c) || abs(t) < n) for some n
end
# base case for data types
if isa(t, DataType)
tP = t.parameters
if isType(t)
# Treat Type{T} and T as equivalent to allow taking typeof any
# source type (DataType) anywhere as Type{...}, as long as it isn't
# nesting as Type{Type{...}}
tt = unwrap_unionall(t.parameters[1])
if isa(tt, Union) || isa(tt, TypeVar) || isType(tt)
return !is_derived_type_from_any(tt, sources, depth + 1)
else
isType(c) && (c = unwrap_unionall(c.parameters[1]))
return type_more_complex(tt, c, sources, depth, 0, 0)
end
elseif isa(c, DataType) && t.name === c.name
cP = c.parameters
length(cP) < length(tP) && return true
length(cP) > length(tP) && !isvarargtype(tP[end]) && depth == 1 && return false
ntail = length(cP) - length(tP) # assume parameters were dropped from the tuple head
# allow creating variation within a nested tuple, but only so deep
if t.name === Tuple.name && tupledepth > 0
tupledepth -= 1
else
tupledepth = 0
end
isgenerator = (t.name.name === :Generator && t.name.module === _topmod(t.name.module))
for i = 1:length(tP)
tPi = tP[i]
cPi = cP[i + ntail]
if isgenerator
let tPi = unwrap_unionall(tPi),
cPi = unwrap_unionall(cPi)
if isa(tPi, DataType) && isa(cPi, DataType) &&
!isabstracttype(tPi) && !isabstracttype(cPi) &&
sym_isless(cPi.name.name, tPi.name.name)
# allow collect on (anonymous) Generators to nest, provided that their functions are appropriately ordered
# TODO: is there a better way?
continue
end
end
end
type_more_complex(tPi, cPi, sources, depth + 1, tupledepth, 0) && return true
end
return false
end
end
return true
end
union_count_abstract(x::Union) = union_count_abstract(x.a) + union_count_abstract(x.b)
union_count_abstract(@nospecialize(x)) = !isdispatchelem(x)
function issimpleenoughtype(@nospecialize t)
t = ignorelimited(t)
return unionlen(t) + union_count_abstract(t) <= MAX_TYPEUNION_LENGTH &&
unioncomplexity(t) <= MAX_TYPEUNION_COMPLEXITY
end
# pick a wider type that contains both typea and typeb,
# with some limits on how "large" it can get,
# but without losing too much precision in common cases
# and also trying to be mostly associative and commutative
function tmerge(@nospecialize(typea), @nospecialize(typeb))
typea === Union{} && return typeb
typeb === Union{} && return typea
suba = typea ⊑ typeb
suba && issimpleenoughtype(typeb) && return typeb
subb = typeb ⊑ typea
suba && subb && return typea
subb && issimpleenoughtype(typea) && return typea
# type-lattice for LimitedAccuracy wrapper
# the merge create a slightly narrower type than needed, but we can't
# represent the precise intersection of causes and don't attempt to
# enumerate some of these cases where we could
if isa(typea, LimitedAccuracy) && isa(typeb, LimitedAccuracy)
if typea.causes ⊆ typeb.causes
causes = typeb.causes
elseif typeb.causes ⊆ typea.causes
causes = typea.causes
else
causes = union!(copy(typea.causes), typeb.causes)
end
return LimitedAccuracy(tmerge(typea.typ, typeb.typ), causes)
elseif isa(typea, LimitedAccuracy)
return LimitedAccuracy(tmerge(typea.typ, typeb), typea.causes)
elseif isa(typeb, LimitedAccuracy)
return LimitedAccuracy(tmerge(typea, typeb.typ), typeb.causes)
end
# type-lattice for MaybeUndef wrapper
if isa(typea, MaybeUndef) || isa(typeb, MaybeUndef)
return MaybeUndef(tmerge(
isa(typea, MaybeUndef) ? typea.typ : typea,
isa(typeb, MaybeUndef) ? typeb.typ : typeb))
end
# type-lattice for Conditional wrapper
if isa(typea, Conditional) && isa(typeb, Const)
if typeb.val === true
typeb = Conditional(typea.var, Any, Union{})
elseif typeb.val === false
typeb = Conditional(typea.var, Union{}, Any)
end
end
if isa(typeb, Conditional) && isa(typea, Const)
if typea.val === true
typea = Conditional(typeb.var, Any, Union{})
elseif typea.val === false
typea = Conditional(typeb.var, Union{}, Any)
end
end
if isa(typea, Conditional) && isa(typeb, Conditional)
if is_same_conditionals(typea, typeb)
vtype = tmerge(typea.vtype, typeb.vtype)
elsetype = tmerge(typea.elsetype, typeb.elsetype)
if vtype != elsetype
return Conditional(typea.var, vtype, elsetype)
end
end
val = maybe_extract_const_bool(typea)
if val isa Bool && val === maybe_extract_const_bool(typeb)
return Const(val)
end
return Bool
end
# type-lattice for InterConditional wrapper, InterConditional will never be merged with Conditional
if isa(typea, InterConditional) && isa(typeb, Const)
if typeb.val === true
typeb = InterConditional(typea.slot, Any, Union{})
elseif typeb.val === false
typeb = InterConditional(typea.slot, Union{}, Any)
end
end
if isa(typeb, InterConditional) && isa(typea, Const)
if typea.val === true
typea = InterConditional(typeb.slot, Any, Union{})
elseif typea.val === false
typea = InterConditional(typeb.slot, Union{}, Any)
end
end
if isa(typea, InterConditional) && isa(typeb, InterConditional)
if is_same_conditionals(typea, typeb)
vtype = tmerge(typea.vtype, typeb.vtype)
elsetype = tmerge(typea.elsetype, typeb.elsetype)
if vtype != elsetype
return InterConditional(typea.slot, vtype, elsetype)
end
end
val = maybe_extract_const_bool(typea)
if val isa Bool && val === maybe_extract_const_bool(typeb)
return Const(val)
end
return Bool
end
# type-lattice for Const and PartialStruct wrappers
if (isa(typea, PartialStruct) || isa(typea, Const)) &&
(isa(typeb, PartialStruct) || isa(typeb, Const)) &&
widenconst(typea) === widenconst(typeb)
typea_nfields = nfields_tfunc(typea)
typeb_nfields = nfields_tfunc(typeb)
if !isa(typea_nfields, Const) || !isa(typeb_nfields, Const) || typea_nfields.val !== typeb_nfields.val
return widenconst(typea)
end
type_nfields = typea_nfields.val::Int
fields = Vector{Any}(undef, type_nfields)
anyconst = false
for i = 1:type_nfields
fields[i] = tmerge(getfield_tfunc(typea, Const(i)),
getfield_tfunc(typeb, Const(i)))
anyconst |= has_nontrivial_const_info(fields[i])
end
return anyconst ? PartialStruct(widenconst(typea), fields) :
widenconst(typea)
end
if isa(typea, PartialOpaque) && isa(typeb, PartialOpaque) && widenconst(typea) == widenconst(typeb)
if !(typea.source === typeb.source &&
typea.isva === typeb.isva &&
typea.parent === typeb.parent)
return widenconst(typea)
end
return PartialOpaque(typea.typ, tmerge(typea.env, typeb.env),
typea.isva, typea.parent, typea.source)
end
# no special type-inference lattice, join the types
typea, typeb = widenconst(typea), widenconst(typeb)
if !isa(typea, Type) || !isa(typeb, Type)
# XXX: this should never happen
return Any
end
typea == typeb && return typea
# it's always ok to form a Union of two concrete types
if (isconcretetype(typea) || isType(typea)) && (isconcretetype(typeb) || isType(typeb))
return Union{typea, typeb}
end
# collect the list of types from past tmerge calls returning Union
# and then reduce over that list
types = Any[]
_uniontypes(typea, types)
_uniontypes(typeb, types)
typenames = Vector{Core.TypeName}(undef, length(types))
for i in 1:length(types)
# check that we will be able to analyze (and simplify) everything
# bail if everything isn't a well-formed DataType
ti = types[i]
uw = unwrap_unionall(ti)
(uw isa DataType && ti <: uw.name.wrapper) || return Any
typenames[i] = uw.name
end
u = Union{types...}
if issimpleenoughtype(u)
return u
end
# see if any of the union elements have the same TypeName
# in which case, simplify this tmerge by replacing it with
# the widest possible version of itself (the wrapper)
for i in 1:length(types)
ti = types[i]
for j in (i + 1):length(types)
if typenames[i] === typenames[j]
tj = types[j]
if ti <: tj
types[i] = Union{}
typenames[i] = Any.name
break
elseif tj <: ti
types[j] = Union{}
typenames[j] = Any.name
else
if typenames[i] === Tuple.name
# try to widen Tuple slower: make a single non-concrete Tuple containing both
# converge the Tuple element-wise if they are the same length
# see 4ee2b41552a6bc95465c12ca66146d69b354317b, be59686f7613a2ccfd63491c7b354d0b16a95c05,
widen = tuplemerge(unwrap_unionall(ti)::DataType, unwrap_unionall(tj)::DataType)
widen = rewrap_unionall(rewrap_unionall(widen, ti), tj)
else
wr = typenames[i].wrapper
uw = unwrap_unionall(wr)::DataType
ui = unwrap_unionall(ti)::DataType
uj = unwrap_unionall(tj)::DataType
merged = wr
for k = 1:length(uw.parameters)
ui_k = ui.parameters[k]
if ui_k === uj.parameters[k] && !has_free_typevars(ui_k)
merged = merged{ui_k}
else
merged = merged{uw.parameters[k]}
end
end
widen = rewrap_unionall(merged, wr)
end
types[i] = Union{}
typenames[i] = Any.name
types[j] = widen
break
end
end
end
end
u = Union{types...}
# don't let type unions get too big, if the above didn't reduce it enough
if issimpleenoughtype(u)
return u
end
# don't let the slow widening of Tuple cause the whole type to grow too fast
for i in 1:length(types)
if typenames[i] === Tuple.name
widen = unwrap_unionall(types[i])
if isa(widen, DataType) && !isvatuple(widen)
widen = NTuple{length(widen.parameters), Any}
else
widen = Tuple
end
types[i] = widen
u = Union{types...}
if issimpleenoughtype(u)
return u
end
break
end
end
# finally, just return the widest possible type
return Any
end
# the inverse of switchtupleunion, with limits on max element union size
function tuplemerge(a::DataType, b::DataType)
@assert a.name === b.name === Tuple.name "assertion failure"
ap, bp = a.parameters, b.parameters
lar = length(ap)::Int
lbr = length(bp)::Int
va = lar > 0 && isvarargtype(ap[lar])
vb = lbr > 0 && isvarargtype(bp[lbr])
if lar == lbr && !va && !vb
lt = lar
vt = false
else
lt = 0 # or min(lar - va, lbr - vb)
vt = true
end
# combine the common elements
p = Vector{Any}(undef, lt + vt)
for i = 1:lt
ui = Union{ap[i], bp[i]}
p[i] = issimpleenoughtype(ui) ? ui : Any
end
# merge the remaining tail into a single, simple Tuple{Vararg{T}} (#22120)
if vt
tail = Union{}
for loop_b = (false, true)
for i = (lt + 1):(loop_b ? lbr : lar)
ti = unwrapva(loop_b ? bp[i] : ap[i])
while ti isa TypeVar
ti = ti.ub
end
# compare (ti <-> tail), (wrapper ti <-> tail), (ti <-> wrapper tail), then (wrapper ti <-> wrapper tail)
# until we find the first element that contains the other in the pair
# TODO: this result would be more stable (and more associative and more commutative)
# if we either joined all of the element wrappers first into a wide-tail, then picked between that or an exact tail,
# or (equivalently?) iteratively took super-types until reaching a common wrapper
# e.g. consider the results of `tuplemerge(Tuple{Complex}, Tuple{Number, Int})` and of
# `tuplemerge(Tuple{Int}, Tuple{String}, Tuple{Int, String})`
if !(ti <: tail)
if tail <: ti
tail = ti # widen to ti
else
uw = unwrap_unionall(tail)
if uw isa DataType && tail <: uw.name.wrapper
# widen tail to wrapper(tail)
tail = uw.name.wrapper
if !(ti <: tail)
#assert !(tail <: ti)
uw = unwrap_unionall(ti)
if uw isa DataType && ti <: uw.name.wrapper
# widen ti to wrapper(ti)
ti = uw.name.wrapper
#assert !(ti <: tail)
if tail <: ti
tail = ti
else
tail = Any # couldn't find common super-type
end
else
tail = Any # couldn't analyze type
end
end
else
tail = Any # couldn't analyze type
end
end
end
tail === Any && return Tuple # short-circuit loop
end
end
@assert !(tail === Union{})
p[lt + 1] = Vararg{tail}
end
return Tuple{p...}
end
# compute typeintersect over the extended inference lattice
# where v is in the extended lattice, and t is a Type
function tmeet(@nospecialize(v), @nospecialize(t))
if isa(v, Const)
if !has_free_typevars(t) && !isa(v.val, t)
return Bottom
end
return v
elseif isa(v, PartialStruct)
has_free_typevars(t) && return v
widev = widenconst(v)
if widev <: t
return v
end
ti = typeintersect(widev, t)
if ti === Bottom
return Bottom
end
@assert widev <: Tuple
new_fields = Vector{Any}(undef, length(v.fields))
for i = 1:length(new_fields)
vfi = v.fields[i]
if isvarargtype(vfi)
new_fields[i] = vfi
else
new_fields[i] = tmeet(vfi, widenconst(getfield_tfunc(t, Const(i))))
if new_fields[i] === Bottom
return Bottom
end
end
end
return tuple_tfunc(new_fields)
elseif isa(v, Conditional)
if !(Bool <: t)
return Bottom
end
return v
end
return typeintersect(widenconst(v), t)
end