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subtype.c
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// This file is a part of Julia. License is MIT: https://julialang.org/license
/*
subtyping predicate
Uses the algorithm described in section 4.2.2 of https://github.com/JeffBezanson/phdthesis/
This code adds the following features to the core algorithm:
- Type variables can be restricted to range over only concrete types.
This is done by returning false if such a variable's lower bound is not concrete.
- Diagonal rule: a type variable is concrete if it occurs more than once in
covariant position, and never in invariant position. This sounds like a syntactic
property, but actually isn't since it depends on which occurrences of a type
variable the algorithm actually uses.
- Unconstrained type vars (Bottom<:T<:Any) can match non-type values.
- Vararg types have an int-valued length parameter N (in `Vararg{T,N}`).
- Type{T}<:S if isa(T,S). Existing code assumes this, but it's not strictly
correct since a type can equal `T` without having the same representation.
- Free type variables are tolerated. This can hopefully be removed after a
deprecation period.
*/
#include <stdlib.h>
#include <string.h>
#ifdef _OS_WINDOWS_
#include <malloc.h>
#endif
#include "julia.h"
#include "julia_internal.h"
#include "julia_assert.h"
#ifdef __cplusplus
extern "C" {
#endif
// stack of bits to keep track of which combination of Union components we are
// looking at (0 for Union.a, 1 for Union.b). forall_exists_subtype and
// exists_subtype loop over all combinations by updating a binary count in
// this structure.
// Union type decision points are discovered while the algorithm works.
// If a new Union decision is encountered, the `more` flag is set to tell
// the forall/exists loop to grow the stack.
// TODO: the stack probably needs to be artificially large because of some
// deeper problem (see #21191) and could be shrunk once that is fixed
typedef struct {
int16_t depth;
int16_t more;
int16_t used;
uint32_t stack[100]; // stack of bits represented as a bit vector
} jl_unionstate_t;
typedef struct {
int16_t depth;
int16_t more;
int16_t used;
void *stack;
} jl_saved_unionstate_t;
// Linked list storing the type variable environment. A new jl_varbinding_t
// is pushed for each UnionAll type we encounter. `lb` and `ub` are updated
// during the computation.
// Most of the complexity is due to the "diagonal rule", requiring us to
// identify which type vars range over only concrete types.
typedef struct jl_varbinding_t {
jl_tvar_t *var;
jl_value_t *lb;
jl_value_t *ub;
int8_t right; // whether this variable came from the right side of `A <: B`
int8_t occurs_inv; // occurs in invariant position
int8_t occurs_cov; // # of occurrences in covariant position
int8_t concrete; // 1 if another variable has a constraint forcing this one to be concrete
// constraintkind: in covariant position, we try three different ways to compute var ∩ type:
// let ub = var.ub ∩ type
// 0 - var.ub <: type ? var : ub
// 1 - var.ub = ub; return var
// 2 - either (var.ub = ub; return var), or return ub
int8_t constraintkind;
// intvalued: must be integer-valued; i.e. occurs as N in Vararg{_,N}
// 0: No restriction
// 1: must be unbounded/ or fixed to a `Int`/typevar
// 2: we have some imprecise vararg length intersection that can be improved if this var is const valued.
int8_t intvalued;
int8_t limited;
int16_t depth0; // # of invariant constructors nested around the UnionAll type for this var
// when this variable's integer value is compared to that of another,
// it equals `other + offset`. used by vararg length parameters.
int16_t offset;
// array of typevars that our bounds depend on, whose UnionAlls need to be
// moved outside ours.
jl_array_t *innervars;
struct jl_varbinding_t *prev;
} jl_varbinding_t;
// subtype algorithm state
typedef struct jl_stenv_t {
// N.B.: varbindings are created on the stack and rooted there
jl_varbinding_t *vars; // type variable environment
jl_unionstate_t Lunions; // union state for unions on the left of A <: B
jl_unionstate_t Runions; // union state for unions on the right
// N.B.: envout is gc-rooted
jl_value_t **envout; // for passing caller the computed bounds of right-side variables
int envsz; // length of envout
int envidx; // current index in envout
int invdepth; // # of invariant constructors we're nested in on the left
int Rinvdepth; // # of invariant constructors we're nested in on the right
int ignore_free; // treat free vars as black boxes; used during intersection
int intersection; // true iff subtype is being called from intersection
int emptiness_only; // true iff intersection only needs to test for emptiness
int triangular; // when intersecting Ref{X} with Ref{<:Y}
} jl_stenv_t;
// state manipulation utilities
// look up a type variable in an environment
#ifdef __clang_gcanalyzer__
static jl_varbinding_t *lookup(jl_stenv_t *e, jl_tvar_t *v) JL_GLOBALLY_ROOTED JL_NOTSAFEPOINT;
#else
static jl_varbinding_t *lookup(jl_stenv_t *e, jl_tvar_t *v) JL_GLOBALLY_ROOTED JL_NOTSAFEPOINT
{
jl_varbinding_t *b = e->vars;
while (b != NULL) {
if (b->var == v) return b;
b = b->prev;
}
return b;
}
#endif
static int statestack_get(jl_unionstate_t *st, int i) JL_NOTSAFEPOINT
{
assert(i >= 0 && i < sizeof(st->stack) * 8);
// get the `i`th bit in an array of 32-bit words
return (st->stack[i>>5] & (1u<<(i&31))) != 0;
}
static void statestack_set(jl_unionstate_t *st, int i, int val) JL_NOTSAFEPOINT
{
assert(i >= 0 && i < sizeof(st->stack) * 8);
if (val)
st->stack[i>>5] |= (1u<<(i&31));
else
st->stack[i>>5] &= ~(1u<<(i&31));
}
#define push_unionstate(saved, src) \
do { \
(saved)->depth = (src)->depth; \
(saved)->more = (src)->more; \
(saved)->used = (src)->used; \
(saved)->stack = alloca(((src)->used+7)/8); \
memcpy((saved)->stack, &(src)->stack, ((src)->used+7)/8); \
} while (0);
#define pop_unionstate(dst, saved) \
do { \
(dst)->depth = (saved)->depth; \
(dst)->more = (saved)->more; \
(dst)->used = (saved)->used; \
memcpy(&(dst)->stack, (saved)->stack, ((saved)->used+7)/8); \
} while (0);
typedef struct {
int8_t *buf;
int rdepth;
int8_t _space[16];
} jl_savedenv_t;
static void save_env(jl_stenv_t *e, jl_value_t **root, jl_savedenv_t *se)
{
jl_varbinding_t *v = e->vars;
int len=0;
while (v != NULL) {
len++;
v = v->prev;
}
if (root)
*root = (jl_value_t*)jl_alloc_svec(len * 3);
se->buf = (int8_t*)(len > 8 ? malloc_s(len * 2) : &se->_space);
#ifdef __clang_gcanalyzer__
memset(se->buf, 0, len * 2);
#endif
int i=0, j=0; v = e->vars;
while (v != NULL) {
if (root) {
jl_svecset(*root, i++, v->lb);
jl_svecset(*root, i++, v->ub);
jl_svecset(*root, i++, (jl_value_t*)v->innervars);
}
se->buf[j++] = v->occurs_inv;
se->buf[j++] = v->occurs_cov;
v = v->prev;
}
se->rdepth = e->Runions.depth;
}
static void free_env(jl_savedenv_t *se) JL_NOTSAFEPOINT
{
if (se->buf != se->_space)
free(se->buf);
se->buf = NULL;
}
static void restore_env(jl_stenv_t *e, jl_value_t *root, jl_savedenv_t *se) JL_NOTSAFEPOINT
{
jl_varbinding_t *v = e->vars;
int i = 0, j = 0;
while (v != NULL) {
if (root) v->lb = jl_svecref(root, i++);
if (root) v->ub = jl_svecref(root, i++);
if (root) v->innervars = (jl_array_t*)jl_svecref(root, i++);
v->occurs_inv = se->buf[j++];
v->occurs_cov = se->buf[j++];
v = v->prev;
}
e->Runions.depth = se->rdepth;
if (e->envout && e->envidx < e->envsz)
memset(&e->envout[e->envidx], 0, (e->envsz - e->envidx)*sizeof(void*));
}
static int current_env_length(jl_stenv_t *e)
{
jl_varbinding_t *v = e->vars;
int len = 0;
while (v) {
len++;
v = v->prev;
}
return len;
}
// type utilities
// quickly test that two types are identical
static int obviously_egal(jl_value_t *a, jl_value_t *b)
{
if (a == (jl_value_t*)jl_typeofbottom_type->super)
a = (jl_value_t*)jl_typeofbottom_type; // supertype(typeof(Union{})) is equal to, although distinct from, itself
if (b == (jl_value_t*)jl_typeofbottom_type->super)
b = (jl_value_t*)jl_typeofbottom_type; // supertype(typeof(Union{})) is equal to, although distinct from, itself
if (a == b) return 1;
if (jl_typeof(a) != jl_typeof(b)) return 0;
if (jl_is_datatype(a)) {
jl_datatype_t *ad = (jl_datatype_t*)a;
jl_datatype_t *bd = (jl_datatype_t*)b;
if (ad->name != bd->name) return 0;
if (ad->isconcretetype || bd->isconcretetype) return 0;
size_t i, np = jl_nparams(ad);
if (np != jl_nparams(bd)) return 0;
for (i = 0; i < np; i++) {
if (!obviously_egal(jl_tparam(ad,i), jl_tparam(bd,i)))
return 0;
}
return 1;
}
if (jl_is_uniontype(a)) {
return obviously_egal(((jl_uniontype_t*)a)->a, ((jl_uniontype_t*)b)->a) &&
obviously_egal(((jl_uniontype_t*)a)->b, ((jl_uniontype_t*)b)->b);
}
if (jl_is_unionall(a)) {
return ((jl_unionall_t*)a)->var == ((jl_unionall_t*)b)->var &&
obviously_egal(((jl_unionall_t*)a)->body, ((jl_unionall_t*)b)->body);
}
if (jl_is_vararg(a)) {
jl_vararg_t *vma = (jl_vararg_t *)a;
jl_vararg_t *vmb = (jl_vararg_t *)b;
return obviously_egal(jl_unwrap_vararg(vma), jl_unwrap_vararg(vmb)) &&
((!vma->N && !vmb->N) || (vma->N && vmb->N && obviously_egal(vma->N, vmb->N)));
}
if (jl_is_typevar(a)) return 0;
return !jl_is_type(a) && jl_egal(a,b);
}
static int obviously_unequal(jl_value_t *a, jl_value_t *b)
{
if (a == (jl_value_t*)jl_typeofbottom_type->super)
a = (jl_value_t*)jl_typeofbottom_type; // supertype(typeof(Union{})) is equal to, although distinct from, itself
if (b == (jl_value_t*)jl_typeofbottom_type->super)
b = (jl_value_t*)jl_typeofbottom_type; // supertype(typeof(Union{})) is equal to, although distinct from, itself
if (a == b)
return 0;
if (jl_is_unionall(a))
a = jl_unwrap_unionall(a);
if (jl_is_unionall(b))
b = jl_unwrap_unionall(b);
if (jl_is_datatype(a)) {
if (b == jl_bottom_type)
return 1;
if (jl_is_datatype(b)) {
jl_datatype_t *ad = (jl_datatype_t*)a;
jl_datatype_t *bd = (jl_datatype_t*)b;
if (a == (jl_value_t*)jl_typeofbottom_type && bd->name == jl_type_typename)
return obviously_unequal(jl_bottom_type, jl_tparam(bd, 0));
if (ad->name == jl_type_typename && b == (jl_value_t*)jl_typeofbottom_type)
return obviously_unequal(jl_tparam(ad, 0), jl_bottom_type);
if (ad->name != bd->name)
return 1;
int istuple = (ad->name == jl_tuple_typename);
if ((jl_is_concrete_type(a) || jl_is_concrete_type(b)) &&
jl_type_equality_is_identity(a, b)) {
if (!istuple && ad->name != jl_type_typename) // HACK: can't properly normalize Tuple{Float64} == Tuple{<:Float64} like types or Type{T} types
return 1;
}
size_t i, np;
if (istuple) {
size_t na = jl_nparams(ad), nb = jl_nparams(bd);
if (jl_is_va_tuple(ad)) {
na -= 1;
if (jl_is_va_tuple(bd))
nb -= 1;
}
else if (jl_is_va_tuple(bd)) {
nb -= 1;
}
else if (na != nb) {
return 1;
}
np = na < nb ? na : nb;
}
else {
np = jl_nparams(ad);
if (np != jl_nparams(bd))
return 1;
}
for (i = 0; i < np; i++) {
if (obviously_unequal(jl_tparam(ad, i), jl_tparam(bd, i)))
return 1;
}
}
}
else if (a == jl_bottom_type && jl_is_datatype(b)) {
return 1;
}
if (jl_is_typevar(a) && jl_is_typevar(b) && obviously_unequal(((jl_tvar_t*)a)->ub, ((jl_tvar_t*)b)->ub))
return 1;
if (jl_is_long(a)) {
if (jl_is_long(b) && jl_unbox_long(a) != jl_unbox_long(b))
return 1;
}
else if (jl_is_long(b)) {
return 1;
}
if ((jl_is_symbol(a) || jl_is_symbol(b)) && a != b)
return 1;
return 0;
}
int jl_obviously_unequal(jl_value_t *a, jl_value_t *b)
{
return obviously_unequal(a, b);
}
static int in_union(jl_value_t *u, jl_value_t *x) JL_NOTSAFEPOINT
{
if (u == x) return 1;
if (!jl_is_uniontype(u)) return 0;
return in_union(((jl_uniontype_t*)u)->a, x) || in_union(((jl_uniontype_t*)u)->b, x);
}
int obviously_disjoint(jl_value_t *a, jl_value_t *b, int specificity)
{
if (a == b || a == (jl_value_t*)jl_any_type || b == (jl_value_t*)jl_any_type)
return 0;
if (specificity && a == (jl_value_t*)jl_typeofbottom_type)
return 0;
if (jl_is_concrete_type(a) && jl_is_concrete_type(b) &&
jl_type_equality_is_identity(a, b) &&
(((jl_datatype_t*)a)->name != jl_tuple_typename ||
((jl_datatype_t*)b)->name != jl_tuple_typename))
return 1;
if (jl_is_unionall(a)) a = jl_unwrap_unionall(a);
if (jl_is_unionall(b)) b = jl_unwrap_unionall(b);
if (jl_is_uniontype(a))
return obviously_disjoint(((jl_uniontype_t *)a)->a, b, specificity) &&
obviously_disjoint(((jl_uniontype_t *)a)->b, b, specificity);
if (jl_is_uniontype(b))
return obviously_disjoint(a, ((jl_uniontype_t *)b)->a, specificity) &&
obviously_disjoint(a, ((jl_uniontype_t *)b)->b, specificity);
if (jl_is_datatype(a) && jl_is_datatype(b)) {
jl_datatype_t *ad = (jl_datatype_t*)a, *bd = (jl_datatype_t*)b;
if (ad->name != bd->name) {
jl_datatype_t *temp = ad;
while (temp != jl_any_type && temp->name != bd->name)
temp = temp->super;
if (temp == jl_any_type) {
temp = bd;
while (temp != jl_any_type && temp->name != ad->name)
temp = temp->super;
if (temp == jl_any_type)
return 1;
bd = temp;
}
else {
ad = temp;
}
if (specificity) {
// account for declared subtypes taking priority (issue #21710)
return 0;
}
}
int istuple = (ad->name == jl_tuple_typename);
size_t np;
if (istuple) {
size_t na = jl_nparams(ad), nb = jl_nparams(bd);
if (jl_is_va_tuple(ad)) {
na -= 1;
if (jl_is_va_tuple(bd))
nb -= 1;
}
else if (jl_is_va_tuple(bd)) {
nb -= 1;
}
else if (!specificity && na != nb) {
// note: some disjoint types (e.g. tuples of different lengths) can be more specific
return 1;
}
np = na < nb ? na : nb;
}
else {
np = jl_nparams(ad);
}
size_t i;
for (i = 0; i < np; i++) {
jl_value_t *ai = jl_tparam(ad, i);
jl_value_t *bi = jl_tparam(bd, i);
if (jl_is_typevar(ai) || jl_is_typevar(bi))
continue; // it's possible that Union{} is in this intersection
if (jl_is_type(ai)) {
if (jl_is_type(bi)) {
if (istuple && (ai == jl_bottom_type || bi == jl_bottom_type))
; // TODO: this can return 1 if and when Tuple{Union{}} === Union{}
else if (obviously_disjoint(ai, bi, specificity))
return 1;
}
else if (ai != (jl_value_t*)jl_any_type) {
return 1;
}
}
else if (jl_is_type(bi)) {
if (bi != (jl_value_t*)jl_any_type)
return 1;
}
else if (!jl_egal(ai, bi)) {
return 1;
}
}
}
else if (a == jl_bottom_type || b == jl_bottom_type) {
return 1;
}
return 0;
}
// compute a least upper bound of `a` and `b`
static jl_value_t *simple_join(jl_value_t *a, jl_value_t *b)
{
if (a == jl_bottom_type || b == (jl_value_t*)jl_any_type || obviously_egal(a,b))
return b;
if (b == jl_bottom_type || a == (jl_value_t*)jl_any_type)
return a;
if (!(jl_is_type(a) || jl_is_typevar(a)) || !(jl_is_type(b) || jl_is_typevar(b)))
return (jl_value_t*)jl_any_type;
if (jl_is_uniontype(a) && in_union(a, b))
return a;
if (jl_is_uniontype(b) && in_union(b, a))
return b;
if (jl_is_kind(a) && jl_is_type_type(b) && jl_typeof(jl_tparam0(b)) == a)
return a;
if (jl_is_kind(b) && jl_is_type_type(a) && jl_typeof(jl_tparam0(a)) == b)
return b;
if (jl_is_typevar(a) && obviously_egal(b, ((jl_tvar_t*)a)->lb))
return a;
if (jl_is_typevar(b) && obviously_egal(a, ((jl_tvar_t*)b)->lb))
return b;
if (!jl_has_free_typevars(a) && !jl_has_free_typevars(b) &&
// issue #24521: don't merge Type{T} where typeof(T) varies
!(jl_is_type_type(a) && jl_is_type_type(b) && jl_typeof(jl_tparam0(a)) != jl_typeof(jl_tparam0(b)))) {
if (jl_subtype(a, b)) return b;
if (jl_subtype(b, a)) return a;
}
return jl_new_struct(jl_uniontype_type, a, b);
}
jl_value_t *simple_intersect(jl_value_t *a, jl_value_t *b, int overesi);
// Compute a greatest lower bound of `a` and `b`
// For the subtype path, we need to over-estimate this by returning `b` in many cases.
// But for `merge_env`, we'd better under-estimate and return a `Union{}`
static jl_value_t *simple_meet(jl_value_t *a, jl_value_t *b, int overesi)
{
if (a == (jl_value_t*)jl_any_type || b == jl_bottom_type || obviously_egal(a,b))
return b;
if (b == (jl_value_t*)jl_any_type || a == jl_bottom_type)
return a;
if (!(jl_is_type(a) || jl_is_typevar(a)) || !(jl_is_type(b) || jl_is_typevar(b)))
return jl_bottom_type;
if (jl_is_kind(a) && jl_is_type_type(b) && jl_typeof(jl_tparam0(b)) == a)
return b;
if (jl_is_kind(b) && jl_is_type_type(a) && jl_typeof(jl_tparam0(a)) == b)
return a;
if (jl_is_typevar(a) && obviously_egal(b, ((jl_tvar_t*)a)->ub))
return a;
if (jl_is_typevar(b) && obviously_egal(a, ((jl_tvar_t*)b)->ub))
return b;
return simple_intersect(a, b, overesi);
}
static jl_unionall_t *rename_unionall(jl_unionall_t *u)
{
jl_tvar_t *v = jl_new_typevar(u->var->name, u->var->lb, u->var->ub);
jl_value_t *t = NULL;
JL_GC_PUSH2(&v, &t);
t = jl_instantiate_unionall(u, (jl_value_t*)v);
t = jl_new_struct(jl_unionall_type, v, t);
JL_GC_POP();
return (jl_unionall_t*)t;
}
// main subtyping algorithm
static int subtype(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int param);
static int next_union_state(jl_stenv_t *e, int8_t R) JL_NOTSAFEPOINT
{
jl_unionstate_t *state = R ? &e->Runions : &e->Lunions;
if (state->more == 0)
return 0;
// reset `used` and let `pick_union_decision` clean the stack.
state->used = state->more;
statestack_set(state, state->used - 1, 1);
return 1;
}
static int pick_union_decision(jl_stenv_t *e, int8_t R) JL_NOTSAFEPOINT
{
jl_unionstate_t *state = R ? &e->Runions : &e->Lunions;
if (state->depth >= state->used) {
statestack_set(state, state->used, 0);
state->used++;
}
int ui = statestack_get(state, state->depth);
state->depth++;
if (ui == 0)
state->more = state->depth; // memorize that this was the deepest available choice
return ui;
}
static jl_value_t *pick_union_element(jl_value_t *u JL_PROPAGATES_ROOT, jl_stenv_t *e, int8_t R) JL_NOTSAFEPOINT
{
do {
if (pick_union_decision(e, R))
u = ((jl_uniontype_t*)u)->b;
else
u = ((jl_uniontype_t*)u)->a;
} while (jl_is_uniontype(u));
return u;
}
static int local_forall_exists_subtype(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int param, int limit_slow);
// subtype for variable bounds consistency check. needs its own forall/exists environment.
static int subtype_ccheck(jl_value_t *x, jl_value_t *y, jl_stenv_t *e)
{
if (x == y)
return 1;
if (x == jl_bottom_type && jl_is_type(y))
return 1;
if (y == (jl_value_t*)jl_any_type && jl_is_type(x))
return 1;
if (jl_is_uniontype(x) && jl_egal(x, y))
return 1;
if (x == (jl_value_t*)jl_any_type && jl_is_datatype(y))
return 0;
jl_saved_unionstate_t oldLunions; push_unionstate(&oldLunions, &e->Lunions);
int sub = local_forall_exists_subtype(x, y, e, 0, 1);
pop_unionstate(&e->Lunions, &oldLunions);
return sub;
}
static int subtype_left_var(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int param)
{
if (x == y && !(jl_is_unionall(y)))
return 1;
if (x == jl_bottom_type && jl_is_type(y))
return 1;
if (y == (jl_value_t*)jl_any_type && jl_is_type(x))
return 1;
if (jl_is_uniontype(x) && jl_egal(x, y))
return 1;
if (x == (jl_value_t*)jl_any_type && jl_is_datatype(y))
return 0;
return subtype(x, y, e, param);
}
// use the current context to record where a variable occurred, for the purpose
// of determining whether the variable is concrete.
static void record_var_occurrence(jl_varbinding_t *vb, jl_stenv_t *e, int param) JL_NOTSAFEPOINT
{
if (vb != NULL && param) {
// saturate counters at 2; we don't need values bigger than that
if (param == 2 && (vb->right ? e->Rinvdepth : e->invdepth) > vb->depth0) {
if (vb->occurs_inv < 2)
vb->occurs_inv++;
}
else if (vb->occurs_cov < 2) {
vb->occurs_cov++;
}
}
}
// is var x's quantifier outside y's in nesting order
static int var_outside(jl_stenv_t *e, jl_tvar_t *x, jl_tvar_t *y)
{
jl_varbinding_t *btemp = e->vars;
while (btemp != NULL) {
if (btemp->var == x) return 0;
if (btemp->var == y) return 1;
btemp = btemp->prev;
}
return 0;
}
static jl_value_t *intersect_aside(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int R, int d);
static int reachable_var(jl_value_t *x, jl_tvar_t *y, jl_stenv_t *e);
// check that type var `b` is <: `a`, and update b's upper bound.
static int var_lt(jl_tvar_t *b, jl_value_t *a, jl_stenv_t *e, int param)
{
jl_varbinding_t *bb = lookup(e, b);
if (bb == NULL)
return e->ignore_free || subtype_left_var(b->ub, a, e, param);
record_var_occurrence(bb, e, param);
if (!bb->right) // check ∀b . b<:a
return subtype_left_var(bb->ub, a, e, param);
if (bb->ub == a)
return 1;
if (!((bb->lb == jl_bottom_type && !jl_is_type(a) && !jl_is_typevar(a)) || subtype_ccheck(bb->lb, a, e)))
return 0;
// for this to work we need to compute issub(left,right) before issub(right,left),
// since otherwise the issub(a, bb.ub) check in var_gt becomes vacuous.
if (e->intersection) {
jl_value_t *ub = intersect_aside(bb->ub, a, e, 0, bb->depth0);
JL_GC_PUSH1(&ub);
if (ub != (jl_value_t*)b && (!jl_is_typevar(ub) || !reachable_var(ub, b, e)))
bb->ub = ub;
JL_GC_POP();
}
else {
bb->ub = simple_meet(bb->ub, a, 1);
}
assert(bb->ub != (jl_value_t*)b);
if (jl_is_typevar(a)) {
jl_varbinding_t *aa = lookup(e, (jl_tvar_t*)a);
if (aa && !aa->right && in_union(bb->lb, a) && bb->depth0 != aa->depth0 && var_outside(e, b, (jl_tvar_t*)a)) {
// an "exists" var cannot equal a "forall" var inside it unless the forall
// var has equal bounds.
return subtype_left_var(aa->ub, aa->lb, e, param);
}
}
return 1;
}
// check that type var `b` is >: `a`, and update b's lower bound.
static int var_gt(jl_tvar_t *b, jl_value_t *a, jl_stenv_t *e, int param)
{
jl_varbinding_t *bb = lookup(e, b);
if (bb == NULL)
return e->ignore_free || subtype_left_var(a, b->lb, e, param);
record_var_occurrence(bb, e, param);
if (!bb->right) // check ∀b . b>:a
return subtype_left_var(a, bb->lb, e, param);
if (bb->lb == bb->ub) {
if (jl_is_typevar(bb->lb) && !jl_is_type(a) && !jl_is_typevar(a))
return var_gt((jl_tvar_t*)bb->lb, a, e, param);
if (jl_is_typevar(a) && !jl_is_type(bb->lb) && !jl_is_typevar(bb->lb))
return var_lt((jl_tvar_t*)a, bb->lb, e, param);
}
if (!((bb->ub == (jl_value_t*)jl_any_type && !jl_is_type(a) && !jl_is_typevar(a)) || subtype_ccheck(a, bb->ub, e)))
return 0;
jl_value_t *lb = simple_join(bb->lb, a);
JL_GC_PUSH1(&lb);
if (!e->intersection || !jl_is_typevar(lb) || !reachable_var(lb, b, e))
bb->lb = lb;
JL_GC_POP();
// this bound should not be directly circular
assert(bb->lb != (jl_value_t*)b);
if (jl_is_typevar(a)) {
jl_varbinding_t *aa = lookup(e, (jl_tvar_t*)a);
if (aa && !aa->right && bb->depth0 != aa->depth0 && param == 2 && var_outside(e, b, (jl_tvar_t*)a))
return subtype_left_var(aa->ub, aa->lb, e, param);
}
return 1;
}
// check that a type is concrete or quasi-concrete (Type{T}).
// this is used to check concrete typevars:
// issubtype is false if the lower bound of a concrete type var is not concrete.
static int is_leaf_bound(jl_value_t *v) JL_NOTSAFEPOINT
{
if (v == jl_bottom_type)
return 1;
if (jl_is_datatype(v)) {
if (((jl_datatype_t*)v)->name->abstract) {
if (jl_is_type_type(v))
return 1;//!jl_has_free_typevars(jl_tparam0(v));
return 0;
}
return ((jl_datatype_t*)v)->isconcretetype;
}
return !jl_is_type(v) && !jl_is_typevar(v);
}
static int is_leaf_typevar(jl_tvar_t *v) JL_NOTSAFEPOINT
{
return is_leaf_bound(v->lb);
}
static jl_value_t *widen_Type(jl_value_t *t JL_PROPAGATES_ROOT) JL_NOTSAFEPOINT
{
if (jl_is_type_type(t) && !jl_is_typevar(jl_tparam0(t)))
return jl_typeof(jl_tparam0(t));
if (jl_is_uniontype(t)) {
jl_value_t *a = widen_Type(((jl_uniontype_t*)t)->a);
jl_value_t *b = widen_Type(((jl_uniontype_t*)t)->b);
if (a == b)
return a;
}
return t;
}
// convert a type with free variables to a typevar bounded by a UnionAll-wrapped
// version of that type.
// TODO: This loses some inference precision. For example in a case where a
// variable bound is `Vector{_}`, we could potentially infer `Type{Vector{_}} where _`,
// but this causes us to infer the larger `Type{T} where T<:Vector` instead.
// However this is needed because many contexts check `isa(sp, TypeVar)` to determine
// when a static parameter value is not known exactly.
static jl_value_t *fix_inferred_var_bound(jl_tvar_t *var, jl_value_t *ty JL_MAYBE_UNROOTED)
{
if (!jl_is_typevar(ty) && jl_has_free_typevars(ty)) {
jl_value_t *ans = ty;
jl_array_t *vs = NULL;
JL_GC_PUSH2(&ans, &vs);
vs = jl_find_free_typevars(ty);
int i;
for (i = 0; i < jl_array_len(vs); i++) {
ans = jl_type_unionall((jl_tvar_t*)jl_array_ptr_ref(vs, i), ans);
}
ans = (jl_value_t*)jl_new_typevar(var->name, jl_bottom_type, ans);
JL_GC_POP();
return ans;
}
return ty;
}
static int var_occurs_inside(jl_value_t *v, jl_tvar_t *var, int inside, int want_inv) JL_NOTSAFEPOINT;
typedef int (*tvar_callback)(void*, int8_t, jl_stenv_t *, int);
static int var_occurs_invariant(jl_value_t *v, jl_tvar_t *var, int inv) JL_NOTSAFEPOINT
{
return var_occurs_inside(v, var, 0, 1);
}
static jl_unionall_t *unalias_unionall(jl_unionall_t *u, jl_stenv_t *e)
{
jl_varbinding_t *btemp = e->vars;
// if the var for this unionall (based on identity) already appears somewhere
// in the environment, rename to get a fresh var.
JL_GC_PUSH1(&u);
while (btemp != NULL) {
if (btemp->var == u->var ||
// outer var can only refer to inner var if bounds changed
(btemp->lb != btemp->var->lb && jl_has_typevar(btemp->lb, u->var)) ||
(btemp->ub != btemp->var->ub && jl_has_typevar(btemp->ub, u->var))) {
u = rename_unionall(u);
break;
}
btemp = btemp->prev;
}
JL_GC_POP();
return u;
}
static int subtype_unionall(jl_value_t *t, jl_unionall_t *u, jl_stenv_t *e, int8_t R, int param)
{
u = unalias_unionall(u, e);
jl_varbinding_t vb = { u->var, u->var->lb, u->var->ub, R, 0, 0, 0, 0, 0, 0,
R ? e->Rinvdepth : e->invdepth, 0, NULL, e->vars };
JL_GC_PUSH4(&u, &vb.lb, &vb.ub, &vb.innervars);
e->vars = &vb;
int ans;
if (R) {
e->envidx++;
ans = subtype(t, u->body, e, param);
e->envidx--;
// widen Type{x} to typeof(x) in argument position
if (!vb.occurs_inv)
vb.lb = widen_Type(vb.lb);
}
else
ans = subtype(u->body, t, e, param);
// handle the "diagonal dispatch" rule, which says that a type var occurring more
// than once, and only in covariant position, is constrained to concrete types. E.g.
// ( Tuple{Int, Int} <: Tuple{T, T} where T) but
// !( Tuple{Int, String} <: Tuple{T, T} where T)
// Then check concreteness by checking that the lower bound is not an abstract type.
int diagonal = vb.occurs_cov > 1 && !var_occurs_invariant(u->body, u->var, 0);
if (ans && (vb.concrete || (diagonal && is_leaf_typevar(u->var)))) {
if (vb.concrete && !diagonal && !is_leaf_bound(vb.ub)) {
// a non-diagonal var can only be a subtype of a diagonal var if its
// upper bound is concrete.
ans = 0;
}
else if (jl_is_typevar(vb.lb)) {
jl_tvar_t *v = (jl_tvar_t*)vb.lb;
jl_varbinding_t *vlb = lookup(e, v);
if (vlb)
vlb->concrete = 1;
}
else if (!is_leaf_bound(vb.lb)) {
ans = 0;
}
}
e->vars = vb.prev;
if (!ans) {
JL_GC_POP();
return 0;
}
jl_varbinding_t *btemp = e->vars;
if (vb.lb != vb.ub) {
while (btemp != NULL) {
jl_value_t *vu = btemp->ub;
jl_value_t *vl = btemp->lb;
// TODO: this takes a significant amount of time
if (btemp->depth0 != vb.depth0 &&
((vu != (jl_value_t*)vb.var && btemp->var->ub != vu && var_occurs_inside(vu, vb.var, 0, 1)) ||
(vl != (jl_value_t*)vb.var && btemp->var->lb != vl && var_occurs_inside(vl, vb.var, 0, 1)))) {
ans = 0; break;
}
btemp = btemp->prev;
}
}
// fill variable values into `envout` up to `envsz`
if (R && ans && e->envidx < e->envsz) {
jl_value_t *val;
if (vb.intvalued && vb.lb == (jl_value_t*)jl_any_type)
val = (jl_value_t*)jl_wrap_vararg(NULL, NULL);
else if (!vb.occurs_inv && vb.lb != jl_bottom_type)
val = is_leaf_bound(vb.lb) ? vb.lb : (jl_value_t*)jl_new_typevar(u->var->name, jl_bottom_type, vb.lb);
else if (vb.lb == vb.ub)
val = vb.lb;
else if (vb.lb != jl_bottom_type)
// TODO: for now return the least solution, which is what
// method parameters expect.
val = vb.lb;
else if (vb.lb == u->var->lb && vb.ub == u->var->ub)
val = (jl_value_t*)u->var;
else
val = (jl_value_t*)jl_new_typevar(u->var->name, vb.lb, vb.ub);
jl_value_t *oldval = e->envout[e->envidx];
// if we try to assign different variable values (due to checking
// multiple union members), consider the value unknown.
if (oldval && !jl_egal(oldval, val))
e->envout[e->envidx] = (jl_value_t*)u->var;
else
e->envout[e->envidx] = fix_inferred_var_bound(u->var, val);
// TODO: substitute the value (if any) of this variable into previous envout entries
}
JL_GC_POP();
return ans;
}
// check n <: (length of vararg type v)
static int check_vararg_length(jl_value_t *v, ssize_t n, jl_stenv_t *e)
{
jl_value_t *N = jl_unwrap_vararg_num(v);
// only do the check if N is free in the tuple type's last parameter
if (N) {
jl_value_t *nn = jl_box_long(n);
JL_GC_PUSH1(&nn);
e->invdepth++;
e->Rinvdepth++;
int ans = subtype(nn, N, e, 2) && subtype(N, nn, e, 0);
e->invdepth--;
e->Rinvdepth--;
JL_GC_POP();
if (!ans)
return 0;
}
return 1;
}
static int forall_exists_equal(jl_value_t *x, jl_value_t *y, jl_stenv_t *e);
static int subtype_tuple_varargs(
jl_vararg_t *vtx, jl_vararg_t *vty,
size_t vx, size_t vy,
jl_stenv_t *e, int param)
{
jl_value_t *xp0 = jl_unwrap_vararg(vtx); jl_value_t *xp1 = jl_unwrap_vararg_num(vtx);
jl_value_t *yp0 = jl_unwrap_vararg(vty); jl_value_t *yp1 = jl_unwrap_vararg_num(vty);
if (!xp1) {
jl_value_t *yl = yp1;
if (yl) {
// Unconstrained on the left, constrained on the right
if (jl_is_typevar(yl)) {
jl_varbinding_t *ylv = lookup(e, (jl_tvar_t*)yl);
if (ylv)
yl = ylv->lb;
}
if (jl_is_long(yl)) {
return 0;
}
}
}
else {
jl_value_t *xl = jl_unwrap_vararg_num(vtx);
if (jl_is_typevar(xl)) {
jl_varbinding_t *xlv = lookup(e, (jl_tvar_t*)xl);
if (xlv)
xl = xlv->lb;
}
if (jl_is_long(xl)) {
if (jl_unbox_long(xl) + 1 == vx) {
// LHS is exhausted. We're a subtype if the RHS is either
// exhausted as well or unbounded (in which case we need to
// set it to 0).
jl_value_t *yl = jl_unwrap_vararg_num(vty);
if (yl) {
if (jl_is_typevar(yl)) {
jl_varbinding_t *ylv = lookup(e, (jl_tvar_t*)yl);
if (ylv)
yl = ylv->lb;
}
if (jl_is_long(yl)) {
return jl_unbox_long(yl) + 1 == vy;
}
} else {
// We can skip the subtype check, but we still
// need to make sure to constrain the length of y
// to 0.
goto constrain_length;
}
}
}
}
// in Vararg{T1} <: Vararg{T2}, need to check subtype twice to
// simulate the possibility of multiple arguments, which is needed
// to implement the diagonal rule correctly.
if (!subtype(xp0, yp0, e, param)) return 0;
if (!subtype(xp0, yp0, e, 1)) return 0;
constrain_length:
if (!yp1) {
return 1;
}
if (!xp1) {
jl_value_t *yl = yp1;
jl_varbinding_t *ylv = NULL;
if (jl_is_typevar(yl)) {
ylv = lookup(e, (jl_tvar_t*)yl);
if (ylv)
yl = ylv->lb;
}
if (jl_is_long(yl)) {
// The length of the x tuple is unconstrained, but the
// length of the y tuple is now fixed (this could have happened
// as a result of the subtype call above).
return 0;
}
if (ylv) {
if (ylv->depth0 != e->invdepth || ylv->occurs_inv)
return 0;
ylv->intvalued = 1;
}
// set lb to Any. Since `intvalued` is set, we'll interpret that
// appropriately.
e->invdepth++;
e->Rinvdepth++;
int ans = subtype((jl_value_t*)jl_any_type, yp1, e, 2);
e->invdepth--;
e->Rinvdepth--;
return ans;
}
// Vararg{T,N} <: Vararg{T2,N2}; equate N and N2
e->invdepth++;
e->Rinvdepth++;
JL_GC_PUSH2(&xp1, &yp1);
if (xp1 && jl_is_long(xp1) && vx != 1)
xp1 = jl_box_long(jl_unbox_long(xp1) - vx + 1);
if (jl_is_long(yp1) && vy != 1)