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jltypes.c
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// This file is a part of Julia. License is MIT: http://julialang.org/license
/*
Types
. type predicates (subtype) and type matching
. type union and intersection
. builtin type definitions
*/
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#ifdef _OS_WINDOWS_
#include <malloc.h>
#endif
#include "julia.h"
#include "julia_internal.h"
#include "builtin_proto.h"
#ifdef __cplusplus
extern "C" {
#endif
jl_datatype_t *jl_any_type;
jl_datatype_t *jl_type_type;
jl_methtable_t *jl_type_type_mt;
jl_datatype_t *jl_typename_type;
jl_datatype_t *jl_sym_type;
jl_datatype_t *jl_symbol_type;
jl_datatype_t *jl_ssavalue_type;
jl_datatype_t *jl_abstractslot_type;
jl_datatype_t *jl_slotnumber_type;
jl_datatype_t *jl_typedslot_type;
jl_datatype_t *jl_simplevector_type;
jl_typename_t *jl_tuple_typename;
jl_tupletype_t *jl_anytuple_type;
jl_datatype_t *jl_anytuple_type_type;
jl_typename_t *jl_vecelement_typename;
jl_datatype_t *jl_vararg_type;
jl_datatype_t *jl_tvar_type;
jl_datatype_t *jl_uniontype_type;
jl_datatype_t *jl_datatype_type;
jl_datatype_t *jl_function_type;
jl_datatype_t *jl_builtin_type;
jl_value_t *jl_bottom_type;
jl_datatype_t *jl_abstractarray_type;
jl_datatype_t *jl_densearray_type;
jl_datatype_t *jl_bool_type;
jl_datatype_t *jl_char_type;
jl_datatype_t *jl_int8_type;
jl_datatype_t *jl_uint8_type;
jl_datatype_t *jl_int16_type;
jl_datatype_t *jl_uint16_type;
jl_datatype_t *jl_int32_type;
jl_datatype_t *jl_uint32_type;
jl_datatype_t *jl_int64_type;
jl_datatype_t *jl_uint64_type;
jl_datatype_t *jl_float16_type;
jl_datatype_t *jl_float32_type;
jl_datatype_t *jl_float64_type;
jl_datatype_t *jl_floatingpoint_type;
jl_datatype_t *jl_number_type;
jl_datatype_t *jl_complex_type;
jl_datatype_t *jl_signed_type;
JL_DLLEXPORT jl_value_t *jl_emptytuple=NULL;
jl_svec_t *jl_emptysvec;
jl_value_t *jl_nothing;
// --- type properties and predicates ---
STATIC_INLINE int is_unspec(jl_datatype_t *dt)
{
return (jl_datatype_t*)dt->name->primary == dt;
}
static int jl_has_typevars__(jl_value_t *v, int incl_wildcard, jl_value_t **p, size_t np)
{
size_t i;
if (jl_typeis(v, jl_tvar_type)) {
if (jl_has_typevars__(((jl_tvar_t*)v)->ub, incl_wildcard, p, np) ||
jl_has_typevars__(((jl_tvar_t*)v)->lb, incl_wildcard, p, np))
return 1;
if (p != NULL) {
for (i = 0; i < np; i++) {
if (v == p[i])
return 1;
}
return 0;
}
if (!((jl_tvar_t*)v)->bound)
return incl_wildcard;
return 1;
}
if (jl_is_typector(v))
return incl_wildcard;
jl_svec_t *t;
int expect = -1;
if (jl_is_uniontype(v)) {
t = ((jl_uniontype_t*)v)->types;
}
else if (jl_is_datatype(v)) {
if (is_unspec((jl_datatype_t*)v))
return 0; // TODO: fix expect in this case
if (p == NULL) {
if (incl_wildcard)
expect = ((jl_datatype_t*)v)->haswildcard;
else
expect = ((jl_datatype_t*)v)->hastypevars;
#ifdef NDEBUG
return expect;
#endif
}
t = ((jl_datatype_t*)v)->parameters;
}
else {
return 0;
}
size_t l = jl_svec_len(t);
for (i = 0; i < l; i++) {
jl_value_t *elt = jl_svecref(t, i);
if (elt != v) {
if (jl_has_typevars__(elt, incl_wildcard, p, np)) {
if (expect >= 0) assert(expect);
return 1;
}
}
}
// probably not necessary; no reason to use match() instead of subtype()
// on the unconstrained version of a type
//if (jl_is_typector(v))
// return jl_svec_len((((jl_typector_t*)v)->parameters) > 0);
if (expect >= 0) assert(!expect);
return 0;
}
JL_DLLEXPORT int jl_has_typevars_(jl_value_t *v, int incl_wildcard)
{
if (jl_is_typevar(v)) return 1;
return jl_has_typevars__(v, incl_wildcard, NULL, 0);
}
static int jl_has_typevars_from(jl_value_t *v, jl_svec_t *p)
{
if (jl_svec_len(p) == 0) return 0;
return jl_has_typevars__(v, 0, jl_svec_data(p), jl_svec_len(p));
}
static int jl_has_typevars_from_v(jl_value_t *v, jl_value_t **p, size_t np)
{
if (np == 0) return 0;
return jl_has_typevars__(v, 0, p, np);
}
JL_DLLEXPORT int jl_has_typevars(jl_value_t *v)
{
if (jl_is_typevar(v)) return 1;
return jl_has_typevars__(v, 0, NULL, 0);
}
JL_DLLEXPORT int (jl_is_leaf_type)(jl_value_t *v)
{
if (jl_is_datatype(v)) {
int isleaf = ((jl_datatype_t*)v)->isleaftype;
#ifdef NDEBUG
return isleaf;
#else
if (((jl_datatype_t*)v)->abstract) {
int x = 0;
if (jl_is_type_type(v)) {
x = !jl_has_typevars(jl_tparam0(v));
}
assert(x == isleaf);
return x;
}
jl_svec_t *t = ((jl_datatype_t*)v)->parameters;
size_t l = jl_svec_len(t);
if (((jl_datatype_t*)v)->name == jl_tuple_typename) {
for(int i=0; i < l; i++) {
if (!jl_is_leaf_type(jl_svecref(t,i))) {
assert(!isleaf);
return 0;
}
}
}
else {
for(int i=0; i < l; i++) {
jl_value_t *p = jl_svecref(t, i);
if (jl_has_typevars(p)) {
assert(!isleaf);
return 0;
}
}
}
assert(isleaf);
return 1;
#endif
}
return 0;
}
static int type_eqv_(jl_value_t *a, jl_value_t *b);
// Return true for any type (Integer or Unsigned) that can fit in a
// size_t and pass back value, else return false
JL_DLLEXPORT int jl_get_size(jl_value_t *val, size_t *pnt)
{
if (jl_is_long(val)) {
ssize_t slen = jl_unbox_long(val);
if (slen < 0)
jl_errorf("size or dimension is negative: %d", slen);
*pnt = slen;
return 1;
}
return 0;
}
// --- type union ---
static int count_union_components(jl_value_t **types, size_t n)
{
size_t i, c=0;
for(i=0; i < n; i++) {
jl_value_t *e = types[i];
if (jl_is_uniontype(e)) {
jl_svec_t *ts = ((jl_uniontype_t*)e)->types;
c += count_union_components(jl_svec_data(ts), jl_svec_len(ts));
}
else {
c++;
}
}
return c;
}
static void flatten_type_union(jl_value_t **types, size_t n, jl_value_t **out, size_t *idx)
{
size_t i;
for(i=0; i < n; i++) {
jl_value_t *e = types[i];
if (jl_is_uniontype(e)) {
jl_svec_t *ts = ((jl_uniontype_t*)e)->types;
flatten_type_union(jl_svec_data(ts), jl_svec_len(ts), out, idx);
}
else {
out[*idx] = e;
(*idx)++;
}
}
}
static int union_elt_morespecific(const void *a, const void *b)
{
jl_value_t *va = *(jl_value_t**)a;
jl_value_t *vb = *(jl_value_t**)b;
if (jl_args_morespecific(va, vb))
return -1;
// impose a partially-arbitrary ordering on Union elements, to make it more
// likely that many Unions will be identical and can be merged.
// NOTE: we know !(a <: b) && !(b <: a), since otherwise one would have
// been eliminated from the Union.
return jl_object_id(va) < jl_object_id(vb) ? -1 : 1;
}
// NOTE: this is a hack to avoid simplifying type unions too early inside
// type definitions. (issue #2365)
int inside_typedef = 0;
static jl_svec_t *jl_compute_type_union(jl_value_t **types, size_t ntypes)
{
size_t n = count_union_components(types, ntypes);
jl_value_t **temp;
JL_GC_PUSHARGS(temp, n+1);
size_t idx=0;
flatten_type_union(types, ntypes, temp, &idx);
assert(idx == n);
size_t i, j, ndel=0;
for(i=0; i < n; i++) {
for(j=0; j < n; j++) {
if (j != i && temp[i] && temp[j]) {
if (temp[i] == temp[j] ||
(!jl_has_typevars(temp[i]) && !jl_has_typevars(temp[j]) &&
!(inside_typedef && (jl_is_typevar(temp[i]) ||
jl_is_typevar(temp[j]))) &&
(type_eqv_(temp[i], temp[j]) ||
jl_subtype(temp[i], temp[j], 0)))) {
temp[i] = NULL;
ndel++;
}
}
}
}
temp[n] = NULL;
jl_svec_t *result = jl_alloc_svec_uninit(n - ndel);
temp[n] = (jl_value_t*)result; // root result tuple while sorting
j=0;
for(i=0; i < n; i++) {
if (temp[i] != NULL) {
jl_svecset(result, j, temp[i]);
j++;
}
}
assert(j == n-ndel);
// sort Union components by specificity, so "complex" type Unions work as
// long as there are no ambiguities (see e.g. issue #126).
// TODO: maybe warn about ambiguities
qsort(jl_svec_data(result), j, sizeof(jl_value_t*), union_elt_morespecific);
JL_GC_POP();
return result;
}
static jl_value_t *jl_type_union_v(jl_value_t **ts, size_t n)
{
jl_ptls_t ptls = jl_get_ptls_states();
if (n == 0) return (jl_value_t*)jl_bottom_type;
size_t i;
for(i=0; i < n; i++) {
jl_value_t *pi = ts[i];
if (!(jl_is_type(pi) || jl_is_typevar(pi)) || jl_is_vararg_type(pi))
jl_type_error_rt("Union", "parameter", (jl_value_t*)jl_type_type, pi);
}
if (n == 1) return ts[0];
jl_svec_t *types = jl_compute_type_union(ts, n);
if (jl_svec_len(types) == 0) return (jl_value_t*)jl_bottom_type;
if (jl_svec_len(types) == 1) return jl_svecref(types, 0);
JL_GC_PUSH1(&types);
jl_uniontype_t *tu =
(jl_uniontype_t*)jl_gc_alloc(ptls, sizeof(jl_uniontype_t),
jl_uniontype_type);
tu->types = types;
jl_gc_wb(tu, types);
JL_GC_POP();
return (jl_value_t*)tu;
}
JL_DLLEXPORT jl_value_t *jl_type_union(jl_svec_t *types)
{
return jl_type_union_v(jl_svec_data(types), jl_svec_len(types));
}
// --- type intersection ---
typedef enum {invariant, covariant} variance_t;
#define MAX_CENV_SIZE 128
typedef struct {
jl_value_t **data;
size_t n;
jl_svec_t *tvars;
} cenv_t;
STATIC_INLINE int is_bnd(jl_tvar_t *tv, cenv_t *env)
{
if (env->tvars == jl_emptysvec)
return tv->bound;
if (jl_is_typevar(env->tvars))
return (jl_tvar_t*)env->tvars == tv;
for(size_t i=0; i < jl_svec_len(env->tvars); i++) {
if ((jl_tvar_t*)jl_svecref(env->tvars,i) == tv)
return 1;
}
return 0;
}
STATIC_INLINE int is_btv(jl_value_t *v)
{
return jl_is_typevar(v) && ((jl_tvar_t*)v)->bound;
}
static void extend_(jl_value_t *var, jl_value_t *val, cenv_t *soln, int allowself)
{
if (!allowself && var == val)
return;
for(int i=0; i < soln->n; i+=2) {
if (soln->data[i]==var &&
(soln->data[i+1]==val || (!jl_is_typevar(val) &&
type_eqv_(soln->data[i+1],val))))
return;
if (soln->data[i]==val && soln->data[i+1]==var)
return;
}
if (soln->n >= MAX_CENV_SIZE)
jl_error("type too large");
soln->data[soln->n++] = var;
soln->data[soln->n++] = val;
}
static void extend(jl_value_t *var, jl_value_t *val, cenv_t *soln)
{
extend_(var, val, soln, 0);
}
static jl_value_t *jl_type_intersect(jl_value_t *a, jl_value_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection,
variance_t var);
static jl_value_t *intersect_union(jl_uniontype_t *a, jl_value_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection,
variance_t var)
{
int eq0 = eqc->n, co0 = penv->n;
size_t i, l = jl_svec_len(a->types);
// shortcut an easy case: union contains type b
if (!jl_is_typevar(b)) {
for(i=0; i < l; i++) {
if (jl_svecref(a->types,i) == b)
return b;
}
}
jl_svec_t *t = jl_alloc_svec(l);
JL_GC_PUSH1(&t);
for(i=0; i < l; i++) {
int eq_l = eqc->n, co_l = penv->n;
jl_value_t *ti = jl_type_intersect(jl_svecref(a->types,i), b,
penv, eqc, recheck_tuple_intersection, var);
if (ti == (jl_value_t*)jl_bottom_type) {
eqc->n = eq0; penv->n = co0;
ti = jl_type_intersect(jl_svecref(a->types,i), b,
penv, eqc, recheck_tuple_intersection, var);
if (ti != (jl_value_t*)jl_bottom_type) {
// tvar conflict among union elements; keep the conflicting
// constraints rolled back
eqc->n = eq0; penv->n = co0;
}
else {
// union element doesn't overlap no matter what.
// so remove only its constraints.
eqc->n = eq_l; penv->n = co_l;
}
}
jl_svecset(t, i, ti);
}
// problem: an intermediate union type we make here might be too
// complex, even though the final type after typevars are replaced
// might be ok.
jl_value_t *tu = jl_type_union(t);
JL_GC_POP();
return tu;
}
/*
Simplification of varargs tuple types:
JL_TUPLE_FIXED: tuples of known length (e.g., JL_VARARG_NONE or JL_VARARG_INT)
JL_TUPLE_VAR: tuples of unknown length (e.g., JL_VARARG_BOUND or JL_VARARG_UNBOUND)
In some cases, JL_VARARG_BOUND tuples get described as JL_TUPLE_FIXED,
if the constraints on length are already known.
lenr = "representation length" (the number of parameters)
lenf = "full length" (including the Vararg length, if known)
In general, lenf >= lenr-1. The lower bound is achieved only for a Vararg of length 0.
*/
typedef enum {
JL_TUPLE_FIXED = 0,
JL_TUPLE_VAR = 1
} jl_tuple_lenkind_t;
// Set the parameters for a single tuple
// returns lenf, sets kind and lenkind
static size_t data_vararg_params(jl_value_t **data, size_t lenr, cenv_t *eqc, jl_vararg_kind_t *kind, jl_tuple_lenkind_t *lenkind)
{
size_t lenf = lenr;
int i;
if (lenr == 0) {
*kind = JL_VARARG_NONE;
*lenkind = JL_TUPLE_FIXED;
return lenf;
}
*lenkind = JL_TUPLE_VAR;
*kind = jl_vararg_kind(data[lenr-1]);
if (*kind == JL_VARARG_NONE || *kind == JL_VARARG_INT)
*lenkind = JL_TUPLE_FIXED;
if (*kind == JL_VARARG_INT || *kind == JL_VARARG_BOUND) {
// try to set N from eqc parameters
jl_value_t *N = jl_tparam1(data[lenr-1]);
if (!jl_is_long(N) && eqc != NULL) {
for (i = 0; i < eqc->n; i+=2)
if (eqc->data[i] == N && jl_is_long(eqc->data[i+1])) {
N = eqc->data[i+1];
break;
}
}
if (jl_is_long(N)) {
lenf += jl_unbox_long(N)-1;
*lenkind = JL_TUPLE_FIXED;
}
}
return lenf;
}
static size_t tuple_vararg_params(jl_svec_t *a, cenv_t *eqc, jl_vararg_kind_t *kind, jl_tuple_lenkind_t *lenkind)
{
return data_vararg_params(jl_svec_data(a), jl_svec_len(a), eqc, kind, lenkind);
}
jl_datatype_t *jl_wrap_vararg(jl_value_t *t, jl_value_t *n)
{
if (n == NULL) {
if (t == NULL)
return (jl_datatype_t*)jl_instantiate_type_with((jl_value_t*)jl_vararg_type, NULL, 0);
jl_value_t *env[2];
env[0] = jl_tparam0(jl_vararg_type);
env[1] = t;
return (jl_datatype_t*)jl_instantiate_type_with((jl_value_t*)jl_vararg_type, env, 1);
}
jl_value_t *env[4];
env[0] = jl_tparam0(jl_vararg_type);
env[1] = t;
env[2] = jl_tparam1(jl_vararg_type);
env[3] = n;
return (jl_datatype_t*)jl_instantiate_type_with((jl_value_t*)jl_vararg_type, env, 2);
}
/*
Tuple intersection
Stage 1: compute lengths of each tuple
--------------------------------------
See above
Stage 2: paired length analysis
-------------------------------
Check and combine lengths. In cells of the following table,
- row 1 is the criterion that must be satisfied, or Bottom will be returned
- row 2 is the allocated length for the output tuple
- row 3, if present, indicates any additional steps taken at the time
of length computation
b
FIXED VAR
|---------------------------------------|
| alenf == blenf | alenf+1 >= blenr |
FIXED | alenf | alenf |
| | bind b? |
a |---------------------------------------|
| blenf+1 >= alenr | |
VAR | blenf | max(alenr,blenr) |
| bind a? | flag? |
|---------------------------------------|
"bind" is performed if the VAR tuple is of state BOUND, using (for
the b BOUND case) N == alenf-blenr+1 for b's length parameter N.
"flag" is set if at least one of the tuples is of state BOUND. With
this, we signify that the intersection of these tuples is going to
have to be repeated once all lengths are constrained.
Stage 3: slot type intersection
-------------------------------
Iterate over each slot of the _output_ tuple, intersecting
corresponding pairs of types. Any intersection failure causes Bottom
to be returned, with one exception illustrated by:
typeintersect(Tuple{A, Vararg{B}}, Tuple{A, Vararg{C}}) == Tuple{A}
where typeintersect(B,C) == Bottom.
*/
static jl_value_t *intersect_tuple(jl_datatype_t *a, jl_datatype_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection, // "flag" above
variance_t var)
{
jl_svec_t *ap = a->parameters, *bp = b->parameters;
size_t alenr = jl_svec_len(ap), blenr = jl_svec_len(bp);
size_t alenf, blenf;
jl_vararg_kind_t akind, bkind;
jl_tuple_lenkind_t alenkind, blenkind;
int bottom = 0;
size_t n;
// Stage 1
alenf = tuple_vararg_params(ap, eqc, &akind, &alenkind);
blenf = tuple_vararg_params(bp, eqc, &bkind, &blenkind);
// Stage 2
if (alenkind == JL_TUPLE_FIXED && blenkind == JL_TUPLE_FIXED) {
bottom = alenf != blenf;
n = alenf;
}
else if (alenkind == JL_TUPLE_FIXED && blenkind == JL_TUPLE_VAR) {
bottom = alenf+1 < blenf;
n = alenf;
if (bkind == JL_VARARG_BOUND)
extend(jl_tparam1(jl_svecref(bp, blenr-1)), jl_box_long(alenf-blenr+1), eqc);
}
else if (alenkind == JL_TUPLE_VAR && blenkind == JL_TUPLE_FIXED) {
bottom = blenf+1 < alenf;
n = blenf;
if (akind == JL_VARARG_BOUND)
extend(jl_tparam1(jl_svecref(ap, alenr-1)), jl_box_long(blenf-alenr+1), eqc);
}
else {
n = alenr > blenr ? alenr : blenr;
// Do we need to store "at least N" constraints in penv?
// Formerly, typeintersect(Tuple{A,Vararg{B}}, NTuple{N,C}) did that
if (akind == JL_VARARG_BOUND || bkind == JL_VARARG_BOUND)
*recheck_tuple_intersection = 1;
}
if (bottom) return (jl_value_t*) jl_bottom_type;
if (n == 0) return jl_typeof(jl_emptytuple);
jl_svec_t *tc = jl_alloc_svec(n);
jl_value_t *result = (jl_value_t*)tc;
jl_value_t *ce = NULL;
JL_GC_PUSH2(&tc, &ce);
size_t ai=0, bi=0, ci;
jl_value_t *ae=NULL, *be=NULL, *an=NULL, *bn=NULL;
int aseq=0, bseq=0;
// Stage 3
for(ci=0; ci < n; ci++) {
if (ai < alenr) {
ae = jl_svecref(ap,ai);
if (jl_is_vararg_type(ae)) {
if (alenkind != JL_TUPLE_FIXED) {
an = jl_tparam1(ae);
aseq = 1;
}
ae = jl_tparam0(ae);
}
ai++;
}
if (bi < blenr) {
be = jl_svecref(bp,bi);
if (jl_is_vararg_type(be)) {
if (blenkind != JL_TUPLE_FIXED) {
bn = jl_tparam1(be);
bseq=1;
}
be = jl_tparam0(be);
}
bi++;
}
assert(ae!=NULL && be!=NULL);
ce = jl_type_intersect(ae, be, penv, eqc, recheck_tuple_intersection, var);
if (ce == (jl_value_t*)jl_bottom_type) {
if (var!=invariant && aseq && bseq) {
// (X∩Y)==∅ → (X...)∩(Y...) == ()
// We don't need to set bindings here because
// *recheck_tuple_intersection = 1
if (n == 1) {
JL_GC_POP();
return (jl_value_t*)jl_typeof(jl_emptytuple);
}
jl_svec_set_len_unsafe(tc, jl_svec_len(tc) - 1);
goto done_intersect_tuple;
}
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
if (aseq && bseq)
ce = (jl_value_t*)jl_wrap_vararg(ce, akind==JL_VARARG_BOUND ? bn : an);
jl_svecset(tc, ci, ce);
}
done_intersect_tuple:
result = (jl_value_t*)jl_apply_tuple_type(tc);
JL_GC_POP();
return result;
}
static jl_value_t *intersect_tag(jl_datatype_t *a, jl_datatype_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection,
variance_t var)
{
assert(a->name == b->name);
assert(jl_svec_len(a->parameters) == jl_svec_len(b->parameters));
jl_svec_t *p = jl_alloc_svec(jl_svec_len(a->parameters));
JL_GC_PUSH1(&p);
jl_value_t *ti;
size_t i;
for(i=0; i < jl_svec_len(p); i++) {
jl_value_t *ap = jl_svecref(a->parameters,i);
jl_value_t *bp = jl_svecref(b->parameters,i);
if (jl_is_typevar(ap)) {
if (var==invariant && jl_is_typevar(bp)) {
if (((jl_tvar_t*)ap)->bound != ((jl_tvar_t*)bp)->bound) {
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
if ((is_unspec(a) && is_bnd((jl_tvar_t*)bp,penv)) ||
(is_bnd((jl_tvar_t*)ap,penv) && is_unspec(b))) {
// Foo{T} and Foo can never be equal since the former
// is always a subtype of the latter
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
}
ti = jl_type_intersect(ap, bp, penv, eqc, recheck_tuple_intersection, invariant);
if (bp == (jl_value_t*)jl_bottom_type &&
!((jl_tvar_t*)ap)->bound) {
// "Union{}" as a type parameter
jl_svecset(p, i, ti);
continue;
}
}
else if (jl_is_typevar(bp)) {
ti = jl_type_intersect(ap, bp, penv, eqc, recheck_tuple_intersection, invariant);
if (ap == (jl_value_t*)jl_bottom_type &&
!((jl_tvar_t*)bp)->bound) {
// "Union{}" as a type parameter
jl_svecset(p, i, ti);
continue;
}
}
else {
int tva = jl_has_typevars_(ap,0);
int tvb = jl_has_typevars_(bp,0);
if (tva || tvb) {
if (jl_subtype_invariant(ap,bp,0) ||
jl_subtype_invariant(bp,ap,0)) {
ti = jl_type_intersect(ap, bp, penv, eqc, recheck_tuple_intersection, invariant);
}
else {
ti = (jl_value_t*)jl_bottom_type;
}
}
else if (type_eqv_(ap,bp)) {
ti = ap;
if (ti == (jl_value_t*)jl_bottom_type) {
// "Union{}" as a type parameter
jl_svecset(p, i, ti);
continue;
}
}
else {
ti = (jl_value_t*)jl_bottom_type;
}
}
if (ti == (jl_value_t*)jl_bottom_type) {
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
jl_svecset(p, i, ti);
}
if (a->name->primary != NULL) {
jl_value_t *res = (jl_value_t*)jl_apply_type(a->name->primary, p);
JL_GC_POP();
return res;
}
assert(0 && "not yet implemented");
return NULL;
}
static long meet_tuple_lengths(long bv, long vv, int *bot)
{
/*
do a meet over the lattice of tuple lengths:
>=0
| \
| 0
>=1
| \
| 1
>=2
| \
| 2
...
">=N" is represented as ~N
*/
if (bv < 0) {
if (vv < 0) {
if (bv < vv)
return bv;
else
return vv;
}
else {
if (~bv > vv) {
*bot = 1;
return 0;
}
}
}
else {
if (vv < 0) {
if (~vv > bv) {
*bot = 1;
return 0;
}
return bv;
}
else {
if (bv != vv) {
*bot = 1;
return 0;
}
}
}
return vv;
}
static int match_intersection_mode = 0;
static jl_value_t *meet_tvars(jl_tvar_t *a, jl_tvar_t *b);
static jl_value_t *intersect_typevar(jl_tvar_t *a, jl_value_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection,
variance_t var)
{
jl_value_t *both=NULL;
jl_tvar_t *new_b=NULL;
JL_GC_PUSH3(&b, &both, &new_b);
if (jl_subtype(b, (jl_value_t*)a, 0)) {
if (!is_bnd(a,penv)) {
JL_GC_POP();
return b;
}
}
else if (var==invariant && !jl_has_typevars_(b,0)) {
// for typevar a and non-typevar type b, b must be within a's bounds
// in invariant contexts.
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
else if (jl_subtype((jl_value_t*)a, b, 0)) {
/*
TODO: get sharper types when the overlap between a typevar and
a type is not simple. Ex:
tintersect(Type{Array{T,n}}, Type{typevar(:_,Vector)})
should give Type{_<:Vector}
*/
if (jl_is_typevar(b)) {
if (!is_bnd((jl_tvar_t*)b,penv)) {
JL_GC_POP();
return (jl_value_t*)a;
}
}
else {
if (a->ub == jl_bottom_type) {
JL_GC_POP();
return jl_bottom_type;
}
if (!is_bnd(a,penv)) {
JL_GC_POP();
return (jl_value_t*)a;
}
}
}
else {
b = jl_type_intersect(a->ub, b, penv, eqc, recheck_tuple_intersection, covariant);
if (b == jl_bottom_type) {
JL_GC_POP();
return b;
}
}
if ((jl_value_t*)a == b) {
JL_GC_POP();
return b;
}
if (var == invariant) {
if (!jl_has_typevars_(b,0) && !jl_is_typevar(b)) {
int i;
for(i=0; i < eqc->n; i+=2) {
if (eqc->data[i] == (jl_value_t*)a) {
jl_value_t *v = eqc->data[i+1];
if (jl_is_typevar(v))
continue;
if (!jl_types_equal(v, b)) {
JL_GC_POP();
return (jl_value_t*)jl_bottom_type;
}
break;
}
}
if (i >= eqc->n)
extend((jl_value_t*)a, b, eqc);
JL_GC_POP();
return (jl_value_t*)a;
}
if (jl_is_typevar(b)) {
both = meet_tvars(a, (jl_tvar_t*)b);
if (both == jl_bottom_type) {
JL_GC_POP();
return both;
}
if (!jl_is_typevar(both))
both = (jl_value_t*)jl_new_typevar(underscore_sym, jl_bottom_type, both);
extend((jl_value_t*)a, both, penv);
extend((jl_value_t*)b, both, penv);
}
if (is_btv(b))
extend(b, (jl_value_t*)a, eqc);
else
extend((jl_value_t*)a, b, eqc);
}
else {
int i;
for(i=0; i < penv->n; i+=2) {
if (penv->data[i] == (jl_value_t*)a && !jl_is_typevar(penv->data[i+1])) {
if (jl_types_equal(b, penv->data[i+1])) {
JL_GC_POP();
return (jl_value_t*)a;
}
break;
}
}
if (jl_is_typevar(b)) {
for(i=0; i < penv->n; i+=2) {
if (penv->data[i] == b && !jl_is_typevar(penv->data[i+1])) {
jl_value_t *ti = jl_type_intersection((jl_value_t*)a, penv->data[i+1]);
if (ti == (jl_value_t*)jl_bottom_type) {
JL_GC_POP();
return ti;
}
break;
}
}
for(i=0; i < eqc->n; i+=2) {
if (eqc->data[i] == b && !jl_is_typevar(eqc->data[i+1])) {
jl_value_t *ti = jl_type_intersection((jl_value_t*)a, eqc->data[i+1]);
if (ti == (jl_value_t*)jl_bottom_type) {
JL_GC_POP();
return ti;
}
break;
}
}
}
extend((jl_value_t*)a, b, penv);
if (jl_is_typevar(b)) {
JL_GC_POP();
return (jl_value_t*)a;
}
else {
new_b = jl_new_typevar(underscore_sym, jl_bottom_type, b);
extend((jl_value_t*)new_b, b, penv);
extend((jl_value_t*)new_b, (jl_value_t*)a, penv);
JL_GC_POP();
return (jl_value_t*)new_b;
}
}
JL_GC_POP();
return (jl_value_t*)a;
}
static jl_value_t *approxify_type(jl_datatype_t *dt, jl_svec_t *pp, int *recheck_tuple_intersection)
{
size_t i, l = jl_svec_len(dt->parameters);
jl_svec_t *p = jl_alloc_svec(l);
JL_GC_PUSH1(&p);
for(i=0; i < l; i++) {
jl_value_t *el = jl_svecref(dt->parameters, i);
if (jl_has_typevars_from(el, pp))
jl_svecset(p, i, jl_new_typevar(underscore_sym, jl_bottom_type, el));
else
jl_svecset(p, i, el);
}
jl_value_t *nt = jl_apply_type(dt->name->primary, p);
JL_GC_POP();
return nt;
}
static jl_value_t *jl_type_intersect(jl_value_t *a, jl_value_t *b,
cenv_t *penv, cenv_t *eqc,
int *recheck_tuple_intersection,
variance_t var)
{
if (jl_is_typector(a))
a = (jl_value_t*)((jl_typector_t*)a)->body;
if (jl_is_typector(b))
b = (jl_value_t*)((jl_typector_t*)b)->body;
if (a == b) return a;
if (jl_is_typevar(a)) {
if (var == covariant && !((jl_tvar_t*)a)->bound)
a = ((jl_tvar_t*)a)->ub;
else if (a != jl_ANY_flag)
return intersect_typevar((jl_tvar_t*)a, b, penv, eqc, recheck_tuple_intersection, var);
}
if (jl_is_typevar(b)) {
if (var == covariant && !((jl_tvar_t*)b)->bound)
b = ((jl_tvar_t*)b)->ub;
else if (b != jl_ANY_flag)
return intersect_typevar((jl_tvar_t*)b, a, penv, eqc, recheck_tuple_intersection, var);
}
if (a == (jl_value_t*)jl_bottom_type || b == (jl_value_t*)jl_bottom_type)
return (jl_value_t*)jl_bottom_type;
if (!jl_has_typevars(a) && !jl_has_typevars(b)) {
if (jl_subtype(a, b, 0))
return a;
if (jl_subtype(b, a, 0))
return b;
}
// union
if (jl_is_uniontype(a))
return intersect_union((jl_uniontype_t*)a, b, penv, eqc, recheck_tuple_intersection, var);
if (jl_is_uniontype(b))
return intersect_union((jl_uniontype_t*)b, a, penv, eqc, recheck_tuple_intersection, var);
if (a == (jl_value_t*)jl_any_type || a == jl_ANY_flag) return b;
if (b == (jl_value_t*)jl_any_type || b == jl_ANY_flag) return a;
// tuple
if (jl_is_tuple_type(a)) {
if (jl_is_tuple_type(b)) {
return intersect_tuple((jl_datatype_t*)a, (jl_datatype_t*)b, penv, eqc, recheck_tuple_intersection, var);
}
}
if (jl_is_tuple_type(b)) {
return jl_type_intersect(b, a, penv, eqc, recheck_tuple_intersection, var);
}
// tag
if (!jl_is_datatype(a) || !jl_is_datatype(b))
return (jl_value_t*)jl_bottom_type;