1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
|
// Copyright 2021 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package types2
import "bytes"
// A termlist represents the type set represented by the union
// t1 ∪ y2 ∪ ... tn of the type sets of the terms t1 to tn.
// A termlist is in normal form if all terms are disjoint.
// termlist operations don't require the operands to be in
// normal form.
type termlist []*term
// topTermlist represents the set of all types.
// It is in normal form.
var topTermlist = termlist{new(term)}
// String prints the termlist exactly (without normalization).
func (xl termlist) String() string {
if len(xl) == 0 {
return "∅"
}
var buf bytes.Buffer
for i, x := range xl {
if i > 0 {
buf.WriteString(" ∪ ")
}
buf.WriteString(x.String())
}
return buf.String()
}
// isEmpty reports whether the termlist xl represents the empty set of types.
func (xl termlist) isEmpty() bool {
// If there's a non-nil term, the entire list is not empty.
// If the termlist is in normal form, this requires at most
// one iteration.
for _, x := range xl {
if x != nil {
return false
}
}
return true
}
// isTop reports whether the termlist xl represents the set of all types.
func (xl termlist) isTop() bool {
// If there's a ⊤ (top) term, the entire list is ⊤ (top).
// If the termlist is in normal form, this requires at most
// one iteration.
for _, x := range xl {
if x != nil && x.typ == nil {
return true
}
}
return false
}
// norm returns the normal form of xl.
func (xl termlist) norm() termlist {
// Quadratic algorithm, but good enough for now.
// TODO(gri) fix asymptotic performance
used := make([]bool, len(xl))
var rl termlist
for i, xi := range xl {
if xi == nil || used[i] {
continue
}
for j := i + 1; j < len(xl); j++ {
xj := xl[j]
if xj == nil || used[j] {
continue
}
if u1, u2 := xi.union(xj); u2 == nil {
// If we encounter a ⊤ (top) term, the entire
// list is ⊤ (top). Exit early.
// (Note that this is not just an optimization;
// if we continue, we may end up with a ⊤ term
// and other terms and the result would not be
// in normal form.)
if u1.typ == nil {
return topTermlist
}
xi = u1
used[j] = true // xj is now unioned into xi - ignore it in future iterations
}
}
rl = append(rl, xi)
}
return rl
}
// If the type set represented by xl is specified by a single (non-⊤) term,
// structuralType returns that type. Otherwise it returns nil.
func (xl termlist) structuralType() Type {
if nl := xl.norm(); len(nl) == 1 {
return nl[0].typ // if nl.isTop() then typ is nil, which is ok
}
return nil
}
// union returns the union xl ∪ yl.
func (xl termlist) union(yl termlist) termlist {
return append(xl, yl...).norm()
}
// intersect returns the intersection xl ∩ yl.
func (xl termlist) intersect(yl termlist) termlist {
if xl.isEmpty() || yl.isEmpty() {
return nil
}
// Quadratic algorithm, but good enough for now.
// TODO(gri) fix asymptotic performance
var rl termlist
for _, x := range xl {
for _, y := range yl {
if r := x.intersect(y); r != nil {
rl = append(rl, r)
}
}
}
return rl.norm()
}
// equal reports whether xl and yl represent the same type set.
func (xl termlist) equal(yl termlist) bool {
// TODO(gri) this should be more efficient
return xl.subsetOf(yl) && yl.subsetOf(xl)
}
// includes reports whether t ∈ xl.
func (xl termlist) includes(t Type) bool {
for _, x := range xl {
if x.includes(t) {
return true
}
}
return false
}
// supersetOf reports whether y ⊆ xl.
func (xl termlist) supersetOf(y *term) bool {
for _, x := range xl {
if y.subsetOf(x) {
return true
}
}
return false
}
// subsetOf reports whether xl ⊆ yl.
func (xl termlist) subsetOf(yl termlist) bool {
if yl.isEmpty() {
return xl.isEmpty()
}
// each term x of xl must be a subset of yl
for _, x := range xl {
if !yl.supersetOf(x) {
return false // x is not a subset yl
}
}
return true
}
|
