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[dev.typeparams] cmd/compile/internal/types2: implement type terms

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Type terms will be used to represent a type set as a list
of type terms. Eventually, a type term may also include
a method set.

Groundwork for the implementation of lazily computed
type sets for union expressions.

Change-Id: Ic88750af21f697ce0b52a2259eff40bee115964c
Reviewed-on: https://go-review.googlesource.com/c/go/+/338049
Trust: Robert Griesemer <gri@golang.org>
Reviewed-by: Robert Findley <rfindley@google.com>
This commit is contained in:
Robert Griesemer 2021-07-27 19:14:30 -07:00
parent f4f503e0a3
commit 2fa8f00915
2 changed files with 371 additions and 0 deletions
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166
src/cmd/compile/internal/types2/typeterm.go Normal file
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// 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
// TODO(gri) use a different symbol instead of ⊤ for the set of all types
// (⊤ is hard to distinguish from T in some fonts)
// A term describes elementary type sets:
//
// ∅: (*term)(nil) == ∅ // set of no types (empty set)
// ⊤: &term{} == ⊤ // set of all types
// T: &term{false, T} == {T} // set of type T
// ~t: &term{true, t} == {t' | under(t') == t} // set of types with underlying type t
//
type term struct {
tilde bool // valid if typ != nil
typ Type
}
func (x *term) String() string {
switch {
case x == nil:
return "∅"
case x.typ == nil:
return "⊤"
case x.tilde:
return "~" + x.typ.String()
default:
return x.typ.String()
}
}
// equal reports whether x and y represent the same type set.
func (x *term) equal(y *term) bool {
// easy cases
switch {
case x == nil || y == nil:
return x == y
case x.typ == nil || y.typ == nil:
return x.typ == y.typ
}
// ∅ ⊂ x, y ⊂ ⊤
return x.tilde == y.tilde && Identical(x.typ, y.typ)
}
// union returns the union x ∪ y: zero, one, or two non-nil terms.
func (x *term) union(y *term) (_, _ *term) {
// easy cases
switch {
case x == nil && y == nil:
return nil, nil // ∅ ∪ ∅ == ∅
case x == nil:
return y, nil // ∅ ∪ y == y
case y == nil:
return x, nil // x ∪ ∅ == x
case x.typ == nil:
return x, nil // ⊤ ∪ y == ⊤
case y.typ == nil:
return y, nil // x ∪ ⊤ == ⊤
}
// ∅ ⊂ x, y ⊂ ⊤
if x.disjoint(y) {
return x, y // x ∪ y == (x, y) if x ∩ y == ∅
}
// x.typ == y.typ
// ~t ∪ ~t == ~t
// ~t ∪ T == ~t
// T ∪ ~t == ~t
// T ∪ T == T
if x.tilde || !y.tilde {
return x, nil
}
return y, nil
}
// intersect returns the intersection x ∩ y.
func (x *term) intersect(y *term) *term {
// easy cases
switch {
case x == nil || y == nil:
return nil // ∅ ∩ y == ∅ and ∩ ∅ == ∅
case x.typ == nil:
return y // ⊤ ∩ y == y
case y.typ == nil:
return x // x ∩ ⊤ == x
}
// ∅ ⊂ x, y ⊂ ⊤
if x.disjoint(y) {
return nil // x ∩ y == ∅ if x ∩ y == ∅
}
// x.typ == y.typ
// ~t ∩ ~t == ~t
// ~t ∩ T == T
// T ∩ ~t == T
// T ∩ T == T
if !x.tilde || y.tilde {
return x
}
return y
}
// includes reports whether t ∈ x.
func (x *term) includes(t Type) bool {
// easy cases
switch {
case x == nil:
return false // t ∈ ∅ == false
case x.typ == nil:
return true // t ∈ ⊤ == true
}
// ∅ ⊂ x ⊂ ⊤
u := t
if x.tilde {
u = under(u)
}
return Identical(x.typ, u)
}
// subsetOf reports whether x ⊆ y.
func (x *term) subsetOf(y *term) bool {
// easy cases
switch {
case x == nil:
return true // ∅ ⊆ y == true
case y == nil:
return false // x ⊆ ∅ == false since x != ∅
case y.typ == nil:
return true // x ⊆ ⊤ == true
case x.typ == nil:
return false // ⊤ ⊆ y == false since y != ⊤
}
// ∅ ⊂ x, y ⊂ ⊤
if x.disjoint(y) {
return false // x ⊆ y == false if x ∩ y == ∅
}
// x.typ == y.typ
// ~t ⊆ ~t == true
// ~t ⊆ T == false
// T ⊆ ~t == true
// T ⊆ T == true
return !x.tilde || y.tilde
}
// disjoint reports whether x ∩ y == ∅.
// x.typ and y.typ must not be nil.
func (x *term) disjoint(y *term) bool {
ux := x.typ
if y.tilde {
ux = under(ux)
}
uy := y.typ
if x.tilde {
uy = under(uy)
}
return !Identical(ux, uy)
}

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src/cmd/compile/internal/types2/typeterm_test.go Normal file
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// 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 (
"strings"
"testing"
)
var testTerms = map[string]*term{
"∅": nil,
"⊤": &term{},
"int": &term{false, Typ[Int]},
"~int": &term{true, Typ[Int]},
"string": &term{false, Typ[String]},
"~string": &term{true, Typ[String]},
// TODO(gri) add a defined type
}
func TestTermString(t *testing.T) {
for want, x := range testTerms {
if got := x.String(); got != want {
t.Errorf("%v.String() == %v; want %v", x, got, want)
}
}
}
func split(s string, n int) []string {
r := strings.Split(s, " ")
if len(r) != n {
panic("invalid test case: " + s)
}
return r
}
func testTerm(name string) *term {
r, ok := testTerms[name]
if !ok {
panic("invalid test argument: " + name)
}
return r
}
func TestTermEqual(t *testing.T) {
for _, test := range []string{
"∅ ∅ T",
"⊤ ⊤ T",
"int int T",
"~int ~int T",
"∅ ⊤ F",
"∅ int F",
"∅ ~int F",
"⊤ int F",
"⊤ ~int F",
"int ~int F",
} {
args := split(test, 3)
x := testTerm(args[0])
y := testTerm(args[1])
want := args[2] == "T"
if got := x.equal(y); got != want {
t.Errorf("%v.equal(%v) = %v; want %v", x, y, got, want)
}
// equal is symmetric
x, y = y, x
if got := x.equal(y); got != want {
t.Errorf("%v.equal(%v) = %v; want %v", x, y, got, want)
}
}
}
func TestTermUnion(t *testing.T) {
for _, test := range []string{
"∅ ∅ ∅ ∅",
"∅ ⊤ ⊤ ∅",
"∅ int int ∅",
"∅ ~int ~int ∅",
"⊤ ⊤ ⊤ ∅",
"⊤ int ⊤ ∅",
"⊤ ~int ⊤ ∅",
"int int int ∅",
"int ~int ~int ∅",
"int string int string",
"int ~string int ~string",
"~int ~string ~int ~string",
// union is symmetric, but the result order isn't - repeat symmetric cases explictly
"⊤ ∅ ⊤ ∅",
"int ∅ int ∅",
"~int ∅ ~int ∅",
"int ⊤ ⊤ ∅",
"~int ⊤ ⊤ ∅",
"~int int ~int ∅",
"string int string int",
"~string int ~string int",
"~string ~int ~string ~int",
} {
args := split(test, 4)
x := testTerm(args[0])
y := testTerm(args[1])
want1 := testTerm(args[2])
want2 := testTerm(args[3])
if got1, got2 := x.union(y); !got1.equal(want1) || !got2.equal(want2) {
t.Errorf("%v.union(%v) = %v, %v; want %v, %v", x, y, got1, got2, want1, want2)
}
}
}
func TestTermIntersection(t *testing.T) {
for _, test := range []string{
"∅ ∅ ∅",
"∅ ⊤ ∅",
"∅ int ∅",
"∅ ~int ∅",
"⊤ ⊤ ⊤",
"⊤ int int",
"⊤ ~int ~int",
"int int int",
"int ~int int",
"int string ∅",
"int ~string ∅",
"~int ~string ∅",
} {
args := split(test, 3)
x := testTerm(args[0])
y := testTerm(args[1])
want := testTerm(args[2])
if got := x.intersect(y); !got.equal(want) {
t.Errorf("%v.intersect(%v) = %v; want %v", x, y, got, want)
}
// intersect is symmetric
x, y = y, x
if got := x.intersect(y); !got.equal(want) {
t.Errorf("%v.intersect(%v) = %v; want %v", x, y, got, want)
}
}
}
func TestTermIncludes(t *testing.T) {
for _, test := range []string{
"∅ int F",
"⊤ int T",
"int int T",
"~int int T",
"string int F",
"~string int F",
} {
args := split(test, 3)
x := testTerm(args[0])
y := testTerm(args[1]).typ
want := args[2] == "T"
if got := x.includes(y); got != want {
t.Errorf("%v.includes(%v) = %v; want %v", x, y, got, want)
}
}
}
func TestTermSubsetOf(t *testing.T) {
for _, test := range []string{
"∅ ∅ T",
"⊤ ⊤ T",
"int int T",
"~int ~int T",
"∅ ⊤ T",
"∅ int T",
"∅ ~int T",
"⊤ int F",
"⊤ ~int F",
"int ~int T",
} {
args := split(test, 3)
x := testTerm(args[0])
y := testTerm(args[1])
want := args[2] == "T"
if got := x.subsetOf(y); got != want {
t.Errorf("%v.subsetOf(%v) = %v; want %v", x, y, got, want)
}
}
}
func TestTermDisjoint(t *testing.T) {
for _, test := range []string{
"int int F",
"~int ~int F",
"int ~int F",
"int string T",
"int ~string T",
"~int ~string T",
} {
args := split(test, 3)
x := testTerm(args[0])
y := testTerm(args[1])
want := args[2] == "T"
if got := x.disjoint(y); got != want {
t.Errorf("%v.disjoint(%v) = %v; want %v", x, y, got, want)
}
// disjoint is symmetric
x, y = y, x
if got := x.disjoint(y); got != want {
t.Errorf("%v.disjoint(%v) = %v; want %v", x, y, got, want)
}
}
}