1 files changed, 166 insertions, 0 deletions
diff --git a/src/go/types/typeterm.go b/src/go/types/typeterm.go
new file mode 100644
index 0000000000..dbd055a580
--- /dev/null
+++ b/src/go/types/typeterm.go
@@ -0,0 +1,166 @@
+// 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 types
+
+// 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)
+}