exp/types/staging: typechecker API

First set of type checker files for review.
The primary concern here is the typechecker
API (types.go).

R=rsc, adonovan, r, rogpeppe
CC=golang-dev
https://golang.org/cl/6490089

src/pkg/exp/types/staging/exprstring.go

@@ -0,0 +1,98 @@
+// Copyright 2012 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
+
+import (
+	"bytes"
+	"fmt"
+	"go/ast"
+)
+
+// exprString returns a (simplified) string representation for an expression.
+func exprString(expr ast.Expr) string {
+	var buf bytes.Buffer
+	writeExpr(&buf, expr)
+	return buf.String()
+}
+
+// TODO(gri) Need to merge with typeString since some expressions are types (try: ([]int)(a))
+func writeExpr(buf *bytes.Buffer, expr ast.Expr) {
+	switch x := expr.(type) {
+	case *ast.Ident:
+		buf.WriteString(x.Name)
+
+	case *ast.BasicLit:
+		buf.WriteString(x.Value)
+
+	case *ast.FuncLit:
+		buf.WriteString("(func literal)")
+
+	case *ast.CompositeLit:
+		buf.WriteString("(composite literal)")
+
+	case *ast.ParenExpr:
+		buf.WriteByte('(')
+		writeExpr(buf, x.X)
+		buf.WriteByte(')')
+
+	case *ast.SelectorExpr:
+		writeExpr(buf, x.X)
+		buf.WriteByte('.')
+		buf.WriteString(x.Sel.Name)
+
+	case *ast.IndexExpr:
+		writeExpr(buf, x.X)
+		buf.WriteByte('[')
+		writeExpr(buf, x.Index)
+		buf.WriteByte(']')
+
+	case *ast.SliceExpr:
+		writeExpr(buf, x.X)
+		buf.WriteByte('[')
+		if x.Low != nil {
+			writeExpr(buf, x.Low)
+		}
+		buf.WriteByte(':')
+		if x.High != nil {
+			writeExpr(buf, x.High)
+		}
+		buf.WriteByte(']')
+
+	case *ast.TypeAssertExpr:
+		writeExpr(buf, x.X)
+		buf.WriteString(".(...)")
+
+	case *ast.CallExpr:
+		writeExpr(buf, x.Fun)
+		buf.WriteByte('(')
+		for i, arg := range x.Args {
+			if i > 0 {
+				buf.WriteString(", ")
+			}
+			writeExpr(buf, arg)
+		}
+		buf.WriteByte(')')
+
+	case *ast.StarExpr:
+		buf.WriteByte('*')
+		writeExpr(buf, x.X)
+
+	case *ast.UnaryExpr:
+		buf.WriteString(x.Op.String())
+		writeExpr(buf, x.X)
+
+	case *ast.BinaryExpr:
+		// The AST preserves source-level parentheses so there is
+		// no need to introduce parentheses here for correctness.
+		writeExpr(buf, x.X)
+		buf.WriteByte(' ')
+		buf.WriteString(x.Op.String())
+		buf.WriteByte(' ')
+		writeExpr(buf, x.Y)
+
+	default:
+		fmt.Fprintf(buf, "<expr %T>", x)
+	}
+}

src/pkg/exp/types/staging/predicates.go

@@ -0,0 +1,210 @@
+// Copyright 2012 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.
+
+// This file implements commonly used type predicates.
+
+package types
+
+func isNamed(typ Type) bool {
+	if _, ok := typ.(*Basic); ok {
+		return ok
+	}
+	_, ok := typ.(*NamedType)
+	return ok
+}
+
+func isBoolean(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsBoolean != 0
+}
+
+func isInteger(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsInteger != 0
+}
+
+func isUnsigned(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsUnsigned != 0
+}
+
+func isFloat(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsFloat != 0
+}
+
+func isComplex(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsComplex != 0
+}
+
+func isNumeric(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsNumeric != 0
+}
+
+func isString(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsString != 0
+}
+
+func isUntyped(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsUntyped != 0
+}
+
+func isOrdered(typ Type) bool {
+	t, ok := underlying(typ).(*Basic)
+	return ok && t.Info&IsOrdered != 0
+}
+
+func isComparable(typ Type) bool {
+	switch t := underlying(typ).(type) {
+	case *Basic:
+		return t.Kind != Invalid
+	case *Pointer, *Chan, *Interface:
+		// assumes types are equal for pointers and channels
+		return true
+	case *Struct:
+		for _, f := range t.Fields {
+			if !isComparable(f.Type) {
+				return false
+			}
+		}
+		return true
+	case *Array:
+		return isComparable(t.Elt)
+	}
+	return false
+}
+
+// underlying returns the underlying type of typ.
+func underlying(typ Type) Type {
+	// Basic types are representing themselves directly even though they are named.
+	if typ, ok := typ.(*NamedType); ok {
+		return typ.Underlying // underlying types are never NamedTypes
+	}
+	return typ
+}
+
+// deref returns a pointer's base type; otherwise it returns typ.
+func deref(typ Type) Type {
+	if typ, ok := underlying(typ).(*Pointer); ok {
+		return typ.Base
+	}
+	return typ
+}
+
+// identical returns true if x and y are identical.
+func isIdentical(x, y Type) bool {
+	if x == y {
+		return true
+	}
+
+	switch x := x.(type) {
+	case *Basic:
+		// Basic types are singletons except for the rune and byte
+		// aliases, thus we cannot solely rely on the x == y check
+		// above.
+		if y, ok := y.(*Basic); ok {
+			return x.Kind == y.Kind
+		}
+
+	case *Array:
+		// Two array types are identical if they have identical element types
+		// and the same array length.
+		if y, ok := y.(*Array); ok {
+			return x.Len == y.Len && isIdentical(x.Elt, y.Elt)
+		}
+
+	case *Slice:
+		// Two slice types are identical if they have identical element types.
+		if y, ok := y.(*Slice); ok {
+			return isIdentical(x.Elt, y.Elt)
+		}
+
+	case *Struct:
+		// Two struct types are identical if they have the same sequence of fields,
+		// and if corresponding fields have the same names, and identical types,
+		// and identical tags. Two anonymous fields are considered to have the same
+		// name. Lower-case field names from different packages are always different.
+		if y, ok := y.(*Struct); ok {
+			// TODO(gri) handle structs from different packages
+			if len(x.Fields) == len(y.Fields) {
+				for i, f := range x.Fields {
+					g := y.Fields[i]
+					if f.Name != g.Name ||
+						!isIdentical(f.Type, g.Type) ||
+						f.Tag != g.Tag ||
+						f.IsAnonymous != g.IsAnonymous {
+						return false
+					}
+				}
+				return true
+			}
+		}
+
+	case *Pointer:
+		// Two pointer types are identical if they have identical base types.
+		if y, ok := y.(*Pointer); ok {
+			return isIdentical(x.Base, y.Base)
+		}
+
+	case *Signature:
+		// Two function types are identical if they have the same number of parameters
+		// and result values, corresponding parameter and result types are identical,
+		// and either both functions are variadic or neither is. Parameter and result
+		// names are not required to match.
+		if y, ok := y.(*Signature); ok {
+			return identicalTypes(x.Params, y.Params) &&
+				identicalTypes(x.Results, y.Results) &&
+				x.IsVariadic == y.IsVariadic
+		}
+
+	case *Interface:
+		// Two interface types are identical if they have the same set of methods with
+		// the same names and identical function types. Lower-case method names from
+		// different packages are always different. The order of the methods is irrelevant.
+		if y, ok := y.(*Interface); ok {
+			return identicalTypes(x.Methods, y.Methods) // methods are sorted
+		}
+
+	case *Map:
+		// Two map types are identical if they have identical key and value types.
+		if y, ok := y.(*Map); ok {
+			return isIdentical(x.Key, y.Key) && isIdentical(x.Elt, y.Elt)
+		}
+
+	case *Chan:
+		// Two channel types are identical if they have identical value types
+		// and the same direction.
+		if y, ok := y.(*Chan); ok {
+			return x.Dir == y.Dir && isIdentical(x.Elt, y.Elt)
+		}
+
+	case *NamedType:
+		// Two named types are identical if their type names originate
+		// in the same type declaration.
+		if y, ok := y.(*NamedType); ok {
+			return x.Obj == y.Obj
+		}
+	}
+
+	return false
+}
+
+// identicalTypes returns true if both lists a and b have the
+// same length and corresponding objects have identical types.
+func identicalTypes(a, b ObjList) bool {
+	if len(a) == len(b) {
+		for i, x := range a {
+			y := b[i]
+			if !isIdentical(x.Type.(Type), y.Type.(Type)) {
+				return false
+			}
+		}
+		return true
+	}
+	return false
+}

src/pkg/exp/types/staging/types.go

@@ -0,0 +1,239 @@
+// Copyright 2011 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 declares the data structures for representing
+// Go types and implements typechecking of an *ast.Package.
+//
+// PACKAGE UNDER CONSTRUCTION. ANY AND ALL PARTS MAY CHANGE.
+//
+package types
+
+import (
+	"go/ast"
+	"go/token"
+	"sort"
+)
+
+// Check typechecks the given package pkg and augments the AST by
+// assigning types to all ast.Objects. Check can be used in two
+// different modes:
+//
+// 1) If a nil types map is provided, Check typechecks the entire
+// package. If no error is returned, the package source code has
+// no type errors. 
+//
+// 2) If a non-nil types map is provided, Check operates like in
+// mode 1) but also records the types for all expressions in the
+// map. Pre-existing expression types in the map are replaced if
+// the expression appears in the AST.
+//
+func Check(fset *token.FileSet, pkg *ast.Package, types map[ast.Expr]Type) error {
+	// return check(fset, pkg, types) // commented out for now to make it compile
+	return nil
+}
+
+// All types implement the Type interface.
+// TODO(gri) Eventually determine what common Type functionality should be exported.
+type Type interface {
+	aType()
+}
+
+// BasicKind describes the kind of basic type.
+type BasicKind int
+
+const (
+	Invalid BasicKind = iota // type is invalid
+
+	// predeclared types
+	Bool
+	Int
+	Int8
+	Int16
+	Int32
+	Int64
+	Uint
+	Uint8
+	Uint16
+	Uint32
+	Uint64
+	Uintptr
+	Float32
+	Float64
+	Complex64
+	Complex128
+	String
+	UnsafePointer
+
+	// types for untyped values
+	UntypedBool
+	UntypedInt
+	UntypedRune
+	UntypedFloat
+	UntypedComplex
+	UntypedString
+	UntypedNil
+
+	// aliases
+	Byte = Uint8
+	Rune = Int32
+)
+
+// BasicInfo is a set of flags describing properties of a basic type.
+type BasicInfo int
+
+// Properties of basic types.
+const (
+	IsBoolean BasicInfo = 1 << iota
+	IsInteger
+	IsUnsigned
+	IsFloat
+	IsComplex
+	IsString
+	IsUntyped
+
+	IsOrdered = IsInteger | IsFloat | IsString
+	IsNumeric = IsInteger | IsFloat | IsComplex
+)
+
+// A Basic represents a basic type.
+type Basic struct {
+	implementsType
+	Kind BasicKind
+	Info BasicInfo
+	Name string
+}
+
+// An Array represents an array type [Len]Elt.
+type Array struct {
+	implementsType
+	Len int64
+	Elt Type
+}
+
+// A Slice represents a slice type []Elt.
+type Slice struct {
+	implementsType
+	Elt Type
+}
+
+type StructField struct {
+	Name        string // unqualified type name for anonymous fields
+	Type        Type
+	Tag         string
+	IsAnonymous bool
+}
+
+// A Struct represents a struct type struct{...}.
+type Struct struct {
+	implementsType
+	Fields []*StructField
+}
+
+// A Pointer represents a pointer type *Base.
+type Pointer struct {
+	implementsType
+	Base Type
+}
+
+// A tuple represents a multi-value function return.
+// TODO(gri) use better name to avoid confusion (Go doesn't have tuples).
+type tuple struct {
+	implementsType
+	list []Type
+}
+
+// A Signature represents a user-defined function type func(...) (...).
+// TODO(gri) consider using "tuples" to represent parameters and results (see comment on tuples).
+type Signature struct {
+	implementsType
+	Recv       *ast.Object // nil if not a method
+	Params     ObjList     // (incoming) parameters from left to right; or nil
+	Results    ObjList     // (outgoing) results from left to right; or nil
+	IsVariadic bool        // true if the last parameter's type is of the form ...T
+}
+
+// builtinId is an id of a builtin function.
+type builtinId int
+
+// Predeclared builtin functions.
+const (
+	// Universe scope
+	_Append builtinId = iota
+	_Cap
+	_Close
+	_Complex
+	_Copy
+	_Delete
+	_Imag
+	_Len
+	_Make
+	_New
+	_Panic
+	_Print
+	_Println
+	_Real
+	_Recover
+
+	// Unsafe package
+	_Alignof
+	_Offsetof
+	_Sizeof
+
+	// Testing support
+	_Assert
+	_Trace
+)
+
+// A builtin represents the type of a built-in function.
+type builtin struct {
+	implementsType
+	id         builtinId
+	name       string
+	nargs      int // number of arguments (minimum if variadic)
+	isVariadic bool
+}
+
+// An Interface represents an interface type interface{...}.
+type Interface struct {
+	implementsType
+	Methods ObjList // interface methods sorted by name; or nil
+}
+
+// A Map represents a map type map[Key]Elt.
+type Map struct {
+	implementsType
+	Key, Elt Type
+}
+
+// A Chan represents a channel type chan Elt, <-chan Elt, or chan<-Elt.
+type Chan struct {
+	implementsType
+	Dir ast.ChanDir
+	Elt Type
+}
+
+// A NamedType represents a named type as declared in a type declaration.
+type NamedType struct {
+	implementsType
+	Obj        *ast.Object // corresponding declared object
+	Underlying Type        // nil if not fully declared yet, never a *NamedType
+	Methods    ObjList     // associated methods; or nil
+}
+
+// An ObjList represents an ordered (in some fashion) list of objects.
+type ObjList []*ast.Object
+
+// ObjList implements sort.Interface.
+func (list ObjList) Len() int           { return len(list) }
+func (list ObjList) Less(i, j int) bool { return list[i].Name < list[j].Name }
+func (list ObjList) Swap(i, j int)      { list[i], list[j] = list[j], list[i] }
+
+// Sort sorts an object list by object name.
+func (list ObjList) Sort() { sort.Sort(list) }
+
+// All concrete types embed implementsType which
+// ensures that all types implement the Type interface.
+type implementsType struct{}
+
+func (*implementsType) aType() {}

src/pkg/exp/types/staging/typestring.go

@@ -0,0 +1,148 @@
+// Copyright 2012 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.
+
+// This file implements the TypeString function.
+
+package types
+
+import (
+	"bytes"
+	"fmt"
+	"go/ast"
+)
+
+// typeString returns a string representation for typ.
+func typeString(typ Type) string {
+	var buf bytes.Buffer
+	writeType(&buf, typ)
+	return buf.String()
+}
+
+func writeParams(buf *bytes.Buffer, params ObjList, isVariadic bool) {
+	buf.WriteByte('(')
+	for i, par := range params {
+		if i > 0 {
+			buf.WriteString(", ")
+		}
+		if par.Name != "" {
+			buf.WriteString(par.Name)
+			buf.WriteByte(' ')
+		}
+		if isVariadic && i == len(params)-1 {
+			buf.WriteString("...")
+		}
+		writeType(buf, par.Type.(Type))
+	}
+	buf.WriteByte(')')
+}
+
+func writeSignature(buf *bytes.Buffer, sig *Signature) {
+	writeParams(buf, sig.Params, sig.IsVariadic)
+	if len(sig.Results) == 0 {
+		// no result
+		return
+	}
+
+	buf.WriteByte(' ')
+	if len(sig.Results) == 1 && sig.Results[0].Name == "" {
+		// single unnamed result
+		writeType(buf, sig.Results[0].Type.(Type))
+		return
+	}
+
+	// multiple or named result(s)
+	writeParams(buf, sig.Results, false)
+}
+
+func writeType(buf *bytes.Buffer, typ Type) {
+	switch t := typ.(type) {
+	case nil:
+		buf.WriteString("<nil>")
+
+	case *Basic:
+		buf.WriteString(t.Name)
+
+	case *Array:
+		fmt.Fprintf(buf, "[%d]", t.Len)
+		writeType(buf, t.Elt)
+
+	case *Slice:
+		buf.WriteString("[]")
+		writeType(buf, t.Elt)
+
+	case *Struct:
+		buf.WriteString("struct{")
+		for i, f := range t.Fields {
+			if i > 0 {
+				buf.WriteString("; ")
+			}
+			if !f.IsAnonymous {
+				buf.WriteString(f.Name)
+				buf.WriteByte(' ')
+			}
+			writeType(buf, f.Type)
+			if f.Tag != "" {
+				fmt.Fprintf(buf, " %q", f.Tag)
+			}
+		}
+		buf.WriteByte('}')
+
+	case *Pointer:
+		buf.WriteByte('*')
+		writeType(buf, t.Base)
+
+	case *tuple:
+		buf.WriteByte('(')
+		for i, typ := range t.list {
+			if i > 0 {
+				buf.WriteString("; ")
+			}
+			writeType(buf, typ)
+		}
+		buf.WriteByte(')')
+
+	case *Signature:
+		buf.WriteString("func")
+		writeSignature(buf, t)
+
+	case *builtin:
+		fmt.Fprintf(buf, "<type of %s>", t.name)
+
+	case *Interface:
+		buf.WriteString("interface{")
+		for i, m := range t.Methods {
+			if i > 0 {
+				buf.WriteString("; ")
+			}
+			buf.WriteString(m.Name)
+			writeSignature(buf, m.Type.(*Signature))
+		}
+		buf.WriteByte('}')
+
+	case *Map:
+		buf.WriteString("map[")
+		writeType(buf, t.Key)
+		buf.WriteByte(']')
+		writeType(buf, t.Elt)
+
+	case *Chan:
+		var s string
+		switch t.Dir {
+		case ast.SEND:
+			s = "chan<- "
+		case ast.RECV:
+			s = "<-chan "
+		default:
+			s = "chan "
+		}
+		buf.WriteString(s)
+		writeType(buf, t.Elt)
+
+	case *NamedType:
+		buf.WriteString(t.Obj.Name)
+
+	default:
+		fmt.Fprintf(buf, "<type %T>", t)
+	}
+}

src/pkg/exp/types/staging/universe.go

@@ -0,0 +1,159 @@
+// Copyright 2011 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.
+
+// This file implements the universe and unsafe package scopes.
+
+package types
+
+import (
+	"go/ast"
+	"strings"
+)
+
+var (
+	aType            implementsType
+	Universe, unsafe *ast.Scope
+	Unsafe           *ast.Object // package unsafe
+)
+
+// Predeclared types, indexed by BasicKind.
+var Typ = [...]*Basic{
+	Invalid: {aType, Invalid, 0, "invalid type"},
+
+	Bool:          {aType, Bool, IsBoolean, "bool"},
+	Int:           {aType, Int, IsInteger, "int"},
+	Int8:          {aType, Int8, IsInteger, "int8"},
+	Int16:         {aType, Int16, IsInteger, "int16"},
+	Int32:         {aType, Int32, IsInteger, "int32"},
+	Int64:         {aType, Int64, IsInteger, "int64"},
+	Uint:          {aType, Uint, IsInteger | IsUnsigned, "uint"},
+	Uint8:         {aType, Uint8, IsInteger | IsUnsigned, "uint8"},
+	Uint16:        {aType, Uint16, IsInteger | IsUnsigned, "uint16"},
+	Uint32:        {aType, Uint32, IsInteger | IsUnsigned, "uint32"},
+	Uint64:        {aType, Uint64, IsInteger | IsUnsigned, "uint64"},
+	Uintptr:       {aType, Uintptr, IsInteger | IsUnsigned, "uintptr"},
+	Float32:       {aType, Float32, IsFloat, "float32"},
+	Float64:       {aType, Float64, IsFloat, "float64"},
+	Complex64:     {aType, Complex64, IsComplex, "complex64"},
+	Complex128:    {aType, Complex128, IsComplex, "complex128"},
+	String:        {aType, String, IsString, "string"},
+	UnsafePointer: {aType, UnsafePointer, 0, "Pointer"},
+
+	UntypedBool:    {aType, UntypedBool, IsBoolean | IsUntyped, "untyped boolean"},
+	UntypedInt:     {aType, UntypedInt, IsInteger | IsUntyped, "untyped integer"},
+	UntypedRune:    {aType, UntypedRune, IsInteger | IsUntyped, "untyped rune"},
+	UntypedFloat:   {aType, UntypedFloat, IsFloat | IsUntyped, "untyped float"},
+	UntypedComplex: {aType, UntypedComplex, IsComplex | IsUntyped, "untyped complex"},
+	UntypedString:  {aType, UntypedString, IsString | IsUntyped, "untyped string"},
+	UntypedNil:     {aType, UntypedNil, IsUntyped, "untyped nil"},
+}
+
+var aliases = [...]*Basic{
+	{aType, Uint8, IsInteger | IsUnsigned, "byte"},
+	{aType, Rune, IsInteger, "rune"},
+}
+
+var predeclaredConstants = [...]*struct {
+	kind BasicKind
+	name string
+	val  interface{}
+}{
+	{UntypedBool, "true", true},
+	{UntypedBool, "false", false},
+	{UntypedInt, "iota", int64(0)},
+	{UntypedNil, "nil", nil},
+}
+
+var predeclaredFunctions = [...]*builtin{
+	{aType, _Append, "append", 1, true},
+	{aType, _Cap, "cap", 1, false},
+	{aType, _Close, "close", 1, false},
+	{aType, _Complex, "complex", 2, false},
+	{aType, _Copy, "copy", 2, false},
+	{aType, _Delete, "delete", 2, false},
+	{aType, _Imag, "imag", 1, false},
+	{aType, _Len, "len", 1, false},
+	{aType, _Make, "make", 1, true},
+	{aType, _New, "new", 1, false},
+	{aType, _Panic, "panic", 1, false},
+	{aType, _Print, "print", 1, true},
+	{aType, _Println, "println", 1, true},
+	{aType, _Real, "real", 1, false},
+	{aType, _Recover, "recover", 0, false},
+
+	{aType, _Alignof, "Alignof", 1, false},
+	{aType, _Offsetof, "Offsetof", 1, false},
+	{aType, _Sizeof, "Sizeof", 1, false},
+}
+
+// commonly used types
+var (
+	emptyInterface = new(Interface)
+)
+
+// commonly used constants
+var (
+	universeIota *ast.Object
+)
+
+func init() {
+	// Universe scope
+	Universe = ast.NewScope(nil)
+
+	// unsafe package and its scope
+	unsafe = ast.NewScope(nil)
+	Unsafe = ast.NewObj(ast.Pkg, "unsafe")
+	Unsafe.Data = unsafe
+
+	// predeclared types
+	for _, t := range Typ {
+		def(ast.Typ, t.Name).Type = t
+	}
+	for _, t := range aliases {
+		def(ast.Typ, t.Name).Type = t
+	}
+
+	// error type
+	{
+		obj := def(ast.Typ, "error")
+		// TODO(gri) set up correct interface type
+		typ := &NamedType{Underlying: &Interface{}, Obj: obj}
+		obj.Type = typ
+	}
+
+	// predeclared constants
+	for _, t := range predeclaredConstants {
+		obj := def(ast.Con, t.name)
+		obj.Type = Typ[t.kind]
+		obj.Data = t.val
+	}
+
+	// predeclared functions
+	for _, f := range predeclaredFunctions {
+		def(ast.Fun, f.name).Type = f
+	}
+
+	universeIota = Universe.Lookup("iota")
+}
+
+// Objects with names containing blanks are internal and not entered into
+// a scope. Objects with exported names are inserted in the unsafe package
+// scope; other objects are inserted in the universe scope.
+//
+func def(kind ast.ObjKind, name string) *ast.Object {
+	obj := ast.NewObj(kind, name)
+	// insert non-internal objects into respective scope
+	if strings.Index(name, " ") < 0 {
+		scope := Universe
+		// exported identifiers go into package unsafe
+		if ast.IsExported(name) {
+			scope = unsafe
+		}
+		if scope.Insert(obj) != nil {
+			panic("internal error: double declaration")
+		}
+		obj.Decl = scope
+	}
+	return obj
+}