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Source file src/go/types/expr.go

Documentation: go/types

  // 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 typechecking of expressions.
  
  package types
  
  import (
  	"fmt"
  	"go/ast"
  	"go/constant"
  	"go/token"
  	"math"
  )
  
  /*
  Basic algorithm:
  
  Expressions are checked recursively, top down. Expression checker functions
  are generally of the form:
  
    func f(x *operand, e *ast.Expr, ...)
  
  where e is the expression to be checked, and x is the result of the check.
  The check performed by f may fail in which case x.mode == invalid, and
  related error messages will have been issued by f.
  
  If a hint argument is present, it is the composite literal element type
  of an outer composite literal; it is used to type-check composite literal
  elements that have no explicit type specification in the source
  (e.g.: []T{{...}, {...}}, the hint is the type T in this case).
  
  All expressions are checked via rawExpr, which dispatches according
  to expression kind. Upon returning, rawExpr is recording the types and
  constant values for all expressions that have an untyped type (those types
  may change on the way up in the expression tree). Usually these are constants,
  but the results of comparisons or non-constant shifts of untyped constants
  may also be untyped, but not constant.
  
  Untyped expressions may eventually become fully typed (i.e., not untyped),
  typically when the value is assigned to a variable, or is used otherwise.
  The updateExprType method is used to record this final type and update
  the recorded types: the type-checked expression tree is again traversed down,
  and the new type is propagated as needed. Untyped constant expression values
  that become fully typed must now be representable by the full type (constant
  sub-expression trees are left alone except for their roots). This mechanism
  ensures that a client sees the actual (run-time) type an untyped value would
  have. It also permits type-checking of lhs shift operands "as if the shift
  were not present": when updateExprType visits an untyped lhs shift operand
  and assigns it it's final type, that type must be an integer type, and a
  constant lhs must be representable as an integer.
  
  When an expression gets its final type, either on the way out from rawExpr,
  on the way down in updateExprType, or at the end of the type checker run,
  the type (and constant value, if any) is recorded via Info.Types, if present.
  */
  
  type opPredicates map[token.Token]func(Type) bool
  
  var unaryOpPredicates = opPredicates{
  	token.ADD: isNumeric,
  	token.SUB: isNumeric,
  	token.XOR: isInteger,
  	token.NOT: isBoolean,
  }
  
  func (check *Checker) op(m opPredicates, x *operand, op token.Token) bool {
  	if pred := m[op]; pred != nil {
  		if !pred(x.typ) {
  			check.invalidOp(x.pos(), "operator %s not defined for %s", op, x)
  			return false
  		}
  	} else {
  		check.invalidAST(x.pos(), "unknown operator %s", op)
  		return false
  	}
  	return true
  }
  
  // The unary expression e may be nil. It's passed in for better error messages only.
  func (check *Checker) unary(x *operand, e *ast.UnaryExpr, op token.Token) {
  	switch op {
  	case token.AND:
  		// spec: "As an exception to the addressability
  		// requirement x may also be a composite literal."
  		if _, ok := unparen(x.expr).(*ast.CompositeLit); !ok && x.mode != variable {
  			check.invalidOp(x.pos(), "cannot take address of %s", x)
  			x.mode = invalid
  			return
  		}
  		x.mode = value
  		x.typ = &Pointer{base: x.typ}
  		return
  
  	case token.ARROW:
  		typ, ok := x.typ.Underlying().(*Chan)
  		if !ok {
  			check.invalidOp(x.pos(), "cannot receive from non-channel %s", x)
  			x.mode = invalid
  			return
  		}
  		if typ.dir == SendOnly {
  			check.invalidOp(x.pos(), "cannot receive from send-only channel %s", x)
  			x.mode = invalid
  			return
  		}
  		x.mode = commaok
  		x.typ = typ.elem
  		check.hasCallOrRecv = true
  		return
  	}
  
  	if !check.op(unaryOpPredicates, x, op) {
  		x.mode = invalid
  		return
  	}
  
  	if x.mode == constant_ {
  		typ := x.typ.Underlying().(*Basic)
  		var prec uint
  		if isUnsigned(typ) {
  			prec = uint(check.conf.sizeof(typ) * 8)
  		}
  		x.val = constant.UnaryOp(op, x.val, prec)
  		// Typed constants must be representable in
  		// their type after each constant operation.
  		if isTyped(typ) {
  			if e != nil {
  				x.expr = e // for better error message
  			}
  			check.representable(x, typ)
  		}
  		return
  	}
  
  	x.mode = value
  	// x.typ remains unchanged
  }
  
  func isShift(op token.Token) bool {
  	return op == token.SHL || op == token.SHR
  }
  
  func isComparison(op token.Token) bool {
  	// Note: tokens are not ordered well to make this much easier
  	switch op {
  	case token.EQL, token.NEQ, token.LSS, token.LEQ, token.GTR, token.GEQ:
  		return true
  	}
  	return false
  }
  
  func fitsFloat32(x constant.Value) bool {
  	f32, _ := constant.Float32Val(x)
  	f := float64(f32)
  	return !math.IsInf(f, 0)
  }
  
  func roundFloat32(x constant.Value) constant.Value {
  	f32, _ := constant.Float32Val(x)
  	f := float64(f32)
  	if !math.IsInf(f, 0) {
  		return constant.MakeFloat64(f)
  	}
  	return nil
  }
  
  func fitsFloat64(x constant.Value) bool {
  	f, _ := constant.Float64Val(x)
  	return !math.IsInf(f, 0)
  }
  
  func roundFloat64(x constant.Value) constant.Value {
  	f, _ := constant.Float64Val(x)
  	if !math.IsInf(f, 0) {
  		return constant.MakeFloat64(f)
  	}
  	return nil
  }
  
  // representableConst reports whether x can be represented as
  // value of the given basic type and for the configuration
  // provided (only needed for int/uint sizes).
  //
  // If rounded != nil, *rounded is set to the rounded value of x for
  // representable floating-point and complex values, and to an Int
  // value for integer values; it is left alone otherwise.
  // It is ok to provide the addressof the first argument for rounded.
  func representableConst(x constant.Value, conf *Config, typ *Basic, rounded *constant.Value) bool {
  	if x.Kind() == constant.Unknown {
  		return true // avoid follow-up errors
  	}
  
  	switch {
  	case isInteger(typ):
  		x := constant.ToInt(x)
  		if x.Kind() != constant.Int {
  			return false
  		}
  		if rounded != nil {
  			*rounded = x
  		}
  		if x, ok := constant.Int64Val(x); ok {
  			switch typ.kind {
  			case Int:
  				var s = uint(conf.sizeof(typ)) * 8
  				return int64(-1)<<(s-1) <= x && x <= int64(1)<<(s-1)-1
  			case Int8:
  				const s = 8
  				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
  			case Int16:
  				const s = 16
  				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
  			case Int32:
  				const s = 32
  				return -1<<(s-1) <= x && x <= 1<<(s-1)-1
  			case Int64, UntypedInt:
  				return true
  			case Uint, Uintptr:
  				if s := uint(conf.sizeof(typ)) * 8; s < 64 {
  					return 0 <= x && x <= int64(1)<<s-1
  				}
  				return 0 <= x
  			case Uint8:
  				const s = 8
  				return 0 <= x && x <= 1<<s-1
  			case Uint16:
  				const s = 16
  				return 0 <= x && x <= 1<<s-1
  			case Uint32:
  				const s = 32
  				return 0 <= x && x <= 1<<s-1
  			case Uint64:
  				return 0 <= x
  			default:
  				unreachable()
  			}
  		}
  		// x does not fit into int64
  		switch n := constant.BitLen(x); typ.kind {
  		case Uint, Uintptr:
  			var s = uint(conf.sizeof(typ)) * 8
  			return constant.Sign(x) >= 0 && n <= int(s)
  		case Uint64:
  			return constant.Sign(x) >= 0 && n <= 64
  		case UntypedInt:
  			return true
  		}
  
  	case isFloat(typ):
  		x := constant.ToFloat(x)
  		if x.Kind() != constant.Float {
  			return false
  		}
  		switch typ.kind {
  		case Float32:
  			if rounded == nil {
  				return fitsFloat32(x)
  			}
  			r := roundFloat32(x)
  			if r != nil {
  				*rounded = r
  				return true
  			}
  		case Float64:
  			if rounded == nil {
  				return fitsFloat64(x)
  			}
  			r := roundFloat64(x)
  			if r != nil {
  				*rounded = r
  				return true
  			}
  		case UntypedFloat:
  			return true
  		default:
  			unreachable()
  		}
  
  	case isComplex(typ):
  		x := constant.ToComplex(x)
  		if x.Kind() != constant.Complex {
  			return false
  		}
  		switch typ.kind {
  		case Complex64:
  			if rounded == nil {
  				return fitsFloat32(constant.Real(x)) && fitsFloat32(constant.Imag(x))
  			}
  			re := roundFloat32(constant.Real(x))
  			im := roundFloat32(constant.Imag(x))
  			if re != nil && im != nil {
  				*rounded = constant.BinaryOp(re, token.ADD, constant.MakeImag(im))
  				return true
  			}
  		case Complex128:
  			if rounded == nil {
  				return fitsFloat64(constant.Real(x)) && fitsFloat64(constant.Imag(x))
  			}
  			re := roundFloat64(constant.Real(x))
  			im := roundFloat64(constant.Imag(x))
  			if re != nil && im != nil {
  				*rounded = constant.BinaryOp(re, token.ADD, constant.MakeImag(im))
  				return true
  			}
  		case UntypedComplex:
  			return true
  		default:
  			unreachable()
  		}
  
  	case isString(typ):
  		return x.Kind() == constant.String
  
  	case isBoolean(typ):
  		return x.Kind() == constant.Bool
  	}
  
  	return false
  }
  
  // representable checks that a constant operand is representable in the given basic type.
  func (check *Checker) representable(x *operand, typ *Basic) {
  	assert(x.mode == constant_)
  	if !representableConst(x.val, check.conf, typ, &x.val) {
  		var msg string
  		if isNumeric(x.typ) && isNumeric(typ) {
  			// numeric conversion : error msg
  			//
  			// integer -> integer : overflows
  			// integer -> float   : overflows (actually not possible)
  			// float   -> integer : truncated
  			// float   -> float   : overflows
  			//
  			if !isInteger(x.typ) && isInteger(typ) {
  				msg = "%s truncated to %s"
  			} else {
  				msg = "%s overflows %s"
  			}
  		} else {
  			msg = "cannot convert %s to %s"
  		}
  		check.errorf(x.pos(), msg, x, typ)
  		x.mode = invalid
  	}
  }
  
  // updateExprType updates the type of x to typ and invokes itself
  // recursively for the operands of x, depending on expression kind.
  // If typ is still an untyped and not the final type, updateExprType
  // only updates the recorded untyped type for x and possibly its
  // operands. Otherwise (i.e., typ is not an untyped type anymore,
  // or it is the final type for x), the type and value are recorded.
  // Also, if x is a constant, it must be representable as a value of typ,
  // and if x is the (formerly untyped) lhs operand of a non-constant
  // shift, it must be an integer value.
  //
  func (check *Checker) updateExprType(x ast.Expr, typ Type, final bool) {
  	old, found := check.untyped[x]
  	if !found {
  		return // nothing to do
  	}
  
  	// update operands of x if necessary
  	switch x := x.(type) {
  	case *ast.BadExpr,
  		*ast.FuncLit,
  		*ast.CompositeLit,
  		*ast.IndexExpr,
  		*ast.SliceExpr,
  		*ast.TypeAssertExpr,
  		*ast.StarExpr,
  		*ast.KeyValueExpr,
  		*ast.ArrayType,
  		*ast.StructType,
  		*ast.FuncType,
  		*ast.InterfaceType,
  		*ast.MapType,
  		*ast.ChanType:
  		// These expression are never untyped - nothing to do.
  		// The respective sub-expressions got their final types
  		// upon assignment or use.
  		if debug {
  			check.dump("%s: found old type(%s): %s (new: %s)", x.Pos(), x, old.typ, typ)
  			unreachable()
  		}
  		return
  
  	case *ast.CallExpr:
  		// Resulting in an untyped constant (e.g., built-in complex).
  		// The respective calls take care of calling updateExprType
  		// for the arguments if necessary.
  
  	case *ast.Ident, *ast.BasicLit, *ast.SelectorExpr:
  		// An identifier denoting a constant, a constant literal,
  		// or a qualified identifier (imported untyped constant).
  		// No operands to take care of.
  
  	case *ast.ParenExpr:
  		check.updateExprType(x.X, typ, final)
  
  	case *ast.UnaryExpr:
  		// If x is a constant, the operands were constants.
  		// They don't need to be updated since they never
  		// get "materialized" into a typed value; and they
  		// will be processed at the end of the type check.
  		if old.val != nil {
  			break
  		}
  		check.updateExprType(x.X, typ, final)
  
  	case *ast.BinaryExpr:
  		if old.val != nil {
  			break // see comment for unary expressions
  		}
  		if isComparison(x.Op) {
  			// The result type is independent of operand types
  			// and the operand types must have final types.
  		} else if isShift(x.Op) {
  			// The result type depends only on lhs operand.
  			// The rhs type was updated when checking the shift.
  			check.updateExprType(x.X, typ, final)
  		} else {
  			// The operand types match the result type.
  			check.updateExprType(x.X, typ, final)
  			check.updateExprType(x.Y, typ, final)
  		}
  
  	default:
  		unreachable()
  	}
  
  	// If the new type is not final and still untyped, just
  	// update the recorded type.
  	if !final && isUntyped(typ) {
  		old.typ = typ.Underlying().(*Basic)
  		check.untyped[x] = old
  		return
  	}
  
  	// Otherwise we have the final (typed or untyped type).
  	// Remove it from the map of yet untyped expressions.
  	delete(check.untyped, x)
  
  	// If x is the lhs of a shift, its final type must be integer.
  	// We already know from the shift check that it is representable
  	// as an integer if it is a constant.
  	if old.isLhs && !isInteger(typ) {
  		check.invalidOp(x.Pos(), "shifted operand %s (type %s) must be integer", x, typ)
  		return
  	}
  
  	// Everything's fine, record final type and value for x.
  	check.recordTypeAndValue(x, old.mode, typ, old.val)
  }
  
  // updateExprVal updates the value of x to val.
  func (check *Checker) updateExprVal(x ast.Expr, val constant.Value) {
  	if info, ok := check.untyped[x]; ok {
  		info.val = val
  		check.untyped[x] = info
  	}
  }
  
  // convertUntyped attempts to set the type of an untyped value to the target type.
  func (check *Checker) convertUntyped(x *operand, target Type) {
  	if x.mode == invalid || isTyped(x.typ) || target == Typ[Invalid] {
  		return
  	}
  
  	// TODO(gri) Sloppy code - clean up. This function is central
  	//           to assignment and expression checking.
  
  	if isUntyped(target) {
  		// both x and target are untyped
  		xkind := x.typ.(*Basic).kind
  		tkind := target.(*Basic).kind
  		if isNumeric(x.typ) && isNumeric(target) {
  			if xkind < tkind {
  				x.typ = target
  				check.updateExprType(x.expr, target, false)
  			}
  		} else if xkind != tkind {
  			goto Error
  		}
  		return
  	}
  
  	// typed target
  	switch t := target.Underlying().(type) {
  	case *Basic:
  		if x.mode == constant_ {
  			check.representable(x, t)
  			if x.mode == invalid {
  				return
  			}
  			// expression value may have been rounded - update if needed
  			check.updateExprVal(x.expr, x.val)
  		} else {
  			// Non-constant untyped values may appear as the
  			// result of comparisons (untyped bool), intermediate
  			// (delayed-checked) rhs operands of shifts, and as
  			// the value nil.
  			switch x.typ.(*Basic).kind {
  			case UntypedBool:
  				if !isBoolean(target) {
  					goto Error
  				}
  			case UntypedInt, UntypedRune, UntypedFloat, UntypedComplex:
  				if !isNumeric(target) {
  					goto Error
  				}
  			case UntypedString:
  				// Non-constant untyped string values are not
  				// permitted by the spec and should not occur.
  				unreachable()
  			case UntypedNil:
  				// Unsafe.Pointer is a basic type that includes nil.
  				if !hasNil(target) {
  					goto Error
  				}
  			default:
  				goto Error
  			}
  		}
  	case *Interface:
  		if !x.isNil() && !t.Empty() /* empty interfaces are ok */ {
  			goto Error
  		}
  		// Update operand types to the default type rather then
  		// the target (interface) type: values must have concrete
  		// dynamic types. If the value is nil, keep it untyped
  		// (this is important for tools such as go vet which need
  		// the dynamic type for argument checking of say, print
  		// functions)
  		if x.isNil() {
  			target = Typ[UntypedNil]
  		} else {
  			// cannot assign untyped values to non-empty interfaces
  			if !t.Empty() {
  				goto Error
  			}
  			target = Default(x.typ)
  		}
  	case *Pointer, *Signature, *Slice, *Map, *Chan:
  		if !x.isNil() {
  			goto Error
  		}
  		// keep nil untyped - see comment for interfaces, above
  		target = Typ[UntypedNil]
  	default:
  		goto Error
  	}
  
  	x.typ = target
  	check.updateExprType(x.expr, target, true) // UntypedNils are final
  	return
  
  Error:
  	check.errorf(x.pos(), "cannot convert %s to %s", x, target)
  	x.mode = invalid
  }
  
  func (check *Checker) comparison(x, y *operand, op token.Token) {
  	// spec: "In any comparison, the first operand must be assignable
  	// to the type of the second operand, or vice versa."
  	err := ""
  	if x.assignableTo(check.conf, y.typ, nil) || y.assignableTo(check.conf, x.typ, nil) {
  		defined := false
  		switch op {
  		case token.EQL, token.NEQ:
  			// spec: "The equality operators == and != apply to operands that are comparable."
  			defined = Comparable(x.typ) || x.isNil() && hasNil(y.typ) || y.isNil() && hasNil(x.typ)
  		case token.LSS, token.LEQ, token.GTR, token.GEQ:
  			// spec: The ordering operators <, <=, >, and >= apply to operands that are ordered."
  			defined = isOrdered(x.typ)
  		default:
  			unreachable()
  		}
  		if !defined {
  			typ := x.typ
  			if x.isNil() {
  				typ = y.typ
  			}
  			err = check.sprintf("operator %s not defined for %s", op, typ)
  		}
  	} else {
  		err = check.sprintf("mismatched types %s and %s", x.typ, y.typ)
  	}
  
  	if err != "" {
  		check.errorf(x.pos(), "cannot compare %s %s %s (%s)", x.expr, op, y.expr, err)
  		x.mode = invalid
  		return
  	}
  
  	if x.mode == constant_ && y.mode == constant_ {
  		x.val = constant.MakeBool(constant.Compare(x.val, op, y.val))
  		// The operands are never materialized; no need to update
  		// their types.
  	} else {
  		x.mode = value
  		// The operands have now their final types, which at run-
  		// time will be materialized. Update the expression trees.
  		// If the current types are untyped, the materialized type
  		// is the respective default type.
  		check.updateExprType(x.expr, Default(x.typ), true)
  		check.updateExprType(y.expr, Default(y.typ), true)
  	}
  
  	// spec: "Comparison operators compare two operands and yield
  	//        an untyped boolean value."
  	x.typ = Typ[UntypedBool]
  }
  
  func (check *Checker) shift(x, y *operand, e *ast.BinaryExpr, op token.Token) {
  	untypedx := isUntyped(x.typ)
  
  	var xval constant.Value
  	if x.mode == constant_ {
  		xval = constant.ToInt(x.val)
  	}
  
  	if isInteger(x.typ) || untypedx && xval != nil && xval.Kind() == constant.Int {
  		// The lhs is of integer type or an untyped constant representable
  		// as an integer. Nothing to do.
  	} else {
  		// shift has no chance
  		check.invalidOp(x.pos(), "shifted operand %s must be integer", x)
  		x.mode = invalid
  		return
  	}
  
  	// spec: "The right operand in a shift expression must have unsigned
  	// integer type or be an untyped constant representable by a value of
  	// type uint."
  	switch {
  	case isUnsigned(y.typ):
  		// nothing to do
  	case isUntyped(y.typ):
  		check.convertUntyped(y, Typ[Uint])
  		if y.mode == invalid {
  			x.mode = invalid
  			return
  		}
  	default:
  		check.invalidOp(y.pos(), "shift count %s must be unsigned integer", y)
  		x.mode = invalid
  		return
  	}
  
  	if x.mode == constant_ {
  		if y.mode == constant_ {
  			// rhs must be an integer value
  			yval := constant.ToInt(y.val)
  			if yval.Kind() != constant.Int {
  				check.invalidOp(y.pos(), "shift count %s must be unsigned integer", y)
  				x.mode = invalid
  				return
  			}
  			// rhs must be within reasonable bounds
  			const shiftBound = 1023 - 1 + 52 // so we can express smallestFloat64
  			s, ok := constant.Uint64Val(yval)
  			if !ok || s > shiftBound {
  				check.invalidOp(y.pos(), "invalid shift count %s", y)
  				x.mode = invalid
  				return
  			}
  			// The lhs is representable as an integer but may not be an integer
  			// (e.g., 2.0, an untyped float) - this can only happen for untyped
  			// non-integer numeric constants. Correct the type so that the shift
  			// result is of integer type.
  			if !isInteger(x.typ) {
  				x.typ = Typ[UntypedInt]
  			}
  			// x is a constant so xval != nil and it must be of Int kind.
  			x.val = constant.Shift(xval, op, uint(s))
  			// Typed constants must be representable in
  			// their type after each constant operation.
  			if isTyped(x.typ) {
  				if e != nil {
  					x.expr = e // for better error message
  				}
  				check.representable(x, x.typ.Underlying().(*Basic))
  			}
  			return
  		}
  
  		// non-constant shift with constant lhs
  		if untypedx {
  			// spec: "If the left operand of a non-constant shift
  			// expression is an untyped constant, the type of the
  			// constant is what it would be if the shift expression
  			// were replaced by its left operand alone.".
  			//
  			// Delay operand checking until we know the final type
  			// by marking the lhs expression as lhs shift operand.
  			//
  			// Usually (in correct programs), the lhs expression
  			// is in the untyped map. However, it is possible to
  			// create incorrect programs where the same expression
  			// is evaluated twice (via a declaration cycle) such
  			// that the lhs expression type is determined in the
  			// first round and thus deleted from the map, and then
  			// not found in the second round (double insertion of
  			// the same expr node still just leads to one entry for
  			// that node, and it can only be deleted once).
  			// Be cautious and check for presence of entry.
  			// Example: var e, f = int(1<<""[f]) // issue 11347
  			if info, found := check.untyped[x.expr]; found {
  				info.isLhs = true
  				check.untyped[x.expr] = info
  			}
  			// keep x's type
  			x.mode = value
  			return
  		}
  	}
  
  	// constant rhs must be >= 0
  	if y.mode == constant_ && constant.Sign(y.val) < 0 {
  		check.invalidOp(y.pos(), "shift count %s must not be negative", y)
  	}
  
  	// non-constant shift - lhs must be an integer
  	if !isInteger(x.typ) {
  		check.invalidOp(x.pos(), "shifted operand %s must be integer", x)
  		x.mode = invalid
  		return
  	}
  
  	x.mode = value
  }
  
  var binaryOpPredicates = opPredicates{
  	token.ADD: func(typ Type) bool { return isNumeric(typ) || isString(typ) },
  	token.SUB: isNumeric,
  	token.MUL: isNumeric,
  	token.QUO: isNumeric,
  	token.REM: isInteger,
  
  	token.AND:     isInteger,
  	token.OR:      isInteger,
  	token.XOR:     isInteger,
  	token.AND_NOT: isInteger,
  
  	token.LAND: isBoolean,
  	token.LOR:  isBoolean,
  }
  
  // The binary expression e may be nil. It's passed in for better error messages only.
  func (check *Checker) binary(x *operand, e *ast.BinaryExpr, lhs, rhs ast.Expr, op token.Token) {
  	var y operand
  
  	check.expr(x, lhs)
  	check.expr(&y, rhs)
  
  	if x.mode == invalid {
  		return
  	}
  	if y.mode == invalid {
  		x.mode = invalid
  		x.expr = y.expr
  		return
  	}
  
  	if isShift(op) {
  		check.shift(x, &y, e, op)
  		return
  	}
  
  	check.convertUntyped(x, y.typ)
  	if x.mode == invalid {
  		return
  	}
  	check.convertUntyped(&y, x.typ)
  	if y.mode == invalid {
  		x.mode = invalid
  		return
  	}
  
  	if isComparison(op) {
  		check.comparison(x, &y, op)
  		return
  	}
  
  	if !Identical(x.typ, y.typ) {
  		// only report an error if we have valid types
  		// (otherwise we had an error reported elsewhere already)
  		if x.typ != Typ[Invalid] && y.typ != Typ[Invalid] {
  			check.invalidOp(x.pos(), "mismatched types %s and %s", x.typ, y.typ)
  		}
  		x.mode = invalid
  		return
  	}
  
  	if !check.op(binaryOpPredicates, x, op) {
  		x.mode = invalid
  		return
  	}
  
  	if op == token.QUO || op == token.REM {
  		// check for zero divisor
  		if (x.mode == constant_ || isInteger(x.typ)) && y.mode == constant_ && constant.Sign(y.val) == 0 {
  			check.invalidOp(y.pos(), "division by zero")
  			x.mode = invalid
  			return
  		}
  
  		// check for divisor underflow in complex division (see issue 20227)
  		if x.mode == constant_ && y.mode == constant_ && isComplex(x.typ) {
  			re, im := constant.Real(y.val), constant.Imag(y.val)
  			re2, im2 := constant.BinaryOp(re, token.MUL, re), constant.BinaryOp(im, token.MUL, im)
  			if constant.Sign(re2) == 0 && constant.Sign(im2) == 0 {
  				check.invalidOp(y.pos(), "division by zero")
  				x.mode = invalid
  				return
  			}
  		}
  	}
  
  	if x.mode == constant_ && y.mode == constant_ {
  		xval := x.val
  		yval := y.val
  		typ := x.typ.Underlying().(*Basic)
  		// force integer division of integer operands
  		if op == token.QUO && isInteger(typ) {
  			op = token.QUO_ASSIGN
  		}
  		x.val = constant.BinaryOp(xval, op, yval)
  		// Typed constants must be representable in
  		// their type after each constant operation.
  		if isTyped(typ) {
  			if e != nil {
  				x.expr = e // for better error message
  			}
  			check.representable(x, typ)
  		}
  		return
  	}
  
  	x.mode = value
  	// x.typ is unchanged
  }
  
  // index checks an index expression for validity.
  // If max >= 0, it is the upper bound for index.
  // If index is valid and the result i >= 0, then i is the constant value of index.
  func (check *Checker) index(index ast.Expr, max int64) (i int64, valid bool) {
  	var x operand
  	check.expr(&x, index)
  	if x.mode == invalid {
  		return
  	}
  
  	// an untyped constant must be representable as Int
  	check.convertUntyped(&x, Typ[Int])
  	if x.mode == invalid {
  		return
  	}
  
  	// the index must be of integer type
  	if !isInteger(x.typ) {
  		check.invalidArg(x.pos(), "index %s must be integer", &x)
  		return
  	}
  
  	// a constant index i must be in bounds
  	if x.mode == constant_ {
  		if constant.Sign(x.val) < 0 {
  			check.invalidArg(x.pos(), "index %s must not be negative", &x)
  			return
  		}
  		i, valid = constant.Int64Val(constant.ToInt(x.val))
  		if !valid || max >= 0 && i >= max {
  			check.errorf(x.pos(), "index %s is out of bounds", &x)
  			return i, false
  		}
  		// 0 <= i [ && i < max ]
  		return i, true
  	}
  
  	return -1, true
  }
  
  // indexElts checks the elements (elts) of an array or slice composite literal
  // against the literal's element type (typ), and the element indices against
  // the literal length if known (length >= 0). It returns the length of the
  // literal (maximum index value + 1).
  //
  func (check *Checker) indexedElts(elts []ast.Expr, typ Type, length int64) int64 {
  	visited := make(map[int64]bool, len(elts))
  	var index, max int64
  	for _, e := range elts {
  		// determine and check index
  		validIndex := false
  		eval := e
  		if kv, _ := e.(*ast.KeyValueExpr); kv != nil {
  			if i, ok := check.index(kv.Key, length); ok {
  				if i >= 0 {
  					index = i
  					validIndex = true
  				} else {
  					check.errorf(e.Pos(), "index %s must be integer constant", kv.Key)
  				}
  			}
  			eval = kv.Value
  		} else if length >= 0 && index >= length {
  			check.errorf(e.Pos(), "index %d is out of bounds (>= %d)", index, length)
  		} else {
  			validIndex = true
  		}
  
  		// if we have a valid index, check for duplicate entries
  		if validIndex {
  			if visited[index] {
  				check.errorf(e.Pos(), "duplicate index %d in array or slice literal", index)
  			}
  			visited[index] = true
  		}
  		index++
  		if index > max {
  			max = index
  		}
  
  		// check element against composite literal element type
  		var x operand
  		check.exprWithHint(&x, eval, typ)
  		check.assignment(&x, typ, "array or slice literal")
  	}
  	return max
  }
  
  // exprKind describes the kind of an expression; the kind
  // determines if an expression is valid in 'statement context'.
  type exprKind int
  
  const (
  	conversion exprKind = iota
  	expression
  	statement
  )
  
  // rawExpr typechecks expression e and initializes x with the expression
  // value or type. If an error occurred, x.mode is set to invalid.
  // If hint != nil, it is the type of a composite literal element.
  //
  func (check *Checker) rawExpr(x *operand, e ast.Expr, hint Type) exprKind {
  	if trace {
  		check.trace(e.Pos(), "%s", e)
  		check.indent++
  		defer func() {
  			check.indent--
  			check.trace(e.Pos(), "=> %s", x)
  		}()
  	}
  
  	kind := check.exprInternal(x, e, hint)
  
  	// convert x into a user-friendly set of values
  	// TODO(gri) this code can be simplified
  	var typ Type
  	var val constant.Value
  	switch x.mode {
  	case invalid:
  		typ = Typ[Invalid]
  	case novalue:
  		typ = (*Tuple)(nil)
  	case constant_:
  		typ = x.typ
  		val = x.val
  	default:
  		typ = x.typ
  	}
  	assert(x.expr != nil && typ != nil)
  
  	if isUntyped(typ) {
  		// delay type and value recording until we know the type
  		// or until the end of type checking
  		check.rememberUntyped(x.expr, false, x.mode, typ.(*Basic), val)
  	} else {
  		check.recordTypeAndValue(e, x.mode, typ, val)
  	}
  
  	return kind
  }
  
  // exprInternal contains the core of type checking of expressions.
  // Must only be called by rawExpr.
  //
  func (check *Checker) exprInternal(x *operand, e ast.Expr, hint Type) exprKind {
  	// make sure x has a valid state in case of bailout
  	// (was issue 5770)
  	x.mode = invalid
  	x.typ = Typ[Invalid]
  
  	switch e := e.(type) {
  	case *ast.BadExpr:
  		goto Error // error was reported before
  
  	case *ast.Ident:
  		check.ident(x, e, nil, nil)
  
  	case *ast.Ellipsis:
  		// ellipses are handled explicitly where they are legal
  		// (array composite literals and parameter lists)
  		check.error(e.Pos(), "invalid use of '...'")
  		goto Error
  
  	case *ast.BasicLit:
  		x.setConst(e.Kind, e.Value)
  		if x.mode == invalid {
  			check.invalidAST(e.Pos(), "invalid literal %v", e.Value)
  			goto Error
  		}
  
  	case *ast.FuncLit:
  		if sig, ok := check.typ(e.Type).(*Signature); ok {
  			// Anonymous functions are considered part of the
  			// init expression/func declaration which contains
  			// them: use existing package-level declaration info.
  			check.funcBody(check.decl, "", sig, e.Body)
  			x.mode = value
  			x.typ = sig
  		} else {
  			check.invalidAST(e.Pos(), "invalid function literal %s", e)
  			goto Error
  		}
  
  	case *ast.CompositeLit:
  		var typ, base Type
  
  		switch {
  		case e.Type != nil:
  			// composite literal type present - use it
  			// [...]T array types may only appear with composite literals.
  			// Check for them here so we don't have to handle ... in general.
  			if atyp, _ := e.Type.(*ast.ArrayType); atyp != nil && atyp.Len != nil {
  				if ellip, _ := atyp.Len.(*ast.Ellipsis); ellip != nil && ellip.Elt == nil {
  					// We have an "open" [...]T array type.
  					// Create a new ArrayType with unknown length (-1)
  					// and finish setting it up after analyzing the literal.
  					typ = &Array{len: -1, elem: check.typ(atyp.Elt)}
  					base = typ
  					break
  				}
  			}
  			typ = check.typ(e.Type)
  			base = typ
  
  		case hint != nil:
  			// no composite literal type present - use hint (element type of enclosing type)
  			typ = hint
  			base, _ = deref(typ.Underlying()) // *T implies &T{}
  
  		default:
  			// TODO(gri) provide better error messages depending on context
  			check.error(e.Pos(), "missing type in composite literal")
  			goto Error
  		}
  
  		switch utyp := base.Underlying().(type) {
  		case *Struct:
  			if len(e.Elts) == 0 {
  				break
  			}
  			fields := utyp.fields
  			if _, ok := e.Elts[0].(*ast.KeyValueExpr); ok {
  				// all elements must have keys
  				visited := make([]bool, len(fields))
  				for _, e := range e.Elts {
  					kv, _ := e.(*ast.KeyValueExpr)
  					if kv == nil {
  						check.error(e.Pos(), "mixture of field:value and value elements in struct literal")
  						continue
  					}
  					key, _ := kv.Key.(*ast.Ident)
  					if key == nil {
  						check.errorf(kv.Pos(), "invalid field name %s in struct literal", kv.Key)
  						continue
  					}
  					i := fieldIndex(utyp.fields, check.pkg, key.Name)
  					if i < 0 {
  						check.errorf(kv.Pos(), "unknown field %s in struct literal", key.Name)
  						continue
  					}
  					fld := fields[i]
  					check.recordUse(key, fld)
  					// 0 <= i < len(fields)
  					if visited[i] {
  						check.errorf(kv.Pos(), "duplicate field name %s in struct literal", key.Name)
  						continue
  					}
  					visited[i] = true
  					check.expr(x, kv.Value)
  					etyp := fld.typ
  					check.assignment(x, etyp, "struct literal")
  				}
  			} else {
  				// no element must have a key
  				for i, e := range e.Elts {
  					if kv, _ := e.(*ast.KeyValueExpr); kv != nil {
  						check.error(kv.Pos(), "mixture of field:value and value elements in struct literal")
  						continue
  					}
  					check.expr(x, e)
  					if i >= len(fields) {
  						check.error(x.pos(), "too many values in struct literal")
  						break // cannot continue
  					}
  					// i < len(fields)
  					fld := fields[i]
  					if !fld.Exported() && fld.pkg != check.pkg {
  						check.errorf(x.pos(), "implicit assignment to unexported field %s in %s literal", fld.name, typ)
  						continue
  					}
  					etyp := fld.typ
  					check.assignment(x, etyp, "struct literal")
  				}
  				if len(e.Elts) < len(fields) {
  					check.error(e.Rbrace, "too few values in struct literal")
  					// ok to continue
  				}
  			}
  
  		case *Array:
  			// Prevent crash if the array referred to is not yet set up.
  			// This is a stop-gap solution; a better approach would use the mechanism of
  			// Checker.ident (typexpr.go) using a path of types. But that would require
  			// passing the path everywhere (all expression-checking methods, not just
  			// type expression checking), and we're not set up for that (quite possibly
  			// an indication that cycle detection needs to be rethought). Was issue #18643.
  			if utyp.elem == nil {
  				check.error(e.Pos(), "illegal cycle in type declaration")
  				goto Error
  			}
  			n := check.indexedElts(e.Elts, utyp.elem, utyp.len)
  			// If we have an "open" [...]T array, set the length now that we know it
  			// and record the type for [...] (usually done by check.typExpr which is
  			// not called for [...]).
  			if utyp.len < 0 {
  				utyp.len = n
  				check.recordTypeAndValue(e.Type, typexpr, utyp, nil)
  			}
  
  		case *Slice:
  			// Prevent crash if the slice referred to is not yet set up.
  			// See analogous comment for *Array.
  			if utyp.elem == nil {
  				check.error(e.Pos(), "illegal cycle in type declaration")
  				goto Error
  			}
  			check.indexedElts(e.Elts, utyp.elem, -1)
  
  		case *Map:
  			// Prevent crash if the map referred to is not yet set up.
  			// See analogous comment for *Array.
  			if utyp.key == nil || utyp.elem == nil {
  				check.error(e.Pos(), "illegal cycle in type declaration")
  				goto Error
  			}
  			visited := make(map[interface{}][]Type, len(e.Elts))
  			for _, e := range e.Elts {
  				kv, _ := e.(*ast.KeyValueExpr)
  				if kv == nil {
  					check.error(e.Pos(), "missing key in map literal")
  					continue
  				}
  				check.exprWithHint(x, kv.Key, utyp.key)
  				check.assignment(x, utyp.key, "map literal")
  				if x.mode == invalid {
  					continue
  				}
  				if x.mode == constant_ {
  					duplicate := false
  					// if the key is of interface type, the type is also significant when checking for duplicates
  					if _, ok := utyp.key.Underlying().(*Interface); ok {
  						for _, vtyp := range visited[x.val] {
  							if Identical(vtyp, x.typ) {
  								duplicate = true
  								break
  							}
  						}
  						visited[x.val] = append(visited[x.val], x.typ)
  					} else {
  						_, duplicate = visited[x.val]
  						visited[x.val] = nil
  					}
  					if duplicate {
  						check.errorf(x.pos(), "duplicate key %s in map literal", x.val)
  						continue
  					}
  				}
  				check.exprWithHint(x, kv.Value, utyp.elem)
  				check.assignment(x, utyp.elem, "map literal")
  			}
  
  		default:
  			// when "using" all elements unpack KeyValueExpr
  			// explicitly because check.use doesn't accept them
  			for _, e := range e.Elts {
  				if kv, _ := e.(*ast.KeyValueExpr); kv != nil {
  					// Ideally, we should also "use" kv.Key but we can't know
  					// if it's an externally defined struct key or not. Going
  					// forward anyway can lead to other errors. Give up instead.
  					e = kv.Value
  				}
  				check.use(e)
  			}
  			// if utyp is invalid, an error was reported before
  			if utyp != Typ[Invalid] {
  				check.errorf(e.Pos(), "invalid composite literal type %s", typ)
  				goto Error
  			}
  		}
  
  		x.mode = value
  		x.typ = typ
  
  	case *ast.ParenExpr:
  		kind := check.rawExpr(x, e.X, nil)
  		x.expr = e
  		return kind
  
  	case *ast.SelectorExpr:
  		check.selector(x, e)
  
  	case *ast.IndexExpr:
  		check.expr(x, e.X)
  		if x.mode == invalid {
  			check.use(e.Index)
  			goto Error
  		}
  
  		valid := false
  		length := int64(-1) // valid if >= 0
  		switch typ := x.typ.Underlying().(type) {
  		case *Basic:
  			if isString(typ) {
  				valid = true
  				if x.mode == constant_ {
  					length = int64(len(constant.StringVal(x.val)))
  				}
  				// an indexed string always yields a byte value
  				// (not a constant) even if the string and the
  				// index are constant
  				x.mode = value
  				x.typ = universeByte // use 'byte' name
  			}
  
  		case *Array:
  			valid = true
  			length = typ.len
  			if x.mode != variable {
  				x.mode = value
  			}
  			x.typ = typ.elem
  
  		case *Pointer:
  			if typ, _ := typ.base.Underlying().(*Array); typ != nil {
  				valid = true
  				length = typ.len
  				x.mode = variable
  				x.typ = typ.elem
  			}
  
  		case *Slice:
  			valid = true
  			x.mode = variable
  			x.typ = typ.elem
  
  		case *Map:
  			var key operand
  			check.expr(&key, e.Index)
  			check.assignment(&key, typ.key, "map index")
  			if x.mode == invalid {
  				goto Error
  			}
  			x.mode = mapindex
  			x.typ = typ.elem
  			x.expr = e
  			return expression
  		}
  
  		if !valid {
  			check.invalidOp(x.pos(), "cannot index %s", x)
  			goto Error
  		}
  
  		if e.Index == nil {
  			check.invalidAST(e.Pos(), "missing index for %s", x)
  			goto Error
  		}
  
  		check.index(e.Index, length)
  		// ok to continue
  
  	case *ast.SliceExpr:
  		check.expr(x, e.X)
  		if x.mode == invalid {
  			check.use(e.Low, e.High, e.Max)
  			goto Error
  		}
  
  		valid := false
  		length := int64(-1) // valid if >= 0
  		switch typ := x.typ.Underlying().(type) {
  		case *Basic:
  			if isString(typ) {
  				if e.Slice3 {
  					check.invalidOp(x.pos(), "3-index slice of string")
  					goto Error
  				}
  				valid = true
  				if x.mode == constant_ {
  					length = int64(len(constant.StringVal(x.val)))
  				}
  				// spec: "For untyped string operands the result
  				// is a non-constant value of type string."
  				if typ.kind == UntypedString {
  					x.typ = Typ[String]
  				}
  			}
  
  		case *Array:
  			valid = true
  			length = typ.len
  			if x.mode != variable {
  				check.invalidOp(x.pos(), "cannot slice %s (value not addressable)", x)
  				goto Error
  			}
  			x.typ = &Slice{elem: typ.elem}
  
  		case *Pointer:
  			if typ, _ := typ.base.Underlying().(*Array); typ != nil {
  				valid = true
  				length = typ.len
  				x.typ = &Slice{elem: typ.elem}
  			}
  
  		case *Slice:
  			valid = true
  			// x.typ doesn't change
  		}
  
  		if !valid {
  			check.invalidOp(x.pos(), "cannot slice %s", x)
  			goto Error
  		}
  
  		x.mode = value
  
  		// spec: "Only the first index may be omitted; it defaults to 0."
  		if e.Slice3 && (e.High == nil || e.Max == nil) {
  			check.error(e.Rbrack, "2nd and 3rd index required in 3-index slice")
  			goto Error
  		}
  
  		// check indices
  		var ind [3]int64
  		for i, expr := range []ast.Expr{e.Low, e.High, e.Max} {
  			x := int64(-1)
  			switch {
  			case expr != nil:
  				// The "capacity" is only known statically for strings, arrays,
  				// and pointers to arrays, and it is the same as the length for
  				// those types.
  				max := int64(-1)
  				if length >= 0 {
  					max = length + 1
  				}
  				if t, ok := check.index(expr, max); ok && t >= 0 {
  					x = t
  				}
  			case i == 0:
  				// default is 0 for the first index
  				x = 0
  			case length >= 0:
  				// default is length (== capacity) otherwise
  				x = length
  			}
  			ind[i] = x
  		}
  
  		// constant indices must be in range
  		// (check.index already checks that existing indices >= 0)
  	L:
  		for i, x := range ind[:len(ind)-1] {
  			if x > 0 {
  				for _, y := range ind[i+1:] {
  					if y >= 0 && x > y {
  						check.errorf(e.Rbrack, "invalid slice indices: %d > %d", x, y)
  						break L // only report one error, ok to continue
  					}
  				}
  			}
  		}
  
  	case *ast.TypeAssertExpr:
  		check.expr(x, e.X)
  		if x.mode == invalid {
  			goto Error
  		}
  		xtyp, _ := x.typ.Underlying().(*Interface)
  		if xtyp == nil {
  			check.invalidOp(x.pos(), "%s is not an interface", x)
  			goto Error
  		}
  		// x.(type) expressions are handled explicitly in type switches
  		if e.Type == nil {
  			check.invalidAST(e.Pos(), "use of .(type) outside type switch")
  			goto Error
  		}
  		T := check.typ(e.Type)
  		if T == Typ[Invalid] {
  			goto Error
  		}
  		check.typeAssertion(x.pos(), x, xtyp, T)
  		x.mode = commaok
  		x.typ = T
  
  	case *ast.CallExpr:
  		return check.call(x, e)
  
  	case *ast.StarExpr:
  		check.exprOrType(x, e.X)
  		switch x.mode {
  		case invalid:
  			goto Error
  		case typexpr:
  			x.typ = &Pointer{base: x.typ}
  		default:
  			if typ, ok := x.typ.Underlying().(*Pointer); ok {
  				x.mode = variable
  				x.typ = typ.base
  			} else {
  				check.invalidOp(x.pos(), "cannot indirect %s", x)
  				goto Error
  			}
  		}
  
  	case *ast.UnaryExpr:
  		check.expr(x, e.X)
  		if x.mode == invalid {
  			goto Error
  		}
  		check.unary(x, e, e.Op)
  		if x.mode == invalid {
  			goto Error
  		}
  		if e.Op == token.ARROW {
  			x.expr = e
  			return statement // receive operations may appear in statement context
  		}
  
  	case *ast.BinaryExpr:
  		check.binary(x, e, e.X, e.Y, e.Op)
  		if x.mode == invalid {
  			goto Error
  		}
  
  	case *ast.KeyValueExpr:
  		// key:value expressions are handled in composite literals
  		check.invalidAST(e.Pos(), "no key:value expected")
  		goto Error
  
  	case *ast.ArrayType, *ast.StructType, *ast.FuncType,
  		*ast.InterfaceType, *ast.MapType, *ast.ChanType:
  		x.mode = typexpr
  		x.typ = check.typ(e)
  		// Note: rawExpr (caller of exprInternal) will call check.recordTypeAndValue
  		// even though check.typ has already called it. This is fine as both
  		// times the same expression and type are recorded. It is also not a
  		// performance issue because we only reach here for composite literal
  		// types, which are comparatively rare.
  
  	default:
  		panic(fmt.Sprintf("%s: unknown expression type %T", check.fset.Position(e.Pos()), e))
  	}
  
  	// everything went well
  	x.expr = e
  	return expression
  
  Error:
  	x.mode = invalid
  	x.expr = e
  	return statement // avoid follow-up errors
  }
  
  // typeAssertion checks that x.(T) is legal; xtyp must be the type of x.
  func (check *Checker) typeAssertion(pos token.Pos, x *operand, xtyp *Interface, T Type) {
  	method, wrongType := assertableTo(xtyp, T)
  	if method == nil {
  		return
  	}
  
  	var msg string
  	if wrongType {
  		msg = "wrong type for method"
  	} else {
  		msg = "missing method"
  	}
  	check.errorf(pos, "%s cannot have dynamic type %s (%s %s)", x, T, msg, method.name)
  }
  
  func (check *Checker) singleValue(x *operand) {
  	if x.mode == value {
  		// tuple types are never named - no need for underlying type below
  		if t, ok := x.typ.(*Tuple); ok {
  			assert(t.Len() != 1)
  			check.errorf(x.pos(), "%d-valued %s where single value is expected", t.Len(), x)
  			x.mode = invalid
  		}
  	}
  }
  
  // expr typechecks expression e and initializes x with the expression value.
  // The result must be a single value.
  // If an error occurred, x.mode is set to invalid.
  //
  func (check *Checker) expr(x *operand, e ast.Expr) {
  	check.multiExpr(x, e)
  	check.singleValue(x)
  }
  
  // multiExpr is like expr but the result may be a multi-value.
  func (check *Checker) multiExpr(x *operand, e ast.Expr) {
  	check.rawExpr(x, e, nil)
  	var msg string
  	switch x.mode {
  	default:
  		return
  	case novalue:
  		msg = "%s used as value"
  	case builtin:
  		msg = "%s must be called"
  	case typexpr:
  		msg = "%s is not an expression"
  	}
  	check.errorf(x.pos(), msg, x)
  	x.mode = invalid
  }
  
  // exprWithHint typechecks expression e and initializes x with the expression value;
  // hint is the type of a composite literal element.
  // If an error occurred, x.mode is set to invalid.
  //
  func (check *Checker) exprWithHint(x *operand, e ast.Expr, hint Type) {
  	assert(hint != nil)
  	check.rawExpr(x, e, hint)
  	check.singleValue(x)
  	var msg string
  	switch x.mode {
  	default:
  		return
  	case novalue:
  		msg = "%s used as value"
  	case builtin:
  		msg = "%s must be called"
  	case typexpr:
  		msg = "%s is not an expression"
  	}
  	check.errorf(x.pos(), msg, x)
  	x.mode = invalid
  }
  
  // exprOrType typechecks expression or type e and initializes x with the expression value or type.
  // If an error occurred, x.mode is set to invalid.
  //
  func (check *Checker) exprOrType(x *operand, e ast.Expr) {
  	check.rawExpr(x, e, nil)
  	check.singleValue(x)
  	if x.mode == novalue {
  		check.errorf(x.pos(), "%s used as value or type", x)
  		x.mode = invalid
  	}
  }
  

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