缘起
目标
难点
总体流程
main.go
tokens/tokens.go
states/states.go
lexer/lexer.go
parser/tStackNode.go
parser/parser.go
输出
缘起最近拜读前桥和弥[日]的<<自制编程语言>>
开头一章便是教读者使用lex/yacc工具
制作四则运算器
其中yacc的移进/归约/梯度下降的思想很有启发
于是使用golang练习之
目标制作一个四则运算器, 从os.Stdin读入一行表达式, 然后输出计算过程和结果
支持+ - * /
支持左右括号
支持负数
难点记号扫描(lexer)
逐字符扫描记号
单字符记号可直接识别, + - * / ( )
多字符记号, 此处只有浮点数, 通过有限状态的转换进行识别
<INITIAL> + '-' = INT_STATUS
<INITIAL> + 'd' = INT_STATUS
<INT_STATUS> + '.' = DOT_STATUS
<INT_STATUS> + 'SPACE | + | - | * | / | ( | )' = INITIAL
<DOT_STATUS> + 'd' = FRAG_STATUS
<FRAG_STATUS> + 'SPACE | + | - | * | / | ( | )' = INITIAL
运算优先级
/优先级最高, 可以立即归约计算
括号次之, 遇到右括号, 应当触发+ -归约
程序末尾, 没有新的记号剩余, 对+ -进行归约
识别负数
简单起见, 本程序总是使用浮点数作为基本计算单位
把负号识别为浮点数的可选部分: 浮点数 = -?d+(.d+)?
总体流程从os.Stdin读入一行表达式字符串
逐字符扫描记号流, 放入记号队列
逐记号出队, 置入计算栈
判断栈顶是否符合归约条件, 是则进行计算
记号队列空, 对计算栈进行最终计算
输出结果
main.go从os.Stdin循环读入行
调用lexer.Parse获得记号流
调用parser.Parse进行计算
func main() {
reader := bufio.NewReader(os.Stdin)
for {
fmt.Printf("=> ")
arrBytes, _, err := reader.ReadLine()
if err != nil {
panic(err.Error())
}
line := strings.TrimSpace(string(arrBytes))
expression := line
tokens, e := lexer.Parse(expression)
if e != nil {
println(e.Error())
} else {
e,v := parser.Parse(tokens)
if e != nil {
println(e.Error())
}
fmt.Println(strconv.FormatFloat(v, 'f', 10, 64))
}
}
}
tokens/tokens.go
定义记号
package tokens
type TOKENS string
const IntLiteral TOKENS = "INT"
const DoubleLiteral TOKENS = "DBL"
const ADD TOKENS = "ADD"
const SUB TOKENS = "SUB"
const MUL TOKENS = "MUL"
const DIV TOKENS = "DIV"
const LB TOKENS = "LB"
const RB TOKENS = "RB"
const UNKNOWN TOKENS = "UNKNOWN"
type Token struct {
Token TOKENS
Value string
Position int
}
func OfRune(t TOKENS, r rune, from int) *Token {
return &Token {
Token: t,
Value : string(r),
Position: from,
}
}
func OfString(t TOKENS, s string, from int) *Token {
return &Token {
Token: t,
Value : s,
Position: from,
}
}
states/states.go
定义lexer的状态
type STATES int
const INITIAL STATES = 1
const INT_STATUS STATES = 11
const DOT_STATUS STATES = 12
const FRAG_STATUS STATES = 13
lexer/lexer.go
记号扫描
type tLexerState struct {
state states.STATES
tokens []*tokens.Token
buffer []rune
i0 int
i1 int
d0 int
d1 int
}
func (me *tLexerState) AppendToken(t *tokens.Token) {
me.tokens = append(me.tokens, t)
}
func (me *tLexerState) AppendChar(it rune) {
me.buffer = append(me.buffer, it)
}
func (me *tLexerState) BufferSize() int {
return len(me.buffer)
}
func (me *tLexerState) IntSize() int {
return me.i1 - me.i0 + 1
}
func (me *tLexerState) FragSize() int {
return me.d1 - me.d0 + 1
}
func Parse(line string) ([]*tokens.Token, error) {
var state = &(tLexerState{
state: states.INITIAL,
tokens: make([]*tokens.Token, 0),
buffer: make([]rune, 0),
i0 : 0,
i1 : 0,
d0: 0,
d1: 0,
})
for i, it := range line + "\n" {
e := parseChar(state, i, it)
if e != nil {
return nil, e
}
}
return state.tokens, nil
}
func parseChar(state *tLexerState, i int, it rune) error {
var e error = nil
switch state.state {
case states.INITIAL:
e = parseCharWhenInitial(state, i, it)
break
case states.INT_STATUS:
e = parseCharWhenInt(state, i, it)
break
case states.DOT_STATUS:
e = parseCharWhenDot(state, i, it)
break
case states.FRAG_STATUS:
e = parseCharWhenFrag(state, i, it)
break
}
return e
}
func parseCharWhenInitial(state *tLexerState, i int, it rune) error {
if is_minus(it) || is_0_to_9(it) {
state.state = states.INT_STATUS
state.buffer = make([]rune, 0)
state.buffer = append(state.buffer, it)
state.i0 = i
state.i1 = i
} else if is_space(it){
return nil
} else if is_add(it) {
state.AppendToken(tokens.OfRune(tokens.ADD, it, i))
} else if is_sub(it) {
state.AppendToken(tokens.OfRune(tokens.SUB, it, i))
} else if is_mul(it) {
state.AppendToken(tokens.OfRune(tokens.MUL, it, i))
} else if is_div(it) {
state.AppendToken(tokens.OfRune(tokens.DIV, it, i))
} else if is_lb(it) {
state.AppendToken(tokens.OfRune(tokens.LB, it, i))
} else if is_rb(it) {
state.AppendToken(tokens.OfRune(tokens.RB, it, i))
} else {
return errors.New(fmt.Sprintf("parseCharWhenInitial, invalid char %c at %d", it, i))
}
return nil
}
func parseCharWhenInt(state *tLexerState, i int, it rune) error {
if is_0_to_9(it) {
if state.BufferSize() >= 10 {
return errors.New(fmt.Sprintf("too large int number at %v", i))
} else {
state.AppendChar(it)
state.i1 = i
}
} else if is_dot(it) {
state.AppendChar(it)
state.state = states.DOT_STATUS
} else if is_space(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.state = states.INITIAL
} else if is_rb(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.RB, it, i))
state.state = states.INITIAL
} else if is_add(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.ADD, it, i))
state.state = states.INITIAL
} else if is_sub(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.SUB, it, i))
state.state = states.INITIAL
} else if is_mul(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.MUL, it, i))
state.state = states.INITIAL
} else if is_div(it) {
state.AppendToken(tokens.OfString(tokens.IntLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.DIV, it, i))
state.state = states.INITIAL
} else {
return errors.New(fmt.Sprintf("parseCharWhenInt, invalid char %c at %d", it, i))
}
return nil
}
func parseCharWhenDot(state *tLexerState, i int, it rune) error {
if is_0_to_9(it) {
state.state = states.FRAG_STATUS
state.AppendChar(it)
state.d0 = i
state.d1 = i
} else {
return errors.New(fmt.Sprintf("parseCharWhenDot, invalid char %c at %d", it, i))
}
return nil
}
func parseCharWhenFrag(state *tLexerState, i int, it rune) error {
if is_0_to_9(it) {
if state.FragSize() >= 10 {
return errors.New(fmt.Sprintf("too many chars for a double value at %d", i))
} else {
state.AppendChar(it)
state.d1 = i
}
} else if is_space(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.state = states.INITIAL
} else if is_add(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.ADD, it, i))
state.state = states.INITIAL
} else if is_sub(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.SUB, it, i))
state.state = states.INITIAL
} else if is_mul(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.MUL, it, i))
state.state = states.INITIAL
} else if is_div(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.DIV, it, i))
state.state = states.INITIAL
} else if is_rb(it) {
state.AppendToken(tokens.OfString(tokens.DoubleLiteral, string(state.buffer), state.i1))
state.AppendToken(tokens.OfRune(tokens.RB, it, i))
state.state = states.INITIAL
} else {
return errors.New(fmt.Sprintf("parseCharWhenFrag, invalid char %c at %d", it, i))
}
return nil
}
parser/tStackNode.go
定义计算栈的一个节点. 计算栈中有两种节点: 已归约的值节点, 和尚未计算的记号节点
type tStackNodeType int
const NODE_VALUE tStackNodeType = 1
const NODE_TOKEN tStackNodeType = 2
type tStackNode struct {
flag tStackNodeType
token *tokens.Token
value float64
}
func newValueNode(value float64) *tStackNode {
return &tStackNode{
flag: NODE_VALUE,
value: value,
token: nil,
}
}
func newTokenNode(token *tokens.Token) *tStackNode {
return &tStackNode{
flag: NODE_TOKEN,
token: token,
value: 0,
}
}
func (me *tStackNode) getTokenType() tokens.TOKENS {
switch me.flag {
case NODE_VALUE:
return tokens.DoubleLiteral
case NODE_TOKEN:
switch me.token.Token {
case tokens.IntLiteral:
fallthrough
case tokens.DoubleLiteral:
return tokens.DoubleLiteral
default:
return me.token.Token
}
}
return tokens.UNKNOWN
}
func (me *tStackNode) getDoubleValue() float64 {
switch me.flag {
case NODE_VALUE:
return me.value
case NODE_TOKEN:
switch me.token.Token {
case tokens.IntLiteral:
fallthrough
case tokens.DoubleLiteral:
v1,e1 := strconv.ParseFloat(me.token.Value, 64)
if e1 != nil {
panic(e1)
}
return v1
}
}
panic("value not avaiable")
}
parser/parser.go
type tParser struct {
tokens []*tokens.Token
stack []*tStackNode
total int
position int
}
func newParser(tokens []*tokens.Token) *tParser {
return &tParser{
tokens: tokens,
stack: make([]*tStackNode, 0),
total : len(tokens),
position: -1,
}
}
func (me *tParser) showStack() string {
lst := make([]string, 0)
for _,it := range me.stack {
switch it.flag {
case NODE_VALUE:
lst = append(lst, strconv.FormatFloat(it.value, 'f', 10, 64))
break
case NODE_TOKEN:
switch it.token.Token {
case tokens.DoubleLiteral:
fallthrough
case tokens.IntLiteral:
lst = append(lst, it.token.Value)
break
default:
lst = append(lst, it.token.Value)
break
}
}
}
return strings.Join(lst, " ")
}
func (me *tParser) moreToken() bool {
return me.position < me.total - 1
}
func (me *tParser) nextToken() *tokens.Token {
if !me.moreToken() {
return nil
}
me.position++
return me.currentToken()
}
func (me *tParser) currentToken() *tokens.Token {
if me.position >= me.total {
return nil
}
return me.tokens[me.position]
}
func (me *tParser) reduce() {
sCurrentStack := ""
var fnCheckState = func() {
sStackState := me.showStack()
if sStackState != sCurrentStack {
sCurrentStack = sStackState
fmt.Printf("stack => %s\n", sStackState)
}
}
for {
fnCheckState()
if me.reduceMulOrDiv() {
continue
}
if me.reduceBrackets() {
continue
}
if !me.moreToken() {
if me.reduceAddOrSub() {
break
}
}
fnCheckState()
//time.Sleep(1*time.Second)
break
}
}
func (me *tParser) stackPop() *tStackNode {
if me.isStackEmpty() {
return nil
}
var iStackSize = len(me.stack)
var last = me.stack[iStackSize - 1]
me.stack = me.stack[:(iStackSize-1)]
return last
}
func (me *tParser) stackPopN(n int) []*tStackNode {
if me.isStackEmpty() {
return nil
}
var iStackSize = len(me.stack)
if iStackSize < n {
return nil
}
var lstTailItems = me.stack[(iStackSize - n):]
me.stack = me.stack[:(iStackSize-n)]
return lstTailItems
}
func (me *tParser) stackTakeN(n int) []*tStackNode {
if me.isStackEmpty() {
return nil
}
var iStackSize = len(me.stack)
if iStackSize < n {
return nil
}
var lstHeadItems = me.stack[:n]
me.stack = me.stack[n+1:]
return lstHeadItems
}
func (me *tParser) stackPush(it *tStackNode) {
me.stack = append(me.stack, it)
}
func (me *tParser) reduceMulOrDiv() bool {
if me.isStackEmpty() {
return false
}
if me.isStackRMatch(tokens.DoubleLiteral, tokens.MUL, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(3)
v1 := lstTailNodes[0].getDoubleValue()
v2 := lstTailNodes[2].getDoubleValue()
var v = v1*v2
me.stackPush(newValueNode(v))
return true
} else if me.isStackRMatch(tokens.DoubleLiteral, tokens.DIV, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(3)
v1 := lstTailNodes[0].getDoubleValue()
v2 := lstTailNodes[2].getDoubleValue()
if v2 == 0 {
panic(fmt.Sprintf("div by zero, %v / %v", v1, v2))
}
var v = v1/v2
me.stackPush(newValueNode(v))
return true
}
return false
}
func (me *tParser) reduceBrackets() bool {
if me.isStackEmpty() {
return false
}
if me.isStackRMatch(tokens.RB) {
rb := me.stackPop()
var v float64 = 0
for {
if me.isStackRMatch(tokens.LB, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(2)
v += lstTailNodes[1].getDoubleValue()
me.stackPush(newValueNode(v))
return true
} else if me.isStackRMatch(tokens.ADD, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(2)
v1 := lstTailNodes[1].getDoubleValue()
v = v + v1
} else if me.isStackRMatch(tokens.SUB, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(2)
v1 := lstTailNodes[1].getDoubleValue()
v = v - v1
} else {
panic(fmt.Sprintf("LB not found at %v", rb.token.Position))
}
}
}
return false
}
func (me *tParser) reduceAddOrSub() bool {
var v float64 = 0
for {
if me.isStackEmpty() {
break
}
if me.isStackRMatch(tokens.ADD, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(2)
v1 := lstTailNodes[1].getDoubleValue()
v = v + v1
} else if me.isStackRMatch(tokens.SUB, tokens.DoubleLiteral) {
var lstTailNodes = me.stackPopN(2)
v1 := lstTailNodes[1].getDoubleValue()
v = v - v1
} else if len(me.stack)==1 && me.isStackRMatch(tokens.DoubleLiteral) {
it := me.stackPop()
v += it.getDoubleValue()
me.stackPush(newValueNode(v))
return true
} else {
panic("invalid expression")
}
}
return false
}
func (me *tParser) isStackEmpty() bool {
return len(me.stack) == 0
}
func (me *tParser) isStackRMatch(args...tokens.TOKENS) bool {
var iArgsSize = len(args)
if iArgsSize <= 0 {
return false
}
var iStackSize = len(me.stack)
if iStackSize < iArgsSize {
return false
}
for i,it := range args {
var n = iStackSize - iArgsSize + i
var xStackNode = me.stack[n]
if it != xStackNode.getTokenType() {
return false
}
}
return true
}
func (me *tParser) isStackLMatch(args...tokens.TOKENS) bool {
var iArgsSize = len(args)
if iArgsSize <= 0 {
return false
}
var iStackSize = len(me.stack)
if iStackSize < iArgsSize {
return false
}
for i,it := range args {
var xStackNode = me.stack[i]
if it != xStackNode.getTokenType() {
return false
}
}
return true
}
func (me *tParser) parse() (error, float64) {
for {
t := me.nextToken()
if t == nil {
break
}
me.stackPush(newTokenNode(t))
me.reduce()
}
var iStackSize = len(me.stack)
if iStackSize == 1 && me.stack[0].getTokenType() == tokens.DoubleLiteral {
return nil, me.stack[0].getDoubleValue()
}
panic(fmt.Sprintf("failed parsing expression %s", me.showStack()))
}
func Parse(tokens []*tokens.Token) (error, float64) {
parser := newParser(tokens)
return parser.parse()
}
输出
=> 1+2*(3-4*(5/6+(7-8*9)))
stack => 1
stack => 1 +
stack => 1 + 2
stack => 1 + 2 *
stack => 1 + 2 * (
stack => 1 + 2 * ( 3
stack => 1 + 2 * ( 3 -
stack => 1 + 2 * ( 3 - 4
stack => 1 + 2 * ( 3 - 4 *
stack => 1 + 2 * ( 3 - 4 * (
stack => 1 + 2 * ( 3 - 4 * ( 5
stack => 1 + 2 * ( 3 - 4 * ( 5 /
stack => 1 + 2 * ( 3 - 4 * ( 5 / 6
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 +
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + (
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 -
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 - 8
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 - 8 *
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 - 8 * 9
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 - 72.0000000000
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + ( 7 - 72.0000000000 )
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + -65.0000000000
stack => 1 + 2 * ( 3 - 4 * ( 0.8333333333 + -65.0000000000 )
stack => 1 + 2 * ( 3 - 4 * -64.1666666667
stack => 1 + 2 * ( 3 - -256.6666666667
stack => 1 + 2 * ( 3 - -256.6666666667 )
stack => 1 + 2 * 259.6666666667
stack => 1 + 519.3333333333
520.3333333333
=>
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