手撸 golang 四则运算 计算器 yacc 归约

缘起

最近拜读前桥和弥 [日] 的 << 自制编程语言 >>
结尾一章便是教读者应用 lex/yacc 工具
制作四则运算器
其中 yacc 的移进 / 归约 / 梯度降落的思维很有启发
于是应用 golang 练习之

指标

• 制作一个四则运算器, 从 os.Stdin 读入一行表达式, 而后输入计算过程和后果
• 反对 + – * /
• 反对左右括号
• 反对正数

难点

• 记号扫描(lexer)

  • 逐字符扫描记号
  • 单字符记号可间接辨认, + – * / ()

  • 多字符记号, 此处只有浮点数, 通过无限状态的转换进行辨认

    • <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, 能够立刻归约计算
  • 括号次之, 遇到右括号, 该当触发 + - 归约
  • 程序开端, 没有新的记号残余, 对 + - 进行归约

• 辨认正数

  • 简略起见, 本程序总是应用浮点数作为根本计算单位
  • 把负号辨认为浮点数的可选局部: 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
• 判断栈顶是否合乎归约条件, 是则进行计算
• 记号队列空, 对计算栈进行最终计算
• 输入后果

main.go

从 os.Stdin 循环读入行
调用 lexer.Parse 取得记号流
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()}

输入

=> 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
=>