X-Git-Url: https://git.kianting.info/?a=blobdiff_plain;f=src%2Findex.ts;h=46c4a7205501d288c574df83980d0e910e4bfd63;hb=4fd4c8a4b69464bf1ac74af920175308656e6f6b;hp=5ca3a12b008cf290bfdc3a21675da93324132912;hpb=cf712efc21fa3a711b8a09b953539c7a7c90f5d6;p=clo

diff --git a/src/index.ts b/src/index.ts
index 5ca3a12..46c4a72 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -1,512 +1,476 @@
-import { match } from "assert";
-
 var fs = require('fs');
-
-export type Some<T> = { _tag: "Some"; value: T };
-export type None = {_tag: "None"};
-
+import { argv, resourceUsage } from 'node:process';
+import * as tk from './tokenize.js';
+import * as util from 'util';
+import { drawEllipsePath, reduceRotation } from 'pdf-lib';
+import { isAnyArrayBuffer, isTypedArray } from 'node:util/types';
+import { error } from 'node:console';
+import { isUndefined } from 'node:util';
 
 /**
- * wrap a x in a `Some(T)`
- * @param x : variable to be wrapped.
- * @returns wrapped `x`.
+ * debug reprensenting
  */
-function toSome<T>(x: T): Some<T>{
-    return  { _tag: "Some", value: x};  
-}
+let repr = (x : any)=>{return util.inspect(x, {depth: null})};
+
 /**
- * @description Like the `Some(a)` and `None` in Rust.
- *
- * @example
- * ```ts
- * let exam1 : Maybe<Number> = { _tag: "Some", value: 12 };
- * let exam2 : Maybe<Number> = None;
- * ```
+ * token tree type.
  */
-export type Maybe<T> = Some<T> | None;
-
+type tkTree = tkTree[] | tk.Token
 
 /**
- * @description
- * the pair of the string to be matched later and the string that have been matched
- * @var matched : have been matched
- * @var remained : will be tested whether it'll be matched.
- * @var matched_type (optional): the type of the matched string
-*/
-export interface MatcheePair {
-    matched : string
-    remained : string
-    matched_type?: TokenType 
+ * concated 2 `tkTree`s
+ * @param x the array to be concated
+ * @param y the item or array to ve concated
+ * @returns concated tkTree array, or thrown error if can't be concated.
+ */
+function concat(x: tkTree, y:tkTree): tkTree[] {
+    if (Array.isArray(x)){
+            return x.concat(y);
+    }else{
+        throw new Error("the tkTree can't be concated, because it's not an array.");
+        
+    }
+}
+
+function slice(x: tkTree, index?:number, end?:number): tkTree[] {
+    if (Array.isArray(x)){
+            return x.slice(index,end);
+    }else{
+        throw new Error("the tkTree can't be concated, because it's not an array.");
+        
+    }
 }
 
 /**
- * The types of Token
- *    NL, // newline
- * 
- *   SP, // half-width space and tab
- * 
- * ID, // identifier
- * 
- * STR, // string
- * 
- * OP, // operator or something like it
- * 
- * FLO, // float num
+ * TokenMatcheePair for tokens' parser combinator
+ *  
+ * matched: the matched (now and before) tokens
  * 
- * INT, // integer
+ * remained: tokens to be matched
  * 
- * I_* // integer manipulation
- * 
- * F_* // float manipulation
- * 
- * SEMI_C// semi-colon
+ * ast: abstract syntax tree
  */
-export enum TokenType{
-    NL, // newlinw
-    SP, // half-width space and tab
-    ID, // identifier
-    STR, // string
-    FLO, // float num
-    INT, // integer
-    F_ADD,
-    F_SUB,
-    F_MUL,
-    F_DIV,
-    I_ADD, 
-    I_SUB, 
-    I_MUL, 
-    I_DIV,
-    L_PAREN, // (
-    R_PAREN, // )
-    L_BRACK, // [
-    R_BRACK, // ]
-    L_BRACE, // {
-    R_BRACE, // }
-    COMMA, // ,
-    DOT, // .
-    COLON, // :
-    SEMI_C, // ;
-    AT, // @
-    HASH, // #
-    EQ, // ==
-    SET, // =
-    GT, // > greater than
-    LT, // <less than
-    GE, // >=
-    LE, // <=
-    R_ARROW, // ->
-
+export interface TokenMatcheePair {
+    matched: tk.Token[]
+    remained: tk.Token[]
+    ast : tkTree[]
 }
 
 /**
- * tokenized token.
- * @var text : the content text
- * @var type (optional): the type of the token
- * @var col : the column number
- * @var ln : the line number
+ * convert a `tkTree` AST to S-expr string
+ * @param t the `tkTree`
+ * @returns S-expr String
  */
-export interface Token{
-    text: string,
-    type?: TokenType,
-    col: number,
-    ln: number,
+export function tkTreeToSExp(t: tkTree): string{
+    var str = "";
+
+    if (Array.isArray(t)){
+        let strArray = t.map((x)=>tkTreeToSExp(x));
+        str = "(" + strArray.join(" ") + ")";
+    }else{
+        if (t=== undefined){
+            str = "%undefined"
+        }else{
+            str = t.text;
+        }
+    }
+
+    return str;
 }
 
 /**
  * @description
- * it returns a function which test if the first char of the `remained` part of
- *  the argument of the function is `c`, if it's true, update the `MatchedPair` wrapped
+ * match one token type.
+ * 
+ * it returns a function which test if the type of first token of the `remained` part of
+ *  the argument of the function is `typ` , if it's true, update the `TokenMatcheePair` wrapped
  * in `Some`. Otherwise, it returns `None`.
- *  * @param c : the char to be test.
- * @returns the updated `MatchedPair` wrapped in `Some(x)` or `None`.
+ *  * @param typ : the type to be test.
+ * @returns the updated `TokenMatcheePair` wrapped in `Some(x)` or `None`.
  */
-export function match1Char(c : string) : (m: MatcheePair) => Maybe<MatcheePair> {
-    return (m : MatcheePair)=>{
-        if (m.remained.length == 0){
+export function m1TType(typ: tk.TokenType):
+    (m: TokenMatcheePair) => tk.Maybe<TokenMatcheePair> {
+    return (m: TokenMatcheePair) => {
+        if (m.remained.length == 0) {
             return { _tag: "None" };
         }
-        const charToBeMatched = m.remained[0];
-        if (charToBeMatched === c){
-            return {_tag: "Some", value :{
-                    matched : m.matched + charToBeMatched,
-                    remained : m.remained.substring(1)}};
+        /**
+         * token to be matched
+         * */
+        const ttbm = m.remained[0];
+        
+        if (ttbm.type == typ) {
+            let new_matched = m.matched.concat(ttbm);
+            let result : tk.Some<TokenMatcheePair> = {
+                _tag: "Some", value: {
+                    matched: new_matched,
+                    remained: m.remained.slice(1),
+                    ast:  ([ttbm]),
+                }
+            };
+            return result;
         }
-        else{
-            return {_tag: "None"};
+        else {
+            return { _tag: "None" };
         }
     }
 };
 
 /**
- * 
- * @param m : the `MatcheePair` to be consumed.
- * @returns if the length of `m.remained` >= 1; consumes the matchee by 1 char and wraps it in `Some`,
- * otherwise, returns `None`.
+ * type int
  */
-export function matchAny(m : MatcheePair) : Maybe<MatcheePair>{
-    if (m.remained.length >= 1){
-        return {_tag: "Some", value :{
-            matched : m.matched + m.remained[0],
-            remained : m.remained.substring(1)}};
-    }else{
-        return {_tag: "None"};
-    }
-}
+let tInt  = m1TType(tk.TokenType.INT);
+let tId  = m1TType(tk.TokenType.ID);
+
+
+let tAdd  = m1TType(tk.TokenType.I_ADD);
+let tSub = m1TType(tk.TokenType.I_SUB);
+let tMul  = m1TType(tk.TokenType.I_MUL);
+let tDiv = m1TType(tk.TokenType.I_DIV);
+let tLParen = m1TType(tk.TokenType.L_PAREN);
+let tRParen = m1TType(tk.TokenType.R_PAREN);
+let tComma = m1TType(tk.TokenType.COMMA);
+let toSome = tk.toSome;
+
+
+argv.forEach((val, index) => {
+    console.log(`${index}=${val}`);
+});
 
-/**
- * @description
- * it returns a function which test if the first char of the `remained` part of
- *  the argument of the function is between `l` and `u`, if it's true, update the `MatchedPair` wrapped
- * in `Some`. Otherwise, it returns `None`.
- *  * @param l : lower bound char, 1-char string
- *  * @param u : upper bound char, 1-char string
- * @returns the updated `MatchedPair` wrapped in `Some(x)` or `None`.
- */
-export function matchRange(l : string, u : string) : (m: MatcheePair) => Maybe<MatcheePair> {
-    let lCodepoint = charToCodepoint(l);
-    let uCodepoint = charToCodepoint(u);
-    if (l > u){
-        throw new Error("Error: the codepoint of `"+l+"` is not smaller than `"+u+"`)");
-    }
-    return (m : MatcheePair)=>{
-        if (m.remained.length < 1){
-            return {_tag : "None"};
-        }
-        const charToBeMatched = m.remained[0];
-        const codePointToBeMatched = charToCodepoint(charToBeMatched);
-        if (codePointToBeMatched >= lCodepoint && codePointToBeMatched <= uCodepoint){
-            return {_tag: "Some", value :{
-                    matched : m.matched + charToBeMatched,
-                    remained : m.remained.substring(1)}};
-        }
-        else{
-            return {_tag: "None"};
-        }
-    }
-};
 
 /**
- * convert the one-char string to codepoint.
- * @param s : the string to code point.
- * @returns if `s.length > 1` return error; otherwise, return the codepoint of `s`.
+ * like `m ==> f` in ocaml
+ * @param m matchee wrapped
+ * @param f matching function
+ * @returns wrapped result
  */
-export function charToCodepoint(s : string): number{
-    if (s.length > 1){
-        throw new Error("Error: the length of input string for "+s+ "is "+s.length+`,
-        however, it should be 1.`);
+function thenDo(m : tk.Maybe<TokenMatcheePair>, f : Function){
+    if (m._tag == "None"){
+        return m;
     }else{
-        return s.charCodeAt(0);
+        var a : tk.Maybe<TokenMatcheePair> = f(m.value);
+        if (a._tag == "Some"){
+            a.value.ast = concat(m.value.ast, a.value.ast);
+        }
+
+        return a;
     }
 }
 
 /**
- *  @description thendo(input, f, ...) like
- * a ==> f
- * @param input: the wrapped input. 
- * @param f: the function to be applied.
- * 
- * @returns:the applied wrapped result `MatcheePair`.
+ * like `f1 | f2` in regex
+ * @param f1 the first tried function
+ * @param f2 the second tried function
+ * @returns wrapped result
  */
-export function thenDo<T>(input : Maybe<T>, f : Function) : Maybe<T>{
-    if (input._tag == "None"){
-        return input;
-    }
-    else{
-        let inner = input.value;
-        return f(inner);
-    }
+function orDo(f1 : Function, f2 : Function){
+    return (x : TokenMatcheePair) =>{
+        let res1 : tk.Maybe<TokenMatcheePair> = f1(x);
+        if (res1._tag == "Some"){
+            return res1;
+        }else{
+            let res2 : tk.Maybe<TokenMatcheePair> = f2(x);
+            return res2;
+        }
+    } 
 }
 
+
 /**
- * @description "or", like the regex `( f1 | f2 )` . 
- * It returns a function `f` of which the argument is`x`.
- * if `f1(x)` is None, then `f` returns `f2(x)`. Otherwise, 
- * `F` returns `f1(x)`.
- * @param f1 : 1st function to be compared
- * @param f2 : 2nd function to be compared
- * @returns:the combined function
+ * 
+ * @param m : the `MatcheePair` to be consumed.
+ * @returns if the length of `m.remained` >= 1; consumes the matchee by 1 token
+ *  and wraps it in `Some`,
+ * otherwise, returns `None`.
  */
-export function orDo<T>(f1 : Function, f2: Function) : (x : T ) => Maybe<T>{
-    return (x) => {
-        let f1x : Maybe<T> = (f1(x));
-        {
-            if (f1x._tag == "None"){
-                return f2(x);
+export function matchAny(m: TokenMatcheePair): tk.Maybe<TokenMatcheePair> {
+    if (m.remained.length >= 1) {
+        return {
+            _tag: "Some", value: {
+                matched: m.matched.concat(m.remained[0]),
+                remained: m.remained.slice(1),
+                ast :  [m.remained[0]],
             }
-            else{
-                return f1x;
-            }
-        }
-    };
+        };
+    } else {
+        return { _tag: "None" };
+    }
 }
 
-
 /**
+ * Danger : Maybe it's not enough to work.
 * @description repeating matching function `f` 
 * zero or more times, like the asterisk `*` in regex `f*` . 
 * @param f : the function to be repeated 0+ times.
 * @returns:the combined function
 */
-export function zeroOrMoreDo<T>(f : Function): (x : T) => Maybe<T>{
-    return (x)=>{
-        var wrapped_old_x : Maybe<T> = {_tag: "Some", value : x};
-        var wrapped_new_x : Maybe<T> = wrapped_old_x;
-
-        while (wrapped_new_x._tag != "None"){
-            wrapped_old_x = wrapped_new_x;
-            wrapped_new_x = thenDo(wrapped_old_x, f);
-        };
+export function OnceOrMoreDo(f: Function): (x: TokenMatcheePair) =>
+    tk.Maybe<TokenMatcheePair> {
+    return (x) => {
+        var wrappedOldX: tk.Maybe<TokenMatcheePair> = { _tag: "Some", value: x };
+        var wrappedNewX: tk.Maybe<TokenMatcheePair> = wrappedOldX;
 
-        return wrapped_old_x;
-    };
-}
+        var counter = -1;
+
+        while (wrappedNewX._tag != "None") {
+            wrappedOldX = wrappedNewX;
+            wrappedNewX = thenDo(wrappedOldX, f);
+            counter += 1;
 
-/**
-* @description Not. like the `^` inside regex of [^f].
-* returns a function `F(x)` such that if  `f(x)` is `None`,
-* returns the x consuming a char; if `f(x)` is not None, F(x)
-* returns `None`.
-* @param f: the function forbidden to be matched.
-* @returns: combined function `F`.
-*/
-export function notDo<T>(f : Function): (x : T) => Maybe<T>{
-    return (x)=>{
-        let wrapped_x : Maybe<T> = {
-            _tag : "Some",
-            value : x
         };
-        let f_x = thenDo(wrapped_x, f);
-        
-        if (f_x._tag != "None"){
-            return {_tag:"None"};
-        }else{
-            return thenDo(wrapped_x, matchAny);
+
+        if (counter <= 0){
+            return { _tag: "None"};
         }
-    };
+        let ast = wrappedOldX.value.ast ;
+        wrappedOldX.value.ast =ast.slice(ast.length-counter);
+        console.log(repr(wrappedOldX.value.ast));
+
+        return wrappedOldX; };
 }
 
 /**
- * if `x` is matched by `f` once, returns `f(x)`. Otherwise, 
- * returns x
- * similar to `?` in regex `f?`.
- * @param f : the function to be matched
- * @returns return wrapped f(x)
+ * aux function for midfix operator
+ * @param f function
+ * @param signal the rule name
+ * @returns 
  */
-export function zeroOrOnceDo<T>(f : Function): (x : T) => Maybe<T>{
-    return (x)=>{
-        var wrapped_old_x : Maybe<T> = {_tag: "Some", value : x};
-        var wrapped_new_x = thenDo(wrapped_old_x, f);
+let midfix = (f : Function, signal? : string) => (x : TokenMatcheePair)=>{
+    var a = f(x);
+    if (a._tag == "Some"){
+        let ast_tail : tkTree[] = slice(a.value.ast,a.value.ast.length-3);
+        let new_ast = [ast_tail];
+        a.value.ast = new_ast;
 
-        if (wrapped_new_x._tag != "None"){
-            return wrapped_new_x;
-        }else{
-        return wrapped_old_x;
-        }
-    };
-}
+        // console.log("+"+signal+"+"+repr(a));
 
+        
+    }
+    return a;
+}
 
-export function tokenize(input : string){
-    var input_matchee_pair : Maybe<MatcheePair> = toSome(
-        {matched:"",
-        remained: input});
-
-    /**
-     * generate a parser of a basic term (b_term)
-     * @param pattern : the pattern parser
-     * @param token_type : the returning token type
-     * @returns a wrapped parser.
-     */
-    function bTerm(pattern : Function, token_type : TokenType){
-        return (x : MatcheePair) =>{
-            let wrapped_x = toSome(x);
-            let result = pattern(wrapped_x); 
-            if (result._tag == "Some") {
-                result.value.matched_type = token_type;
+let circumfix = (f : Function, signal? : string) => (x : TokenMatcheePair)=>{
+    var a : tk.Maybe<TokenMatcheePair> = f(x);
+    if (a._tag == "Some"){
+        console.log("$$$"+repr(a.value.ast));
+        let inner = a.value.ast[a.value.ast.length-2];
+        var ast_middle : tkTree[];
+        // the list should not be (%list) (%apply) (%lambda) etc.
+        if (Array.isArray(inner)){
+            if ('text' in inner[0]  && (inner[0].text.slice(0,1) != "%")){
+                ast_middle = inner;
             }
-            return result;
+            else{
+                ast_middle = [inner];
+            }
+        }
+        else{
+            ast_middle = [inner];
         }
+        let new_ast = [ast_middle];
+        a.value.ast = new_ast;
     }
+    return a;
+}
+
+/** single1 = tInt | "(" expr ")"*/
+let single1 = circumfix((x : TokenMatcheePair) =>
+    thenDo(thenDo(thenDo(toSome(x), tLParen), expr), tRParen), "fac1");
+let single2= tInt;
+let single = orDo(single1, single2);
+
+/** args = single "," args | single */
+let args1 = (x: TokenMatcheePair)=>{
+    var ret = thenDo(thenDo(thenDo(toSome(x), single), tComma), args);
+    if (ret._tag == "Some"){
+        let retLength = ret.value.ast.length;
+        ret.value.ast = [[ret.value.ast[retLength-3]].concat(ret.value.ast[retLength-1])];
+        console.log("$$"+repr(ret.value.ast));
+    }
+    return ret;
+};
+
+let args2 = single;
+
+let args = orDo(args1, args2);
+
 
-    let d = matchRange('0','9'); // \d
-    // [+-]
-    let plusMinus = orDo(match1Char('+'), match1Char('-'));
-    let s_aux = orDo(match1Char(' '), match1Char('\t')); // (" " | "\t")
-
-    // integer = ([+]|[-])?\d\d*
-    let integer = bTerm((x : Maybe<MatcheePair>)=>
-                            thenDo(thenDo(thenDo(x, 
-                            zeroOrOnceDo(plusMinus)),d),
-                            zeroOrMoreDo(d)),
-                        TokenType.INT);
-    // space = [ \t]+
-    let space = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, s_aux), zeroOrMoreDo(s_aux)),
-        TokenType.INT);
-
-    // newline = \r?\n
-    let newline = bTerm((x : Maybe<MatcheePair>)=>
-    thenDo(thenDo(x, 
-        zeroOrOnceDo(match1Char('\r'))),
-        match1Char('\n')),
-        TokenType.NL);
-
-    // [_A-Za-z]
-    let idHead = orDo(orDo(matchRange('a','z'),matchRange('A','Z')), match1Char('_'));
-    let idRemained = orDo(idHead, matchRange('0','9')); // [_A-Za-z0-9]
-
-    // id = [_A-Za-z][_A-Za-z0-9]*
-    let id = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, 
-            idHead),
-            zeroOrMoreDo(idRemained)),
-            TokenType.ID);
-    let doublequote = match1Char("\"");
-    // [\\][\"]
-    let escapeReverseSlash = (x:MatcheePair)=>
-        thenDo(thenDo(toSome(x), match1Char("\\")), doublequote);
-    // ([\\]["]|[^\"])*
-    let stringInnerPattern = zeroOrMoreDo(
-        orDo(escapeReverseSlash, notDo(match1Char("\""))));
-
-    // str = ["]([\\]["]|[^"])*["]
-    let str = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(thenDo(x,doublequote),
-        stringInnerPattern),doublequote),
-        TokenType.STR);
-
-    // float = [+-]?\d+[.]\d+
-    function floatPattern(x : Maybe<MatcheePair>){
-        return thenDo(thenDo(thenDo(thenDo(thenDo(thenDo(x, 
-        zeroOrOnceDo(plusMinus)),d),
-        zeroOrMoreDo(d)),
-        match1Char(".")),d),
-        zeroOrMoreDo(d))};
-    let float = bTerm(floatPattern, TokenType.FLO);
-
-    // operators
-    // +.
-    let floatAdd = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, match1Char("+")),match1Char(".")),
-        TokenType.F_ADD);
-    // +.
-    let floatSub = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, match1Char("-")),match1Char(".")),
-        TokenType.F_SUB);  
-
-    // *.
-    let floatMul = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, match1Char("*")),match1Char(".")),
-        TokenType.F_MUL);
-
-    // /.
-    let floatDiv = bTerm((x : Maybe<MatcheePair>)=>
-        thenDo(thenDo(x, match1Char("/")),match1Char(".")),
-        TokenType.F_DIV);
-
-    // ==
-    let eq = bTerm((x : Maybe<MatcheePair>)=>
-    thenDo(thenDo(x, match1Char("=")),match1Char("=")),
-    TokenType.EQ);
-
-    // >=
-    let ge = bTerm((x : Maybe<MatcheePair>)=>
-    thenDo(thenDo(x, match1Char(">")),match1Char("=")),
-    TokenType.GE);
-
-    // <=
-    let le = bTerm((x : Maybe<MatcheePair>)=>
-    thenDo(thenDo(x, match1Char("<")),match1Char("=")),
-    TokenType.LE);
-
-    // ->
-    let rightArrow = bTerm((x : Maybe<MatcheePair>)=>
-    thenDo(thenDo(x, match1Char("-")),match1Char(">")),
-    TokenType.R_ARROW);
+/** callees = "(" args ")" | "(" ")" */
+
+
+let callees1 = circumfix((x : TokenMatcheePair) =>
+    thenDo(thenDo(thenDo(toSome(x), tLParen), args), tRParen), "callees1");
+let callees2 = (x: TokenMatcheePair)=>{
+    let ret = thenDo(thenDo(toSome(x), tLParen), tRParen);
+    if (ret._tag == "Some"){
+        let new_ast : tkTree[] = [[]];
+        ret.value.ast = new_ast;
+    }
     
-    /**
-     * unary operator : generating the pattern of basic unary operator
-     * @param char : uniry char for the operator
-     * @param token_type : the corresponding token_type
-     */
-    function unaryOp(char: string, token_type: TokenType) {
-        return bTerm((x : Maybe<MatcheePair>)=>thenDo(x, match1Char(char)),
-        token_type);};
-
-    let intAdd = unaryOp('+', TokenType.I_ADD);
-    let intSub = unaryOp('-', TokenType.I_SUB);
-    let intMul = unaryOp('*', TokenType.I_MUL);
-    let intDiv = unaryOp('/', TokenType.I_DIV);
-    let lParen = unaryOp('(', TokenType.L_PAREN);
-    let rParen = unaryOp(')', TokenType.R_PAREN);
-    let lBracket = unaryOp('[', TokenType.L_BRACK);
-    let rBracket = unaryOp(']', TokenType.R_BRACK);
-    let lBrace = unaryOp('{', TokenType.L_BRACE);
-    let rBrace = unaryOp('}', TokenType.R_BRACE);
-    let comma = unaryOp(',', TokenType.COMMA);
-    let dot = unaryOp('.', TokenType.DOT);
-    let colon = unaryOp(':', TokenType.COLON);
-    let semicolon = unaryOp(';', TokenType.SEMI_C);
-    let at = unaryOp('@', TokenType.AT);
-    let hash = unaryOp('#', TokenType.HASH);
-    let set = unaryOp('=', TokenType.SET);
-    let greaterthan = unaryOp('>', TokenType.GT);
-    let lessthan = unaryOp('<', TokenType.LE);
-
-
-    let term = (token_list : Array<Token>, x :  Some<MatcheePair>)=>{
-        var ln = 1;
-        var col = 0;
-        var old_x  = x;
-        let term_list = [float, newline, space, integer,str,  id,
-            floatAdd, floatSub, floatMul, floatDiv,
-            intAdd, intSub, intMul, intDiv,
-            eq, ge, le, rightArrow,
-            lParen, rParen, lBracket, rBracket, lBrace, rBrace,
-            comma, dot, colon, semicolon, at, hash,
-            set,greaterthan, lessthan];
-        let term_aux = term_list.reduce((x,y)=> orDo(x,y));
-
-        var new_x : Maybe<MatcheePair> = thenDo(old_x, term_aux);
-        while (new_x._tag != "None"){
-            if (new_x.value.matched_type != TokenType.NL){
-                col += new_x.value.matched.length;
-                token_list.push({text : new_x.value.matched,
-                                type: new_x.value.matched_type,
-                                ln : ln,
-                                col : col});
-                
-                }
-            else{
-                col = 0;
-                ln += 1;                
+    return ret};
+
+let callees = orDo(callees1, callees2);
+
+
+
+/** %apply R combinating token */
+let applyToken = {
+    text: "%apply",
+    type: tk.TokenType.ID,
+    col: 0,
+    ln: 0,
+}
+
+/** facAux = callees facAux |  callees */
+let facAux1 = (x: TokenMatcheePair)=>{
+    var ret = thenDo(thenDo(toSome(x), callees), facAux);
+    if (ret._tag == "Some"){
+        console.log("1232345"+repr(tkTreeToSExp(ret.value.ast[ret.value.ast.length-1])));
+    let last1  = ret.value.ast[ret.value.ast.length-1];
+    let last2  = ret.value.ast[ret.value.ast.length-2];
+
+    
+    let b : tkTree[] = [applyToken];
+    ret.value.ast = [b.concat([last2, last1])];
+    console.log("11111"+repr(tkTreeToSExp(ret.value.ast)));
+
+    };
+
+return ret;}
+let facAux2 = callees;
+let facAux =  orDo(facAux1, facAux2);
+
+
+
+/** fac = single facAux | single
+ * Issue1 to be fixed.
+ */
+let fac1 = (x: TokenMatcheePair)=>{
+    var ret = thenDo(thenDo(toSome(x), single),facAux);
+    if(ret._tag == "Some"){
+        console.log("777"+repr(tkTreeToSExp(ret.value.ast)));
+        ret.value.ast = [applyToken, ret.value.ast[ret.value.ast.length-2],
+                        ret.value.ast[ret.value.ast.length-1]];
+        ret.value.ast;
+        rearrangeTree(ret.value.ast);
+        console.log("888"+repr(tkTreeToSExp(ret.value.ast)));
+
+    }
+
+    return ret;};
+let fac2 = single;
+let fac = orDo(fac1, fac2);
+
 
-                token_list.push({text : new_x.value.matched,
-                    type: new_x.value.matched_type,
-                    ln : ln,
-                    col : col});
+/**
+ * rearrangeTree : for applyToken subtree from right-combination to 
+ * left-combination
+ * @input x a ast
+ * @return another ast
+ */
+function rearrangeTree(x: any) : any {
     
+        if (x !== undefined){
+            for (var i=1;i<x.length;i++){
+                rearrangeTree(x[i]);
             }
+            console.log("@@"+repr(x[0]));
+
+            if (x[0] == applyToken){
+                if (Array.isArray(x[2]) && x[2][0] == applyToken){
+                    let rl = rearrangeTree(x[2][1]);
+                    let rr = rearrangeTree(x[2][2]);
+                    let l = rearrangeTree(x[1]);
+                    x[0] = applyToken;
+                    x[1] = [applyToken, l, rl];
+                    x[2] = rr;
+                    console.log("@@=="+repr(x));
+
+                    return x;
+                }
+                else{
+                    x[0] = applyToken;
+                    x[1] = rearrangeTree(x[1]);
+                    x[2] = rearrangeTree(x[2]);
+                    console.log("@@=="+repr(x));
 
 
-            old_x = toSome({matched : "",
-                            remained : new_x.value.remained});
-            new_x = thenDo(old_x, term_aux);
-        }
+                    return x;
+                }
+            }
 
-        if (old_x.value.remained.length){
-            console.log(token_list);
-            throw new Error("the code can't be tokenized is near Ln. "+ln+", Col."+col
-                            +", starting with "+ old_x.value.remained.substring(0,10));
+            return x;
         }
-
-        return token_list;
     }
+        
+
+
+
+/**
+ * 
+ * term1 = fac (MUL | DIV) fac
+ */
+
+let term1 = midfix((x : TokenMatcheePair)=>
+            thenDo(thenDo(thenDo(toSome(x), fac), orDo(tMul,tDiv)), fac), "term1");
+
+            
+/**
+ * 
+ * term2 = int MUL int
+ */
+let term2 = fac;
+
+/**
+ * term = term1 | term2
+ */
+let term = orDo(term1, term2);
+ 
+
+/**
+ * 
+ * expr1 = term ADD term
+ */
+let expr1 = midfix((x : TokenMatcheePair)=>
+                thenDo(thenDo(thenDo(toSome(x), term), orDo(tAdd,tSub)), term), "expr1");
+/**
+ * expr2 = term
+ */
+let expr2 = term;
+
+/**
+ * expr = expr1 | expr2
+ */
+let expr = orDo(expr1, expr2);
+
+
+
+let tokens = tk.tokenize("1");
+let tokens2 = tk.tokenize("1(2)");
+let tokens3 = tk.tokenize("1(2)(3)");
+let tokens4 = tk.tokenize("2()(4)(5,6)(7,8,9,10)");
+
+//let tokens = tk.tokenize("(4-(3/4))");
+//tk.tokenize(argv[2]);
+
+let tokensFiltered = tokens4.filter(
+    (x)=>{return (x.type != tk.TokenType.NL
+            && x.type != tk.TokenType.SP)});
+
+
+
+let beta = expr({
+        matched : [] ,
+        remained : tokensFiltered,
+        ast : []});
+
 
-    console.log(term([], input_matchee_pair));
 
-    // TODO: id, string, space, basic operator, 3 marks: @, {, }.
+if (beta._tag == "Some"){
+    beta.value.ast = rearrangeTree(beta.value.ast);
+    console.log(tkTreeToSExp(beta.value.ast));
 
 }
 
+console.log("RESULT="+repr(beta));