3.λ.形而下技术博客

这里只关注技术实现,用代码说话。

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Write a simple parser for MiniLisp by using JavaCC

MiniLisp是什么?

MiniLisp是一个只用几百行代码实现的Lisp。以下是实现的 基本特性。

  • integers, symbols, cons cells,
  • global variables,
  • lexically-scoped local variables,
  • closures,
  • if conditional,
  • primitive functions, such as +, =, <, or list,
  • user-defined functions,
  • a macro system,
  • and a copying garbage collector.

在笔者看来真是麻雀虽小五脏俱全啊。这是一个非常值得研究的项目。

JavaCC是什么?

JavaCC据说是一个非常易用好理解的LL(k)的Parser生成工具。 说它好理解是指它生成的Java代码要比LR类型的容易理解。毕竟LLTop-Down Parser呀。 笔者以前只用过LR(1)类型的工具,JavaCC则从来没用过。

MiniLisp的BNF语法描述没有怎么办?

MiniLisp的作者并没有使用yacc等工具,而是自己手写的Top-Down Parser。所以无法得到 MiniLisp的BNF描述。

没关系,既然是Lisp方言,那么先看看传统的Lisp的BNF语法是什么。这里有一个简单的BNF版本 BNF rules of LISP

s_expression = atomic_symbol \
              / "(" s_expression "."s_expression ")" \
              / list 

list = "(" s_expression < s_expression > ")"

atomic_symbol = letter atom_part

atom_part = empty / letter atom_part / number atom_part

letter = "a" / "b" / " ..." / "z"

number = "1" / "2" / " ..." / "9"

empty = " "

想要实现MiniLisp的Parser,首先要理解这个BNF规则。

MiniLisp的jj文件

以下是用JavaCC生成MiniLisp Parser的jj文件。用javacc编译之后,会报一个警告117行和118行发生conflict。但是笔者已经加上LOOKAHEAD(2)了。 不知道为什么还警告,而且也单独对这部分进行了测试,完全没有问题。另外,这个生成的Parser并没有构造AST。

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options {
STATIC = false;
DEBUG_PARSER = true;
DEBUG_LOOKAHEAD = true;
DEBUG_TOKEN_MANAGER = false;
ERROR_REPORTING = true;
JAVA_UNICODE_ESCAPE = false;
UNICODE_INPUT = false;
IGNORE_CASE = false;
USER_TOKEN_MANAGER = false;
USER_CHAR_STREAM = false;
BUILD_PARSER = true;
BUILD_TOKEN_MANAGER = true;
SANITY_CHECK = true;
FORCE_LA_CHECK = true;
}

PARSER_BEGIN(MiniLisp)

package ym.minilisp;

import ym.minilisp.node.*;
import java.util.*;

public class MiniLisp {

/** Main entry point. */
public static void main(String args[]) throws ParseException {
MiniLisp parser = new MiniLisp(System.in);
parser.Input();
}

}
PARSER_END(MiniLisp)


TOKEN :
{
<EMPTY: [" ","\t","\n","\r"] ([" ","\t","\n","\r"])*>
| <LP: "(">
| <RP: ")">
| <DOT: ".">
| <MINUS: "-">
| <PLUS: "+">
| <EQ: "=">
| <AND: "and">
| <NOT: "not">
| <OR: "or">
| <GT: ">">
| <LT: "<">
| <LE: "<=">
| <GE: ">=">
| <SQUOTE: "'">
| <QUOTE: "quote">
| <NUM: ["1"-"9"] ( ["0"-"9"] )* | "0">
| <ID: (["a"-"z","A"-"Z","_","@","?","$","%","*"]) (~["\n","\r"," ","(",")","\t","#",";","{","}","[","]"])* >
| <COMMENT: ([";"])(~["\n","\r"])* ["\n","\r"]>
}


/** Root production. */
void Input() :
{}
{
( Expr() )* <EOF>
}

void Expr():
{}
{
NonSExpr()
| SExpr()
}


void NonSExpr():
{}
{
<EMPTY>
|<COMMENT>
}


void SExpr() :
{}
{
SymbolExpr()
| <LP> (NonSExpr())* (SExpr() (NonSExpr())* )* [<DOT> (NonSExpr())* (SExpr() (NonSExpr())* )*] <RP>
| SQuoteExpr()
}

void SQuoteExpr():
{}
{
<SQUOTE> SExpr()
}


void SymbolExpr():
{}
{
Symbol() LOOKAHEAD({ getToken(1).kind == LP || getToken(1).kind == RP|| getToken(1).kind == DOT || getToken(1).kind == COMMENT || getToken(1).kind == EMPTY })
}

void Symbol():
{}
{
<PLUS>
| <EQ>
| <AND>
| <NOT>
| <OR>
| <GT>
| <LT>
| <LE>
| <GE>
| LOOKAHEAD(2) <MINUS> <NUM>
| <MINUS>
| <NUM>
| <ID>
}

测试代码

以下是对生成的MiniLisp.java文件进行测试的类。其中test14test15是对 MiniLisp项目下的life.lisp和nqueens.lisp文件内容完整解析测试。 没有报错,说明jj中的规则可以解析MiniLisp。

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package ym.minilisp;

import java.io.StringReader;
import junit.framework.TestCase;
import org.junit.Test;

public class TestParser extends TestCase {

@Test
public void test1() throws ParseException {
String s = "((a.b).(b.(c)))";
call(s);
}

@Test
public void test2() throws ParseException {
String s = "(a b c)";
call(s);
s = "(a b . c)";
call(s);
}

@Test
public void test3() throws ParseException {
String s = "(a .(b c))";
call(s);
}

@Test
public void test4() throws ParseException {
String s = " ( ( a b ) . ( b c ) ) ";
call(s);
}

@Test
public void test5() throws ParseException {
String s = "( a ( a b ) ( b c ) ) ";
call(s);
}

@Test
public void test6() throws ParseException {
String s = "(define a 1) (define b -1) ";
call(s);
}

@Test
public void test7() throws ParseException {
String s = " (+ 1 -2 a b (- 1 2)) ";
call(s);
}

@Test
public void test8() throws ParseException {
String s = " (defun next (board x y)\n"
+ " (let c (count board x y)\n"
+ " (if (alive? board x y)\n"
+ " (or (= c 2) (= c 3))\n"
+ " (= c 3))))";
System.out.println(s);
call(s);
}

@Test
public void test9() throws ParseException {
String s = "(defun count (board x y)\n"
+ " (let at (lambda (x y)\n"
+ " (if (alive? board x y) 1 0))\n"
+ " (+ (at (- x 1) (- y 1))\n"
+ " (at (- x 1) y)\n"
+ " (at (- x 1) (+ y 1))\n"
+ " (at x (- y 1))\n"
+ " (at x (+ y 1))\n"
+ " (at (+ x 1) (- y 1))\n"
+ " (at (+ x 1) y)\n"
+ " (at (+ x 1) (+ y 1)))))";
System.out.println(s);
call(s);
}

@Test
public void test10() throws ParseException {
String s = " '(+ 1 2) ";
call(s);
}

@Test
public void test11() throws ParseException {
String s = "(cons '1 '2)";
call(s);
}

@Test
public void test12() throws ParseException {
String s = "(defmacro progn (expr . rest)\n"
+ " (list (cons 'lambda (cons () (cons expr rest)))))";
call(s);
}

@Test
public void test13() throws ParseException {
String s = ";;fadfsdfasdfasdfasdfa\n"
+ "(cons '1 '2)";
call(s);
}

@Test
public void test131() throws ParseException {
String s = "(cons ;;fadfsdfasdfasdfasdfa\n"
+ " '1 '2)";
call(s);
}

@Test
public void test132() throws ParseException {
String s = ";;fadfsdfasdfasdfasdfa\n"
+ " \n"
+ ";;fadfsdfasdfasdfasdf\n";

call(s);
}

@Test
public void test133() throws ParseException {
String s = "(list ;;fadfsdfasdfasdfasdfa\n"
+ " a ;;fadfsdfasdfasdfasdfa\n "
+ "b)";
call(s);
}

@Test
public void test14() throws ParseException {
String s = ";;;\n"
+ ";;; Conway's game of life\n"
+ ";;;\n"
+ "\n"
+ ";; (progn expr ...)\n"
+ ";; => ((lambda () expr ...))\n"
+ "(defmacro progn (expr . rest)\n"
+ " (list (cons 'lambda (cons () (cons expr rest)))))\n"
+ "\n"
+ "(defun list (x . y)\n"
+ " (cons x y))\n"
+ "\n"
+ "(defun not (x)\n"
+ " (if x () t))\n"
+ "\n"
+ ";; (let var val body ...)\n"
+ ";; => ((lambda (var) body ...) val)\n"
+ "(defmacro let (var val . body)\n"
+ " (cons (cons 'lambda (cons (list var) body))\n"
+ "\t(list val)))\n"
+ "\n"
+ ";; (and e1 e2 ...)\n"
+ ";; => (if e1 (and e2 ...))\n"
+ ";; (and e1)\n"
+ ";; => e1\n"
+ "(defmacro and (expr . rest)\n"
+ " (if rest\n"
+ " (list 'if expr (cons 'and rest))\n"
+ " expr))\n"
+ "\n"
+ ";; (or e1 e2 ...)\n"
+ ";; => (let <tmp> e1\n"
+ ";; (if <tmp> <tmp> (or e2 ...)))\n"
+ ";; (or e1)\n"
+ ";; => e1\n"
+ ";;\n"
+ ";; The reason to use the temporary variables is to avoid evaluating the\n"
+ ";; arguments more than once.\n"
+ "(defmacro or (expr . rest)\n"
+ " (if rest\n"
+ " (let var (gensym)\n"
+ " (list 'let var expr\n"
+ " (list 'if var var (cons 'or rest))))\n"
+ " expr))\n"
+ "\n"
+ ";; (when expr body ...)\n"
+ ";; => (if expr (progn body ...))\n"
+ "(defmacro when (expr . body)\n"
+ " (cons 'if (cons expr (list (cons 'progn body)))))\n"
+ "\n"
+ ";; (unless expr body ...)\n"
+ ";; => (if expr () body ...)\n"
+ "(defmacro unless (expr . body)\n"
+ " (cons 'if (cons expr (cons () body))))\n"
+ "\n"
+ ";;;\n"
+ ";;; Numeric operators\n"
+ ";;;\n"
+ "\n"
+ "(defun <= (e1 e2)\n"
+ " (or (< e1 e2)\n"
+ " (= e1 e2)))\n"
+ "\n"
+ ";;;\n"
+ ";;; List operators\n"
+ ";;;\n"
+ "\n"
+ ";;; Applies each element of lis to fn, and returns their return values as a list.\n"
+ "(defun map (lis fn)\n"
+ " (when lis\n"
+ " (cons (fn (car lis))\n"
+ "\t (map (cdr lis) fn))))\n"
+ "\n"
+ ";; Returns nth element of lis.\n"
+ "(defun nth (lis n)\n"
+ " (if (= n 0)\n"
+ " (car lis)\n"
+ " (nth (cdr lis) (- n 1))))\n"
+ "\n"
+ ";; Returns the nth tail of lis.\n"
+ "(defun nth-tail (lis n)\n"
+ " (if (= n 0)\n"
+ " lis\n"
+ " (nth-tail (cdr lis) (- n 1))))\n"
+ "\n"
+ ";; Returns a list consists of m .. n-1 integers.\n"
+ "(defun %iota (m n)\n"
+ " (unless (<= n m)\n"
+ " (cons m (%iota (+ m 1) n))))\n"
+ "\n"
+ ";; Returns a list consists of 0 ... n-1 integers.\n"
+ "(defun iota (n)\n"
+ " (%iota 0 n))\n"
+ "\n"
+ ";;;\n"
+ ";;; Main\n"
+ ";;;\n"
+ "\n"
+ "(define width 10)\n"
+ "(define height 10)\n"
+ "\n"
+ ";; Returns location (x, y)'s element.\n"
+ "(defun get (board x y)\n"
+ " (nth (nth board y) x))\n"
+ "\n"
+ ";; Returns true if location (x, y)'s value is \"@\".\n"
+ "(defun alive? (board x y)\n"
+ " (and (<= 0 x)\n"
+ " (< x height)\n"
+ " (<= 0 y)\n"
+ " (< y width)\n"
+ " (eq (get board x y) '@)))\n"
+ "\n"
+ ";; Print out the given board.\n"
+ "(defun print (board)\n"
+ " (if (not board)\n"
+ " '$\n"
+ " (println (car board))\n"
+ " (print (cdr board))))\n"
+ "\n"
+ "(defun count (board x y)\n"
+ " (let at (lambda (x y)\n"
+ " (if (alive? board x y) 1 0))\n"
+ " (+ (at (- x 1) (- y 1))\n"
+ " (at (- x 1) y)\n"
+ " (at (- x 1) (+ y 1))\n"
+ " (at x (- y 1))\n"
+ " (at x (+ y 1))\n"
+ " (at (+ x 1) (- y 1))\n"
+ " (at (+ x 1) y)\n"
+ " (at (+ x 1) (+ y 1)))))\n"
+ "\n"
+ "(defun next (board x y)\n"
+ " (let c (count board x y)\n"
+ " (if (alive? board x y)\n"
+ " (or (= c 2) (= c 3))\n"
+ " (= c 3))))\n"
+ "\n"
+ "(defun run (board)\n"
+ " (while t\n"
+ " (print board)\n"
+ " (println '*)\n"
+ " (let newboard (map (iota height)\n"
+ " (lambda (y)\n"
+ " (map (iota width)\n"
+ " (lambda (x)\n"
+ " (if (next board x y) '@ '_)))))\n"
+ " (setq board newboard))))\n"
+ "\n"
+ "(run '((_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ _ _ _ _ _ _ _ _ _)\n"
+ " (_ @ @ @ _ _ _ _ _ _)\n"
+ " (_ _ _ @ _ _ _ _ _ _)\n"
+ " (_ _ @ _ _ _ _ _ _ _)))\n";
call(s);
}

@Test
public void test15() throws ParseException {
String s = ";;;\n"
+ ";;; N-queens puzzle solver.\n"
+ ";;;\n"
+ ";;; The N queens puzzle is the problem of placing N chess queens on an N x N\n"
+ ";;; chessboard so that no two queens attack each\n"
+ ";;; other. http://en.wikipedia.org/wiki/Eight_queens_puzzle\n"
+ ";;;\n"
+ ";;; This program solves N-queens puzzle by depth-first backtracking.\n"
+ ";;;\n"
+ "\n"
+ ";;;\n"
+ ";;; Basic macros\n"
+ ";;;\n"
+ ";;; Because the language does not have quasiquote, we need to construct an\n"
+ ";;; expanded form using cons and list.\n"
+ ";;;\n"
+ "\n"
+ ";; (progn expr ...)\n"
+ ";; => ((lambda () expr ...))\n"
+ "(defmacro progn (expr . rest)\n"
+ " (list (cons 'lambda (cons () (cons expr rest)))))\n"
+ "\n"
+ "(defun list (x . y)\n"
+ " (cons x y))\n"
+ "\n"
+ "(defun not (x)\n"
+ " (if x () t))\n"
+ "\n"
+ ";; (let1 var val body ...)\n"
+ ";; => ((lambda (var) body ...) val)\n"
+ "(defmacro let1 (var val . body)\n"
+ " (cons (cons 'lambda (cons (list var) body))\n"
+ "\t(list val)))\n"
+ "\n"
+ ";; (and e1 e2 ...)\n"
+ ";; => (if e1 (and e2 ...))\n"
+ ";; (and e1)\n"
+ ";; => e1\n"
+ "(defmacro and (expr . rest)\n"
+ " (if rest\n"
+ " (list 'if expr (cons 'and rest))\n"
+ " expr))\n"
+ "\n"
+ ";; (or e1 e2 ...)\n"
+ ";; => (let1 <tmp> e1\n"
+ ";; (if <tmp> <tmp> (or e2 ...)))\n"
+ ";; (or e1)\n"
+ ";; => e1\n"
+ ";;\n"
+ ";; The reason to use the temporary variables is to avoid evaluating the\n"
+ ";; arguments more than once.\n"
+ "(defmacro or (expr . rest)\n"
+ " (if rest\n"
+ " (let1 var (gensym)\n"
+ "\t (list 'let1 var expr\n"
+ "\t\t (list 'if var var (cons 'or rest))))\n"
+ " expr))\n"
+ "\n"
+ ";; (when expr body ...)\n"
+ ";; => (if expr (progn body ...))\n"
+ "(defmacro when (expr . body)\n"
+ " (cons 'if (cons expr (list (cons 'progn body)))))\n"
+ "\n"
+ ";; (unless expr body ...)\n"
+ ";; => (if expr () body ...)\n"
+ "(defmacro unless (expr . body)\n"
+ " (cons 'if (cons expr (cons () body))))\n"
+ "\n"
+ ";;;\n"
+ ";;; Numeric operators\n"
+ ";;;\n"
+ "\n"
+ "(defun <= (e1 e2)\n"
+ " (or (< e1 e2)\n"
+ " (= e1 e2)))\n"
+ "\n"
+ ";;;\n"
+ ";;; List operators\n"
+ ";;;\n"
+ "\n"
+ ";; Applies each element of lis to pred. If pred returns a true value, terminate\n"
+ ";; the evaluation and returns pred's return value. If all of them return (),\n"
+ ";; returns ().\n"
+ "(defun any (lis pred)\n"
+ " (when lis\n"
+ " (or (pred (car lis))\n"
+ "\t(any (cdr lis) pred))))\n"
+ "\n"
+ ";;; Applies each element of lis to fn, and returns their return values as a list.\n"
+ "(defun map (lis fn)\n"
+ " (when lis\n"
+ " (cons (fn (car lis))\n"
+ "\t (map (cdr lis) fn))))\n"
+ "\n"
+ ";; Returns nth element of lis.\n"
+ "(defun nth (lis n)\n"
+ " (if (= n 0)\n"
+ " (car lis)\n"
+ " (nth (cdr lis) (- n 1))))\n"
+ "\n"
+ ";; Returns the nth tail of lis.\n"
+ "(defun nth-tail (lis n)\n"
+ " (if (= n 0)\n"
+ " lis\n"
+ " (nth-tail (cdr lis) (- n 1))))\n"
+ "\n"
+ ";; Returns a list consists of m .. n-1 integers.\n"
+ "(defun %iota (m n)\n"
+ " (unless (<= n m)\n"
+ " (cons m (%iota (+ m 1) n))))\n"
+ "\n"
+ ";; Returns a list consists of 0 ... n-1 integers.\n"
+ "(defun iota (n)\n"
+ " (%iota 0 n))\n"
+ "\n"
+ ";; Returns a new list whose length is len and all members are init.\n"
+ "(defun make-list (len init)\n"
+ " (unless (= len 0)\n"
+ " (cons init (make-list (- len 1) init))))\n"
+ "\n"
+ ";; Applies fn to each element of lis.\n"
+ "(defun for-each (lis fn)\n"
+ " (or (not lis)\n"
+ " (progn (fn (car lis))\n"
+ "\t (for-each (cdr lis) fn))))\n"
+ "\n"
+ ";;;\n"
+ ";;; N-queens solver\n"
+ ";;;\n"
+ "\n"
+ ";; Creates size x size list filled with symbol \"x\".\n"
+ "(defun make-board (size)\n"
+ " (map (iota size)\n"
+ " (lambda (_)\n"
+ "\t (make-list size 'x))))\n"
+ "\n"
+ ";; Returns location (x, y)'s element.\n"
+ "(defun get (board x y)\n"
+ " (nth (nth board x) y))\n"
+ "\n"
+ ";; Set symbol \"@\" to location (x, y).\n"
+ "(defun set (board x y)\n"
+ " (setcar (nth-tail (nth board x) y) '@))\n"
+ "\n"
+ ";; Set symbol \"x\" to location (x, y).\n"
+ "(defun clear (board x y)\n"
+ " (setcar (nth-tail (nth board x) y) 'x))\n"
+ "\n"
+ ";; Returns true if location (x, y)'s value is \"@\".\n"
+ "(defun set? (board x y)\n"
+ " (eq (get board x y) '@))\n"
+ "\n"
+ ";; Print out the given board.\n"
+ "(defun print (board)\n"
+ " (if (not board)\n"
+ " '$\n"
+ " (println (car board))\n"
+ " (print (cdr board))))\n"
+ "\n"
+ ";; Returns true if we cannot place a queen at position (x, y), assuming that\n"
+ ";; queens have already been placed on each row from 0 to x-1.\n"
+ "(defun conflict? (board x y)\n"
+ " (any (iota x)\n"
+ " (lambda (n)\n"
+ "\t (or\n"
+ "\t ;; Check if there's no conflicting queen upward\n"
+ "\t (set? board n y)\n"
+ "\t ;; Upper left\n"
+ "\t (let1 z (+ y (- n x))\n"
+ "\t\t(and (<= 0 z)\n"
+ "\t\t (set? board n z)))\n"
+ "\t ;; Upper right\n"
+ "\t (let1 z (+ y (- x n))\n"
+ "\t\t(and (< z board-size)\n"
+ "\t\t (set? board n z)))))))\n"
+ "\n"
+ ";; Find positions where we can place queens at row x, and continue searching for\n"
+ ";; the next row.\n"
+ "(defun %solve (board x)\n"
+ " (if (= x board-size)\n"
+ " ;; Problem solved\n"
+ " (progn (print board)\n"
+ "\t (println '$))\n"
+ " (for-each (iota board-size)\n"
+ "\t (lambda (y)\n"
+ "\t\t(unless (conflict? board x y)\n"
+ "\t\t (set board x y)\n"
+ "\t\t (%solve board (+ x 1))\n"
+ "\t\t (clear board x y))))))\n"
+ "\n"
+ "(defun solve (board)\n"
+ " (println 'start)\n"
+ " (%solve board 0)\n"
+ " (println 'done))\n"
+ "\n"
+ ";;;\n"
+ ";;; Main\n"
+ ";;;\n"
+ "\n"
+ "(define board-size 8)\n"
+ "(define board (make-board board-size))\n"
+ "(solve board)\n";
call(s);
}

private void call(String s) throws ParseException {
MiniLisp parser = new MiniLisp(new StringReader(s));
parser.Input();
}
}