Recursive descent parser generator
Recursive descent parser generator is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Write a recursive descent parser generator that takes a description of a grammar as input and outputs the source code for a parser in the same language as the generator. (So a generator written in C++ would output C++ source code for the parser.) You can assume that all of the rules have been preprocessed into a form suitable for the construction of a recursive descent parser. Check the following links for more details.
- http://www.cs.engr.uky.edu/~lewis/essays/compilers/rec-des.html (broken)
- http://www.engr.mun.ca/~theo/Misc/exp_parsing.htm
Use the parser generator and a grammar file to build a parser that takes an arithmetic expression and turns it in to three address code. The resulting parser should take this (or something similar) as input:
(one + two) * three - four * five
And generate this (or something similar) as output:
_0001 = one + two _0002 = _0001 * three _0003 = four * five _0004 = _0002 - _0003
C#
This is the code containing the grammar definition and the parser generator.
using System.CodeDom.Compiler;
using System.Linq.Expressions;
public abstract record AST()
{
public abstract string Emit(TextWriter w);
}
public record Leaf(string Text) : AST
{
public override string ToString() =>
$"\"{Text}\"";
public override string Emit(TextWriter w) =>
Text;
}
public record Node(char Op, AST[] Operands) : AST
{
static int NodeID = 0;
public override string ToString() =>
$"{Op}({string.Join(", ", Operands.AsEnumerable())})";
public override string Emit(TextWriter w)
{
var names = Operands.Select(o => o.Emit(w)).ToList();
var id = ++NodeID;
var name = $"_{id:0000}";
switch (Operands.Length)
{
case 1:
w.WriteLine($"{name} = {Op}{names[0]}");
break;
case 2:
w.WriteLine($"{name} = {names[0]} {Op} {names[1]}");
break;
}
return name;
}
}
class ParserGenerator
{
/*
E --> T {( "+" | "-" ) T}
T --> F {( "*" | "/" ) F}
F --> P ["^" F]
P --> v | "(" E ")" | "-" T"
*/
readonly Dictionary<string, Expression<Func<Rule>>> grammar = new()
{
["E"] = () => Seq(NonTerm("T"), While(Operator('+', '-'), Binary(NonTerm("T")))),
["T"] = () => Seq(NonTerm("F"), While(Operator('*', '/'), Binary(NonTerm("F")))),
["F"] = () => Seq(NonTerm("P"), If(Operator('^'), Binary(NonTerm("F")))),
["P"] = () => Options(
Identifier(),
Seq('(', NonTerm("E"), ')'),
Seq(Operator('-'), Unary(NonTerm("T")))),
};
static void Main()
{
using var file = File.CreateText("RDParser.cs");
using IndentedTextWriter w = new(file);
ParserGenerator g = new();
g.Generate("E", w);
}
static void Demo()
{
EParser p = new();
var ast = p.Parse("(one + two) * three - four * five");
Console.WriteLine("Abstract syntax tree:");
Console.WriteLine(ast);
Console.WriteLine();
Console.WriteLine("Generated code:");
ast.Emit(Console.Out);
}
void Generate(string name, IndentedTextWriter w)
{
var rule = grammar[name];
w.WriteLine("using System.Text;");
w.WriteLine();
w.WriteLine($"public class {name}Parser");
Block(w, () =>
{
w.WriteLine("static void Expect(IEnumerator<char> c, char ch)");
Block(w, () =>
{
w.WriteLine("if (Consume(c) != ch)");
w.WriteLine(" throw new Exception();");
});
w.WriteLine();
w.WriteLine("static char Consume(IEnumerator<char> c)");
Block(w, () =>
{
w.WriteLine("var result = c.Current;");
w.WriteLine("_ = c.MoveNext();");
w.WriteLine("return result;");
});
w.WriteLine();
w.WriteLine("static Node MkNode(char op, params AST[] operands) =>");
w.WriteLine(" new(op, operands);");
w.WriteLine();
w.WriteLine("static Leaf MkLeaf(string text) =>");
w.WriteLine(" new(text);");
w.WriteLine();
w.WriteLine($"public AST Parse(string text)");
Block(w, () =>
{
w.WriteLine("const char End = '\\u0003';");
w.WriteLine("text = text.Replace(\" \", \"\") + End;");
w.WriteLine("var c = text.GetEnumerator();");
w.WriteLine("_ = c.MoveNext();");
w.WriteLine($"AST t = {name}(c);");
w.WriteLine("Expect(c, End);");
w.WriteLine("return t;");
});
foreach (var (n, r) in grammar)
{
w.WriteLine();
w.WriteLine($"AST {n}(IEnumerator<char> c)");
Block(w, () =>
{
NonTerminal(w, 't', r.Body);
w.WriteLine("return t;");
});
}
});
}
void NonTerminal(IndentedTextWriter w, char varName, Expression e, int index = 0)
{
if (e is UnaryExpression cast)
{
if (index == 0)
w.WriteLine("Consume(c);");
else
w.WriteLine($"Expect(c, '{cast.Operand}');");
return;
}
var call = e as MethodCallExpression;
var args = call!.Arguments!;
switch (call!.Method.Name)
{
case nameof(NonTerm):
w.WriteLine($"AST {varName} = {(args[0] as ConstantExpression)!.Value}(c);");
break;
case nameof(Seq):
foreach (var arg in ((NewArrayExpression)args[0]).Expressions)
{
NonTerminal(w, varName, arg, index++);
}
break;
case nameof(While):
w.WriteLine($"while ({Peek(args[0])})");
++varName;
Block(w, () =>
{
NonTerminal(w, varName, args[1]);
});
--varName;
break;
case nameof(If):
w.WriteLine($"if ({Peek(args[0])})");
++varName;
Block(w, () =>
{
NonTerminal(w, varName, args[1]);
});
--varName;
break;
case nameof(Binary):
w.WriteLine("var op = Consume(c);");
var t = (char)(varName - 1);
NonTerminal(w, varName, args[0]);
w.WriteLine($"{t} = MkNode(op, {t}, {varName});");
break;
case nameof(Unary):
w.WriteLine("var op = Consume(c);");
NonTerminal(w, varName, args[0]);
w.WriteLine($"{varName} = MkNode(op, {varName});");
break;
case nameof(Options):
var el = "";
w.WriteLine($"AST {varName};");
t = varName;
++varName;
foreach (var arg in ((NewArrayExpression)args[0]).Expressions)
{
w.WriteLine($"{el}if ({Peek(arg)})");
Block(w, () =>
{
NonTerminal(w, varName, arg, index);
w.WriteLine($"{t} = {varName};");
});
el = "else ";
}
--varName;
w.WriteLine("else");
w.WriteLine(" throw new Exception();");
break;
case nameof(Operator):
break;
case nameof(Identifier):
w.WriteLine($"StringBuilder {varName}_ = new();");
w.WriteLine("while (char.IsLetter(c.Current))");
Block(w, () =>
{
w.WriteLine($"{varName}_.Append(Consume(c));");
});
w.WriteLine($"AST {varName} = MkLeaf({varName}_.ToString());");
break;
default:
throw new NotImplementedException();
}
}
string Peek(Expression e)
{
if (e is UnaryExpression cast)
{
return $"c.Current == '{cast.Operand}'";
}
var call = e as MethodCallExpression;
var args = call!.Arguments;
return call!.Method.Name switch
{
nameof(Seq) =>
Peek(((NewArrayExpression)args[0]).Expressions[0]),
nameof(Options) =>
string.Join(" || ", ((NewArrayExpression)args[0]).Expressions.Select(arg => "(" + Peek(arg) + ")")),
nameof(Operator) =>
string.Join(" || ", ((NewArrayExpression)args[0]).Expressions.Select(arg => $"c.Current == '{arg}'")),
nameof(Binary) or nameof(Unary) =>
$"c.Current == '{args[0]}'",
nameof(Identifier) =>
"char.IsLetter(c.Current)",
_ => throw new NotImplementedException(),
};
}
static void Block(IndentedTextWriter w, Action action)
{
w.WriteLine("{");
w.Indent++;
action();
w.Indent--;
w.WriteLine("}");
}
static Rule NonTerm(string name) => new();
static Rule Operator(params char[] ops) => new();
static Rule Seq(params Rule[] rules) => new();
static Rule Options(params Rule[] rules) => new();
static Rule If(Rule cond, Rule r) => new();
static Rule While(Rule cond, Rule r) => new();
static Rule Identifier() => new();
static Rule Binary(Rule r) => new();
static Rule Unary(Rule r) => new();
}
record Rule()
{
public static implicit operator Rule(char ch) => new();
}
- Output:
Running Main from the code above produces the following recursive-descent parser:
using System.Text;
public class EParser
{
static void Expect(IEnumerator<char> c, char ch)
{
if (Consume(c) != ch)
throw new Exception();
}
static char Consume(IEnumerator<char> c)
{
var result = c.Current;
_ = c.MoveNext();
return result;
}
static Node MkNode(char op, params AST[] operands) =>
new(op, operands);
static Leaf MkLeaf(string text) =>
new(text);
public AST Parse(string text)
{
const char End = '\u0003';
text = text.Replace(" ", "") + End;
var c = text.GetEnumerator();
_ = c.MoveNext();
AST t = E(c);
Expect(c, End);
return t;
}
AST E(IEnumerator<char> c)
{
AST t = T(c);
while (c.Current == '+' || c.Current == '-')
{
var op = Consume(c);
AST u = T(c);
t = MkNode(op, t, u);
}
return t;
}
AST T(IEnumerator<char> c)
{
AST t = F(c);
while (c.Current == '*' || c.Current == '/')
{
var op = Consume(c);
AST u = F(c);
t = MkNode(op, t, u);
}
return t;
}
AST F(IEnumerator<char> c)
{
AST t = P(c);
if (c.Current == '^')
{
var op = Consume(c);
AST u = F(c);
t = MkNode(op, t, u);
}
return t;
}
AST P(IEnumerator<char> c)
{
AST t;
if (char.IsLetter(c.Current))
{
StringBuilder u_ = new();
while (char.IsLetter(c.Current))
{
u_.Append(Consume(c));
}
AST u = MkLeaf(u_.ToString());
t = u;
}
else if (c.Current == '(')
{
Consume(c);
AST u = E(c);
Expect(c, ')');
t = u;
}
else if (c.Current == '-')
{
var op = Consume(c);
AST u = T(c);
u = MkNode(op, u);
t = u;
}
else
throw new Exception();
return t;
}
}
Running the Demo method calls the generated parser and produces this output:
Abstract syntax tree:
-(*(+("one", "two"), "three"), *("four", "five"))
Generated code:
_0001 = one + two
_0002 = _0001 * three
_0003 = four * five
_0004 = _0002 - _0003
C++
This program translates an annotated LL(1) grammar into a C++ lexer plus parser. Each rule is required to return a string of some kind and the return values of the already matched nonterminals (and matched text of terminals) can be accessed with $1, $2, etc. which are replaced by the appropriate string variable.
It can't handle newlines as part of the grammar, the error checking is fairly limited and the error reporting is basically non-existent, but the parser it generates (not shown below) is human readable.
#include <fstream>
#include <iostream>
#include <map>
#include <regex>
#include <set>
#include <sstream>
#include <string>
using namespace std;
map<string, string> terminals;
map<string, vector<vector<string>>> nonterminalRules;
map<string, set<string>> nonterminalFirst;
map<string, vector<string>> nonterminalCode;
int main(int argc, char **argv) {
if (argc < 3) {
cout << "Usage: <input file> <output file>" << endl;
return 1;
}
ifstream inFile(argv[1]);
ofstream outFile(argv[2]);
regex blankLine(R"(^\s*$)");
regex terminalPattern(R"((\w+)\s+(.+))");
regex rulePattern(R"(^!!\s*(\w+)\s*->\s*((?:\w+\s*)*)$)");
regex argPattern(R"(\$(\d+))");
smatch results;
// Read terminal patterns
string line;
while (true) {
getline(inFile, line);
// Terminals section ends with a blank line
if (regex_match(line, blankLine))
break;
regex_match(line, results, terminalPattern);
terminals[results[1]] = results[2];
}
outFile << "#include <iostream>" << endl
<< "#include <fstream>" << endl
<< "#include <string>" << endl
<< "#include <regex>" << endl
<< "using namespace std;" << endl
<< endl;
// Generate the token processing functions
outFile << "string input, nextToken, nextTokenValue;" << endl
<< "string prevToken, prevTokenValue;" << endl
<< endl
<< "void advanceToken() {" << endl
<< " static smatch results;" << endl
<< endl
<< " prevToken = nextToken;" << endl
<< " prevTokenValue = nextTokenValue;" << endl
<< endl;
for (auto i = terminals.begin(); i != terminals.end(); ++i) {
string name = i->first + "_pattern";
string pattern = i->second;
outFile << " static regex " << name << "(R\"(^\\s*(" << pattern << "))\");" << endl
<< " if (regex_search(input, results, " << name << ", regex_constants::match_continuous)) {" << endl
<< " nextToken = \"" << i->first << "\";" << endl
<< " nextTokenValue = results[1];" << endl
<< " input = regex_replace(input, " << name << ", \"\");" << endl
<< " return;" << endl
<< " }" << endl
<< endl;
}
outFile << " static regex eof(R\"(\\s*)\");" << endl
<< " if (regex_match(input, results, eof, regex_constants::match_continuous)) {" << endl
<< " nextToken = \"\";" << endl
<< " nextTokenValue = \"\";" << endl
<< " return;" << endl
<< " }" << endl
<< endl
<< " throw \"Unknown token\";" << endl
<< "}" << endl
<< endl
<< "bool same(string symbol) {" << endl
<< " if (symbol == nextToken) {" << endl
<< " advanceToken();" << endl
<< " return true;" << endl
<< " }" << endl
<< " return false;" << endl
<< "}" << endl
<< endl;
// Copy the header code to the output
while (true) {
getline(inFile, line);
// Copy lines until we reach the first rule
if (regex_match(line, results, rulePattern))
break;
outFile << line << endl;
}
// Build the nonterminal table
while (true) {
// results already contains the last matched rule
string name = results[1];
stringstream ss(results[2]);
string tempString;
vector<string> tempVector;
while (ss >> tempString)
tempVector.push_back(tempString);
nonterminalRules[name].push_back(tempVector);
// Read code until another rule is found
string code = "";
while (true) {
getline(inFile, line);
if (!inFile || regex_match(line, results, rulePattern))
break;
// Replace $1 with results[1], etc.
line = regex_replace(line, argPattern, "results[$1]");
code += line + "\n";
}
nonterminalCode[name].push_back(code);
// Stop when we reach the end of the file
if (!inFile)
break;
}
// Generate the first sets, inefficiently
bool done = false;
while (!done)
for (auto i = nonterminalRules.begin(); i != nonterminalRules.end(); ++i) {
string name = i->first;
done = true;
if (nonterminalFirst.find(i->first) == nonterminalFirst.end())
nonterminalFirst[i->first] = set<string>();
for (int j = 0; j < i->second.size(); ++j) {
if (i->second[j].size() == 0)
nonterminalFirst[i->first].insert("");
else {
string first = i->second[j][0];
if (nonterminalFirst.find(first) != nonterminalFirst.end()) {
for (auto k = nonterminalFirst[first].begin(); k != nonterminalFirst[first].end(); ++k) {
if (nonterminalFirst[name].find(*k) == nonterminalFirst[name].end()) {
nonterminalFirst[name].insert(*k);
done = false;
}
}
} else if (nonterminalFirst[name].find(first) == nonterminalFirst[name].end()) {
nonterminalFirst[name].insert(first);
done = false;
}
}
}
}
// Generate function signatures for the nonterminals
for (auto i = nonterminalRules.begin(); i != nonterminalRules.end(); ++i) {
string name = i->first + "_rule";
outFile << "string " << name << "();" << endl;
}
outFile << endl;
// Generate the nonterminal functions
for (auto i = nonterminalRules.begin(); i != nonterminalRules.end(); ++i) {
string name = i->first + "_rule";
outFile << "string " << name << "() {" << endl
<< " vector<string> results;" << endl
<< " results.push_back(\"\");" << endl
<< endl;
// Check if this rule can match an empty string
int epsilon = -1;
for (int j = 0; epsilon == -1 && j < i->second.size(); ++j)
if (i->second[j].size() == 0)
epsilon = j;
// Generate each production
for (int j = 0; j < i->second.size(); ++j) {
// Nothing to generate for an empty rule
if (j == epsilon)
continue;
string token = i->second[j][0];
if (terminals.find(token) != terminals.end())
outFile << " if (nextToken == \"" << i->second[j][0] << "\") {" << endl;
else {
outFile << " if (";
bool first = true;
for (auto k = nonterminalFirst[token].begin(); k != nonterminalFirst[token].end(); ++k, first = false) {
if (!first)
outFile << " || ";
outFile << "nextToken == \"" << (*k) << "\"";
}
outFile << ") {" << endl;
}
for (int k = 0; k < i->second[j].size(); ++k) {
if (terminals.find(i->second[j][k]) != terminals.end()) {
outFile << " if(same(\"" << i->second[j][k] << "\"))" << endl
<< " results.push_back(prevTokenValue);" << endl
<< " else" << endl
<< " throw \"Syntax error - mismatched token\";" << endl;
} else
outFile << " results.push_back(" << i->second[j][k] << "_rule());" << endl;
}
// Copy rule code to output
outFile << nonterminalCode[i->first][j];
outFile << " }" << endl << endl;
}
if (epsilon == -1)
outFile << " throw \"Syntax error - unmatched token\";" << endl;
else
outFile << nonterminalCode[i->first][epsilon];
outFile << "}" << endl << endl;
}
// Generate the main function
outFile << "int main(int argc, char **argv) {" << endl
<< " if(argc < 2) {" << endl
<< " cout << \"Usage: <input file>\" << endl;" << endl
<< " return 1;" << endl
<< " }" << endl
<< endl
<< " ifstream file(argv[1]);" << endl
<< " string line;" << endl
<< " input = \"\";" << endl
<< endl
<< " while(true) {" << endl
<< " getline(file, line);" << endl
<< " if(!file) break;" << endl
<< " input += line + \"\\n\";" << endl
<< " }" << endl
<< endl
<< " advanceToken();" << endl
<< endl
<< " start_rule();" << endl
<< "}" << endl;
}
Example grammar:
plus \+
minus -
times \*
div /
open \(
close \)
num [0-9]+
var [a-z]+
string nextLabel() {
static string label = "0000";
for(int i = label.length() - 1; i >= 0; --i) {
if(label[i] == '9')
label[i] = '0';
else {
++label[i];
break;
}
}
return "_" + label;
}
!! start -> expr start2
if($2 == "")
return $1;
else {
string label = nextLabel();
cout << label << " = " << $1 << " " << $2 << endl;
return label;
}
!! start2 -> plus start
return "+ " + $2;
!! start2 -> minus start
return "- " + $2;
!! start2 ->
return "";
!! expr -> term expr2
if($2 == "")
return $1;
else {
string label = nextLabel();
cout << label << " = " << $1 << " " << $2 << endl;
return label;
}
!! expr2 -> times expr
return "* " + $2;
!! expr2 -> div expr
return "/ " + $2;
!! expr2 ->
return "";
!! term -> var
return $1;
!! term -> num
return $1;
!! term -> open start close
return $2;
Example input to parser (filename passed through command line):
(one + two) * three + four * five
Output (to standard out):
_0001 = one + two _0002 = _0001 * three _0003 = four * five _0004 = _0002 + _0003
FreeBASIC
Const NULL As Any Ptr = 0
Type Token
tType As String * 10 ' "SYMBOL", "IDENT", "EOF"
tVal As String * 50
End Type
Type ASTNode
tType As String * 10 ' "SYMBOL" o "IDENT"
tVal As String * 50
izda As ASTNode Ptr
dcha As ASTNode Ptr
End Type
Dim Shared src As String
Dim Shared sdx As Integer
Dim Shared currChar As String * 1
Dim Shared tok As Token
Dim Shared nxt As Integer
Declare Function primary() As ASTNode Ptr
Function currentChar() As String
Return Iif(sdx > Len(src), "", Mid(src, sdx, 1))
End Function
Sub skipSpaces()
Do
If sdx > Len(src) Then Exit Do
currChar = currentChar()
If Instr(" " + Chr(9) + Chr(13) + Chr(10), currChar) = 0 Then Exit Do
sdx += 1
Loop
End Sub
Sub nextToken()
skipSpaces()
If sdx > Len(src) Then
tok.tType = "EOF"
tok.tVal = ""
Return
End If
currChar = currentChar()
If Instr("()+-/*", currChar) > 0 Then
tok.tType = "SYMBOL"
tok.tVal = currChar
sdx += 1
Elseif (currChar >= "a" And currChar <= "z") Or (currChar >= "A" And currChar <= "Z") Then
Dim As Integer startPos = sdx
Do
sdx += 1
If sdx > Len(src) Then Exit Do
currChar = currentChar()
Loop While (currChar = "_") Or _
(currChar >= "a" And currChar <= "z") Or _
(currChar >= "A" And currChar <= "Z") Or _
(currChar >= "0" And currChar <= "9")
tok.tType = "IDENT"
tok.tVal = Mid(src, startPos, sdx - startPos)
Else
Print "Error: unexpected character '" & currChar & "'"
End 1
End If
End Sub
Function newNode(tType As String, tVal As String, izda As ASTNode Ptr = NULL, dcha As ASTNode Ptr = NULL) As ASTNode Ptr
Dim As ASTNode Ptr node = Allocate(Sizeof(ASTNode))
If node = NULL Then
Print "Error: memory allocation failed"
End 1
End If
node->tType = tType
node->tVal = tVal
node->izda = izda
node->dcha = dcha
Return node
End Function
Function mulExpr() As ASTNode Ptr
Dim As ASTNode Ptr res = primary()
Do
If tok.tType <> "SYMBOL" Or (tok.tVal <> "*" And tok.tVal <> "/") Then Exit Do
Dim As String opVal = tok.tVal
nextToken()
res = newNode("SYMBOL", opVal, res, primary())
Loop
Return res
End Function
Function sumExpr() As ASTNode Ptr
Dim As ASTNode Ptr res = mulExpr()
Do
If tok.tType <> "SYMBOL" Or (tok.tVal <> "+" And tok.tVal <> "-") Then Exit Do
Dim As String opVal = tok.tVal
nextToken()
res = newNode("SYMBOL", opVal, res, mulExpr())
Loop
Return res
End Function
Function primary() As ASTNode Ptr
Dim As ASTNode Ptr res
If tok.tType = "IDENT" Then
res = newNode(tok.tType, tok.tVal)
nextToken()
Elseif tok.tType = "SYMBOL" And tok.tVal = "(" Then
nextToken()
res = sumExpr()
If tok.tType <> "SYMBOL" Or tok.tVal <> ")" Then
Print "Error: ')' was expected"
End 1
End If
nextToken()
Else
Print "Error: invalid primary expression"
End 1
End If
Return res
End Function
Sub printAST(node As ASTNode Ptr, indent As Integer = 0)
If node = NULL Then
Print "Error: null AST node in printAST"
End 1
End If
Dim i As Integer
For i = 1 To indent
Print " ";
Next
If node->tType = "SYMBOL" Then
Print "{{`" & Trim(node->tType) & "`,"
For i = 1 To indent
Print " ";
Next
Print " `" & Trim(node->tVal) & "`},"
printAST(node->izda, indent + 1)
Print ","
printAST(node->dcha, indent + 1)
Print "}";
Elseif node->tType = "IDENT" Then
Print "{`" & Trim(node->tType) & "`,"
For i = 1 To indent
Print " ";
Next
Print " `" & Trim(node->tVal) & "`}";
Else
Print "Error: Unknown AST node type: " & node->tType
End 1
End If
End Sub
Function showAST(ast As ASTNode Ptr) As String
If ast = NULL Then
Print "Error: null AST node"
End 1
End If
If ast->tType = "SYMBOL" Then
Dim lhs As String = showAST(ast->izda)
Dim rhs As String = showAST(ast->dcha)
Dim nid As String
nid = "_" & Right("0000" & Str(nxt), 4)
Print nid & " = " & lhs & " " & Trim(ast->tVal) & " " & rhs
nxt += 1
Return nid
Elseif ast->tType = "IDENT" Then
Return Trim(ast->tVal)
Else
Print "Error: unknown AST node type: " & ast->tType
End 1
End If
End Function
Sub Parse(source As String)
src = source
sdx = 1
nxt = 1
nextToken()
Dim As ASTNode Ptr ast = sumExpr()
Print "Complete syntactic tree:"
printAST(ast)
Print
Print !"\nIntermediate assignments:"
Dim As String result = showAST(ast)
End Sub
' Main program
Parse("(one + two) * three - four * five")
Sleep
- Output:
Complete syntactic tree:
{{`SYMBOL`,
`-`},
{{`SYMBOL`,
`*`},
{{`SYMBOL`,
`+`},
{`IDENT`,
`one`},
{`IDENT`,
`two`}},
{`IDENT`,
`three`}},
{{`SYMBOL`,
`*`},
{`IDENT`,
`four`},
{`IDENT`,
`five`}}}
Intermediate assignments:
_0001 = one + two
_0002 = _0001 * three
_0003 = four * five
_0004 = _0002 - _0003
Go
The standard library already contains a recursive descent parser for Go programs or expressions, written in Go itself, whose output is an abstract syntax tree (AST) representing such code.
I've therefore applied this parser to the expression designated by the task, which only involves binary expressions and identifiers, and written a separate routine to convert the resulting AST into three-address code.
package main
import (
"fmt"
"go/ast"
"go/parser"
"log"
)
func labelStr(label int) string {
return fmt.Sprintf("_%04d", label)
}
type binexp struct {
op, left, right string
kind, index int
}
func main() {
x := "(one + two) * three - four * five"
fmt.Println("Expression to parse: ", x)
f, err := parser.ParseExpr(x)
if err != nil {
log.Fatal(err)
}
fmt.Println("\nThe abstract syntax tree for this expression:")
ast.Print(nil, f)
fmt.Println("\nThe corresponding three-address code:")
var binexps []binexp
// Inspect nodes in depth-first order.
ast.Inspect(f, func(n ast.Node) bool {
switch x := n.(type) {
case *ast.BinaryExpr:
sx, ok1 := x.X.(*ast.Ident)
sy, ok2 := x.Y.(*ast.Ident)
op := x.Op.String()
if ok1 && ok2 {
binexps = append(binexps, binexp{op, sx.Name, sy.Name, 3, 0})
} else if !ok1 && ok2 {
binexps = append(binexps, binexp{op, "<addr>", sy.Name, 2, 0})
} else if ok1 && !ok2 {
binexps = append(binexps, binexp{op, sx.Name, "<addr>", 1, 0})
} else {
binexps = append(binexps, binexp{op, "<addr>", "<addr>", 0, 0})
}
}
return true
})
for i := 0; i < len(binexps); i++ {
binexps[i].index = i
}
label, last := 0, -1
var ops, args []binexp
var labels []string
for i, be := range binexps {
if be.kind == 0 {
ops = append(ops, be)
}
if be.kind != 3 {
continue
}
label++
ls := labelStr(label)
fmt.Printf(" %s = %s %s %s\n", ls, be.left, be.op, be.right)
for j := i - 1; j > last; j-- {
be2 := binexps[j]
if be2.kind == 2 {
label++
ls2 := labelStr(label)
fmt.Printf(" %s = %s %s %s\n", ls2, ls, be2.op, be2.right)
ls = ls2
be = be2
} else if be2.kind == 1 {
label++
ls2 := labelStr(label)
fmt.Printf(" %s = %s %s %s\n", ls2, be2.left, be2.op, ls)
ls = ls2
be = be2
}
}
args = append(args, be)
labels = append(labels, ls)
lea, leo := len(args), len(ops)
for lea >= 2 {
if i < len(binexps)-1 && args[lea-2].index <= ops[leo-1].index {
break
}
label++
ls2 := labelStr(label)
fmt.Printf(" %s = %s %s %s\n", ls2, labels[lea-2], ops[leo-1].op, labels[lea-1])
ops = ops[0 : leo-1]
args = args[0 : lea-1]
labels = labels[0 : lea-1]
lea--
leo--
args[lea-1] = be
labels[lea-1] = ls2
}
last = i
}
}
- Output:
Expression to parse: (one + two) * three - four * five
The abstract syntax tree for this expression:
0 *ast.BinaryExpr {
1 . X: *ast.BinaryExpr {
2 . . X: *ast.ParenExpr {
3 . . . Lparen: 1
4 . . . X: *ast.BinaryExpr {
5 . . . . X: *ast.Ident {
6 . . . . . NamePos: 2
7 . . . . . Name: "one"
8 . . . . . Obj: *ast.Object {
9 . . . . . . Kind: bad
10 . . . . . . Name: ""
11 . . . . . }
12 . . . . }
13 . . . . OpPos: 6
14 . . . . Op: +
15 . . . . Y: *ast.Ident {
16 . . . . . NamePos: 8
17 . . . . . Name: "two"
18 . . . . . Obj: *(obj @ 8)
19 . . . . }
20 . . . }
21 . . . Rparen: 11
22 . . }
23 . . OpPos: 13
24 . . Op: *
25 . . Y: *ast.Ident {
26 . . . NamePos: 15
27 . . . Name: "three"
28 . . . Obj: *(obj @ 8)
29 . . }
30 . }
31 . OpPos: 21
32 . Op: -
33 . Y: *ast.BinaryExpr {
34 . . X: *ast.Ident {
35 . . . NamePos: 23
36 . . . Name: "four"
37 . . . Obj: *(obj @ 8)
38 . . }
39 . . OpPos: 28
40 . . Op: *
41 . . Y: *ast.Ident {
42 . . . NamePos: 30
43 . . . Name: "five"
44 . . . Obj: *(obj @ 8)
45 . . }
46 . }
47 }
The corresponding three-address code:
_0001 = one + two
_0002 = _0001 * three
_0003 = four * five
_0004 = _0002 - _0003
J
J's native recursive descent parser is adequate for this task, if we map names appropriately.
Implementation:
cocurrent 'base'
inlocale=: 4 :0 L:0
x,'_',y,'_'
)
parse=: 3 :0
sentence=. ;:y
opinds=. (;:'+*-')i.sentence
opfuns=. (;:'plus times minus') inlocale 'base'
scratch=. cocreate''
coinsert__scratch 'base'
names=. ~.sentence#~_1<:nc sentence
(names inlocale scratch)=: names
r=. do__scratch ;:inv opinds}((#sentence)#"0 opfuns),sentence
codestroy__scratch''
r
)
term=: 1 :0
2 :('m''',m,'''expr n')
)
expr=:1 :0
:
r=. genname''
emit r,'=:',x,m,y
r
)
plus=: '+' expr
times=: '*' term
minus=: '-' expr
N=: 10000
genname=: 3 :0
'z',}.":N=: N+1
)
emit=: smoutput
Task example:
parse '(one + two) * three - four * five'
z0001=:four*five
z0002=:one+two
z0003=:z0002*three
z0004=:z0003-z0001
z0004
See also https://github.com/jsoftware/general_misc/blob/master/trace.ijs for a model of the underlying parser being employed here.
Julia
The Julia compiler's own parser is a recursive descent parser, and can be used directly here.
const one, two, three, four, five, six, seven, eight, nine = collect(1:9)
function testparser(s)
cod = Meta.parse(s)
println(Meta.lower(Main, cod))
end
testparser("(one + two) * three - four * five")
- Output:
$(Expr(:thunk, CodeInfo(
@ none within `top-level scope'
1 ─ %1 = one + two
│ %2 = %1 * three
│ %3 = four * five
│ %4 = %2 - %3
└── return %4
)))
Perl
#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Recursive_descent_parser_generator
use warnings;
use Path::Tiny;
my $h = qr/\G\s*/;
my $identifier = qr/$h([a-z]\w*)\b/i;
my $literal = qr/$h(['"])(.+?)\1/s;
my (%rules, %called, $usercode, %patches);
my $filename = './generatedparser.pl';
sub node { bless [ @_[1..$#_] ], $_[0] }
sub error { die "ERROR: ", s/\G\s*\K/<**ERROR @_**>/r, "\n" }
sub want { /$h\Q$_[1]\E/gc ? shift : error "missing '$_[1]' " }
sub addin { node $_[0] => ref $_[1] eq $_[0] ? @{$_[1]} : $_[1], pop }
local $_ = do { local $/; @ARGV ? <> : <DATA> }; # the EBNF
$usercode = s/^(#usercode.*)//ms ? $1 : "# no usercode included\n";;
$patches{PATCHUSER} = $usercode . "#end usercode\n"; # grammar support code
s/^\h*#.*\n//gm; # remove comment lines
$patches{PATCHGRAMMAR} = s/^(?:\h*\n)+//r =~ s/\n(?:\h*\n)+\z//r;
while( /$identifier\s*=/gc ) # the start of a rule
{
my $name = $1;
$rules{startsymbol} //= node RULE => $name;
my $tree = expr(0);
$rules{$name} = $rules{$name} ? addin ALT => $rules{$name}, $tree : $tree;
/$h[.;]/gc or error 'missing rule terminator, needs . or ;';
}
/\G\s*\z/ or error "incomplete parse at ", substr $_, pos($_) // 0;
%rules or error "no rules found ";
delete @called{keys %rules};
%called and die "\nERROR: undefined rule(s) <@{[ keys %called]}>\n";
sub expr # precedence climbing parser for grammer rules
{
my $tree =
/$h(NAME)\b/gc ? node $1 : # internal name matcher
/$identifier/gc ? do { $called{$1}++; node RULE => $1 } :
/$literal/gc ? node LIT => $2 :
/$h<(\w+)>/gc ? node ACTION => $1 :
/$h\[/gc ? node OPTION => want expr(0), ']' :
/$h\{/gc ? node REPEAT => want expr(0), '}' :
/$h\(/gc ? want expr(0), ')' :
error 'Invalid expression';
$tree =
/\G\s+/gc ? $tree :
$_[0] <= 1 && /\G(?=[[<{('"a-z])/gci ? addin SEQ => $tree, expr(2) :
$_[0] <= 0 && /\G\|/gc ? addin ALT => $tree, expr(1) :
return $tree while 1;
}
my $perlcode = "# generated code (put in Rule:: package)\n";
for my $rule ( sort keys %rules )
{
my $body = $rules{$rule}->code;
$perlcode .= "\nsub Rule::$rule\n\t{\n\t$body\n\t}\n";
}
$perlcode =~ s/^(?:\h*\n)+(?=\h*\})//gm;
$perlcode .= "\n# preceding code was generated for rules\n";
$patches{PATCHGENERATED} = $perlcode;
sub ALT::code
{
my $all = join " or\n\t", map $_->code, @{ $_[0] };
"( # alt\n\t$all )"
}
sub SEQ::code
{
my $all = join " and\n\t", map $_->code, @{ $_[0] };
"( # seq\n\t$all )"
}
sub REPEAT::code { "do { # repeat\n\t1 while @{[ $_[0][0]->code ]} ; 1 }" }
sub OPTION::code { "( # option\n\t@{[ $_[0][0]->code ]} or 1 )" }
sub RULE::code { "Rule::$_[0][0]()" }
sub ACTION::code { "( $_[0][0]() || 1 )" }
sub NAME::code { "( /\\G\$whitespace(\\w+)/gc and push \@stack, \$1 )" }
sub LIT::code { "( /\\G\$whitespace(\Q$_[0][0]\E)/gc and push \@stack, \$1 )" }
$_ = <<'END'; ##################################### template for generated code
#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Recursive_descent_parser_generator
use warnings; # WARNING: this code is generated
my @stack;
my $whitespace = qr/\s*/;
my $grammar = <<'GRAMMAR'; # make grammar rules available to usercode
PATCHGRAMMAR
GRAMMAR
PATCHUSER
PATCHGENERATED
local $_ = shift // '(one + two) * three - four * five';
eval { begin() }; # eval because it is optional
Rule::startsymbol();
eval { end() }; # eval because it is optional
/\G\s*\z/ or die "ERROR: incomplete parse\n";
END
s/(PATCH\w+)/$patches{$1}/g; # insert grammar variable stuff
path( $filename )->spew( $_ );
chmod 0555, $filename; # readonly, executable
exec 'perl', $filename, @ARGV or die "exec failed $!";
__DATA__
expr = term { plus term <gen3addr> } .
term = factor { times factor <gen3addr> } .
factor = primary [ '^' factor <gen3addr> ] .
primary = '(' expr ')' <removeparens> | NAME .
plus = "+" | "-" .
times = "*" | "/" .
#usercode -- separator for included code for actions
my $temp = '0000';
sub begin { print "parsing: $_\n\n" }
sub gen3addr
{
@stack >= 3 or die "not enough on stack";
my @three = splice @stack, -3, 3, my $t = '_' . ++$temp;
print "$t = @three\n";
}
sub removeparens
{
@stack >= 3 or die "not enough on stack";
splice @stack, -3, 3, $stack[-2];
}
Running the above with no arguments uses a default grammar that will solve the specified example. It produces the following perl script (and then runs it).
#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Recursive_descent_parser_generator
use warnings; # WARNING: this code is generated
my @stack;
my $whitespace = qr/\s*/;
my $grammar = <<'GRAMMAR'; # make grammar rules available to usercode
expr = term { plus term <gen3addr> } .
term = factor { times factor <gen3addr> } .
factor = primary [ '^' factor <gen3addr> ] .
primary = '(' expr ')' <removeparens> | NAME .
plus = "+" | "-" .
times = "*" | "/" .
GRAMMAR
#usercode -- separator for included code for actions
my $temp = '0000';
sub begin { print "parsing: $_\n\n" }
sub gen3addr
{
@stack >= 3 or die "not enough on stack";
my @three = splice @stack, -3, 3, my $t = '_' . ++$temp;
print "$t = @three\n";
}
sub removeparens
{
@stack >= 3 or die "not enough on stack";
splice @stack, -3, 3, $stack[-2];
}
#end usercode
# generated code (put in Rule:: package)
sub Rule::expr
{
( # seq
Rule::term() and
do { # repeat
1 while ( # seq
Rule::plus() and
Rule::term() and
( gen3addr() || 1 ) ) ; 1 } )
}
sub Rule::factor
{
( # seq
Rule::primary() and
( # option
( # seq
( /\G$whitespace(\^)/gc and push @stack, $1 ) and
Rule::factor() and
( gen3addr() || 1 ) ) or 1 ) )
}
sub Rule::plus
{
( # alt
( /\G$whitespace(\+)/gc and push @stack, $1 ) or
( /\G$whitespace(\-)/gc and push @stack, $1 ) )
}
sub Rule::primary
{
( # alt
( # seq
( /\G$whitespace(\()/gc and push @stack, $1 ) and
Rule::expr() and
( /\G$whitespace(\))/gc and push @stack, $1 ) and
( removeparens() || 1 ) ) or
( /\G$whitespace(\w+)/gc and push @stack, $1 ) )
}
sub Rule::startsymbol
{
Rule::expr()
}
sub Rule::term
{
( # seq
Rule::factor() and
do { # repeat
1 while ( # seq
Rule::times() and
Rule::factor() and
( gen3addr() || 1 ) ) ; 1 } )
}
sub Rule::times
{
( # alt
( /\G$whitespace(\*)/gc and push @stack, $1 ) or
( /\G$whitespace(\/)/gc and push @stack, $1 ) )
}
# preceding code was generated for rules
local $_ = shift // '(one + two) * three - four * five';
eval { begin() }; # eval because it is optional
Rule::startsymbol();
eval { end() }; # eval because it is optional
/\G\s*\z/ or die "ERROR: incomplete parse\n";
The above script can also be run stand-alone and produces the following output.
- Output:
parsing: (one + two) * three - four * five _0001 = one + two _0002 = _0001 * three _0003 = four * five _0004 = _0002 - _0003
Different grammars and input can be specified on the command line.
recursivedescentparsergenerator.pl arithexpr.y '2 * 3 + 4 * 5'
and giving this file as "arithexpr.y"
# test arith expr
expr = term { '+' term <fadd> | '-' term <fsub> } .
term = factor { '*' factor <fmul> | '/' factor <fdiv> } .
factor = '(' expr ')' <noparen> | NAME .
#usercode
sub noparen { splice @stack, -3, 3, $stack[-2]; }
sub fadd { splice @stack, -3, 3, $stack[-3] + $stack[-1] }
sub fsub { splice @stack, -3, 3, $stack[-3] - $stack[-1] }
sub fmul { splice @stack, -3, 3, $stack[-3] * $stack[-1] }
sub fdiv { splice @stack, -3, 3, $stack[-3] / $stack[-1] }
sub begin { print "expr = $_\n" }
sub end { print "answer = @{[pop @stack]}\n" }
will produce the following
- Output:
expr = 2 * 3 + 4 * 5 answer = 26
Phix
Technically the task is asking for code which generates something like the following, so I suppose
it would actually meet the spec if it began with constant src = """ and ended with
""" puts(1,src)... (and like several/most other entries on this page, this does not use a formal grammer)
-- -- demo\rosetta\RecursiveDescentParser.exw -- ======================================= -- with javascript_semantics string src integer ch, sdx sequence tok procedure skip_spaces() while 1 do if sdx>length(src) then exit end if ch = src[sdx] if not find(ch,{' ','\t','\r','\n'}) then exit end if sdx += 1 end while end procedure procedure next_token() -- yeilds one of: -- {"SYMBOL",ch} where ch is one of "()+-/*", or -- {"IDENT",string}, or {"EOF"} skip_spaces() integer tokstart = sdx if sdx>length(src) then tok = {"EOF"} elsif find(ch,"()+-/*") then sdx += 1 tok = {"SYMBOL",ch&""} elsif (ch>='a' and ch<='z') or (ch>='A' and ch<='Z') then while true do sdx += 1 if sdx>length(src) then exit end if ch = src[sdx] if ch!='_' and (ch<'a' or ch>'z') and (ch<'A' or ch>'Z') and (ch<'0' or ch>'9') then exit end if end while tok = {"IDENT",src[tokstart..sdx-1]} else ?9/0 end if end procedure forward function sum_expr() function primary() sequence res if tok[1]="IDENT" then res = tok next_token() elsif tok={"SYMBOL","("} then next_token() res = sum_expr() if tok!={"SYMBOL",")"} then ?9/0 end if next_token() else ?9/0 end if return res end function function mul_expr() sequence res = primary() while true do if tok[1]!="SYMBOL" or not find(tok[2],{"*","/"}) then exit end if res = {tok,res,NULL} next_token() res[3] = primary() end while return res end function function sum_expr() sequence res = mul_expr() while true do if tok[1]!="SYMBOL" or not find(tok[2],{"+","-"}) then exit end if res = {tok,res,NULL} next_token() res[3] = mul_expr() end while return res end function integer nxt = 1 function show_ast(sequence ast) if ast[1][1]="SYMBOL" then string op = ast[1][2], lhs = show_ast(ast[2]), rhs = show_ast(ast[3]), nid = sprintf("_%04d",nxt) printf(1,"%s = %s %s %s\n",{nid,lhs,op,rhs}) nxt += 1 return nid elsif ast[1]="IDENT" then return ast[2] end if ?9/0 end function procedure parse(string source) src = source sdx = 1 next_token() sequence ast = sum_expr() if tok!={"EOF"} then ?9/0 end if pp(ast,{pp_Nest,4}) {} = show_ast(ast) end procedure parse("(one + two) * three - four * five") {} = wait_key()
- Output:
{{`SYMBOL`,
`-`},
{{`SYMBOL`,
`*`},
{{`SYMBOL`,
`+`},
{`IDENT`,
`one`},
{`IDENT`,
`two`}},
{`IDENT`,
`three`}},
{{`SYMBOL`,
`*`},
{`IDENT`,
`four`},
{`IDENT`,
`five`}}}
_0001 = one + two
_0002 = _0001 * three
_0003 = four * five
_0004 = _0002 - _0003
Raku
(formerly Perl 6) Instead of writing a full-blown generator, it is possible to solve the task partly by making use of the built-in optimizer and study the relevant AST output
raku --target=optimize -e 'no strict; say ($one + $two) * $three - $four * $five' | tail -11
- QAST::Op(callstatic &say) <sunk> :statement_id<2> say ($one + $two) * $three - $four * $five
- QAST::Op(callstatic &infix:<->) <wanted> -
- QAST::Op(callstatic &infix:<*>) <wanted> *
- QAST::Op(callstatic &infix:<+>) <wanted> :statement_id<3> +
- QAST::Var(local __lowered_lex_5) <wanted> $one
- QAST::Var(local __lowered_lex_4) <wanted> $two
- QAST::Var(local __lowered_lex_3) <wanted> $three
- QAST::Op(callstatic &infix:<*>) <wanted> *
- QAST::Var(local __lowered_lex_2) <wanted> $four
- QAST::Var(local __lowered_lex_1) <wanted> $five
- QAST::WVal(Nil)
As you can see by examining the nested tree, the calculations are done as follows (expressed using a postfix notation)
one two + three * four five * -
Wren
import "./str" for Char
import "./fmt" for Fmt
class RDP {
construct parse(source) {
_src = source
_sdx = 0
_ch = null
_tok = null
_nxt = 1
nextToken()
var ast = sumExpr()
if (_tok[0] != "EOF") Fiber.abort("Something went wrong.")
printAst(ast, 0)
System.print()
showAst(ast)
}
skipSpaces() {
while (true) {
if (_sdx >= _src.count) return
_ch = _src[_sdx]
if (!" \t\r\n".contains(_ch)) return
_sdx = _sdx + 1
}
}
// yields one of:
// ["SYMBOL", ch] where ch is one of "()+-/*", or
// ["IDENT", string] or ["EOF"]
nextToken() {
skipSpaces()
var tokStart = _sdx
if (_sdx >= _src.count) {
_tok = ["EOF"]
} else if ("()+-/*".contains(_ch)) {
_sdx = _sdx + 1
_tok = ["SYMBOL", _ch]
} else if (Char.isAsciiLetter(_ch)) {
while (true) {
_sdx = _sdx + 1
if (_sdx >= _src.count) break
_ch = _src[_sdx]
if (!Char.isAsciiAlphaNum(_ch) && _ch != "_") break
}
_tok = ["IDENT", _src[tokStart..._sdx]]
} else {
Fiber.abort("Invalid token '%(_ch)'.")
}
}
primary() {
var res = []
if (_tok[0] == "IDENT") {
res = _tok.toList
nextToken()
} else if (_tok[0] == "SYMBOL" && _tok[1] == "(") {
nextToken()
res = sumExpr()
if (_tok[0] != "SYMBOL" || _tok[1] != ")") Fiber.abort("Unexpected token '%(_tok)'.")
nextToken()
} else {
Fiber.abort("Unexpected token '%(_tok)'.")
}
return res
}
mulExpr() {
var res = primary()
while (true) {
if (_tok[0] != "SYMBOL" || !"*/".contains(_tok[1])) break
res = [_tok, res, null]
nextToken()
res[2] = primary()
}
return res
}
sumExpr() {
var res = mulExpr()
while (true) {
if (_tok[0] != "SYMBOL" || !"+-".contains(_tok[1])) break
res = [_tok, res, null]
nextToken()
res[2] = mulExpr()
}
return res
}
showAst(ast) {
if (ast[0][0] == "SYMBOL") {
var op = ast[0][1]
var lhs = showAst(ast[1])
var rhs = showAst(ast[2])
var thiz = Fmt.swrite("_$04d", _nxt)
Fmt.print("$s = $s $s $s", thiz, lhs, op, rhs)
_nxt = _nxt + 1
return thiz
} else if (ast[0] == "IDENT") {
return ast[1]
}
Fiber.abort("Something went wrong.")
}
printAst(ast, level) {
for (e in ast) {
var indent = " " * level
if (!(e is List)) {
System.print(indent + e)
} else {
System.print(indent + "{")
printAst(e, level+1)
System.print(indent + "}")
}
}
}
}
RDP.parse("(one + two) * three - four * five")
- Output:
{
SYMBOL
-
}
{
{
SYMBOL
*
}
{
{
SYMBOL
+
}
{
IDENT
one
}
{
IDENT
two
}
}
{
IDENT
three
}
}
{
{
SYMBOL
*
}
{
IDENT
four
}
{
IDENT
five
}
}
_0001 = one + two
_0002 = _0001 * three
_0003 = four * five
_0004 = _0002 - _0003