Currently I'm trying to implement a grammar which is very similar to ruby. To keep it simple, the lexer currently ignores space characters.
However, in some cases the space letter makes big difference:
def some_callback(arg=0)
arg * 100
end
some_callback (1 + 1) + 1 # 300
some_callback(1 + 1) + 1 # 201
some_callback +1 # 100
some_callback+1 # 1
some_callback + 1 # 1
So currently all whitespaces are being ignored by the lexer:
{WHITESPACE} { ; }
And the language says for example something like:
UnaryExpression:
PostfixExpression
| T_PLUS UnaryExpression
| T_MINUS UnaryExpression
;
One way I can think of to solve this problem would be to explicitly add whitespaces to the whole grammar, but doing so the whole grammar would increase a lot in complexity:
// OLD:
AdditiveExpression:
MultiplicativeExpression
| AdditiveExpression T_ADD MultiplicativeExpression
| AdditiveExpression T_SUB MultiplicativeExpression
;
// NEW:
_:
/* empty */
| WHITESPACE _;
AdditiveExpression:
MultiplicativeExpression
| AdditiveExpression _ T_ADD _ MultiplicativeExpression
| AdditiveExpression _ T_SUB _ MultiplicativeExpression
;
//...
UnaryExpression:
PostfixExpression
| T_PLUS UnaryExpression
| T_MINUS UnaryExpression
;
So I liked to ask whether there is any best practice on how to solve this grammar.
Thank you in advance!
Without having a full specification of the syntax you are trying to parse, it's not easy to give a precise answer. In the following, I'm assuming that those are the only two places where the presence (or absence) of whitespace between two tokens affects the parse.
Differentiating between f(...) and f (...) occurs in a surprising number of languages. One common strategy is for the lexer to recognize an identifier which is immediately followed by an open parenthesis as a "FUNCTION_CALL" token.
You'll find that in most awk implementations, for example; in awk, the ambiguity between a function call and concatenation is resolved by requiring that the open parenthesis in a function call immediately follow the identifier. Similarly, the C pre-processor macro definition directive distinguishes between #define foo(A) A (the definition of a macro with arguments) and #define foo (A) (an ordinary macro whose expansion starts with a ( token.
If you're doing this with (f)lex, you can use the / trailing-context operator:
[[:alpha:]_][[:alnum:]_]*/'(' { yylval = strdup(yytext); return FUNC_CALL; }
[[:alpha:]_][[:alnum:]_]* { yylval = strdup(yytext); return IDENT; }
The grammar is now pretty straight-forward:
call: FUNC_CALL '(' expression_list ')' /* foo(1, 2) */
| IDENT expression_list /* foo (1, 2) */
| IDENT /* foo * 3 */
This distinction will not be useful in all syntactic contexts, so it will often prove useful to add a non-terminal which will match either identifier form:
name: IDENT | FUNC_CALL
But you will need to be careful with this non-terminal. In particular, using it as part of the expression grammar could lead to parser conflicts. But in other contexts, it will be fine:
func_defn: "def" name '(' parameters ')' block "end"
(I'm aware that this is not the precise syntax for Ruby function definitions. It's just for illustrative purposes.)
More troubling is the other ambiguity, in which it appears that the unary operators + and - should be treated as part of an integer literal in certain circumstances. The behaviour of the Ruby parser suggests that the lexer is combining the sign character with an immediately following number in the case where it might be the first argument to a function. (That is, in the context <identifier><whitespace><sign><digits> where <identifier> is not an already declared local variable.)
That sort of contextual rule could certainly be added to the lexical scanner using start conditions, although it's more than a little ugly. A not-fully-fleshed out implementation, building on the previous:
%x SIGNED_NUMBERS
%%
[[:alpha:]_][[:alnum:]_]*/'(' { yylval.id = strdup(yytext);
return FUNC_CALL; }
[[:alpha:]_][[:alnum:]_]*/[[:blank:]] { yylval.id = strdup(yytext);
if (!is_local(yylval.id))
BEGIN(SIGNED_NUMBERS);
return IDENT; }
[[:alpha:]_][[:alnum:]_]*/ { yylval.id = strdup(yytext);
return IDENT; }
<SIGNED_NUMBERS>[[:blank:]]+ ;
/* Numeric patterns, one version for each context */
<SIGNED_NUMBERS>[+-]?[[:digit:]]+ { yylval.integer = strtol(yytext, NULL, 0);
BEGIN(INITIAL);
return INTEGER; }
[[:digit:]]+ { yylval.integer = strtol(yytext, NULL, 0);
return INTEGER; }
/* ... */
/* If the next character is not a digit or a sign, rescan in INITIAL state */
<SIGNED_NUMBERS>.|\n { yyless(0); BEGIN(INITIAL); }
Another possible solution would be for the lexer to distinguish sign characters which follow a space and are directly followed by a digit, and then let the parser try to figure out whether or not the sign should be combined with the following number. However, this will still depend on being able to distinguish between local variables and other identifiers, which will still require the lexical feedback through the symbol table.
It's worth noting that the end result of all this complication is a language whose semantics are not very obvious in some corner cases. The fact that f+3 and f +3 produce different results could easily lead to subtle bugs which might be very hard to detect. In many projects using languages with these kinds of ambiguities, the project style guide will prohibit legal constructs with unclear semantics. You might want to take this into account in your language design, if you have not already done so.
Related
I'm parsing a language that doesn't have statement terminators like ;. Expressions are defined as the longest sequence of tokens, so 5-5 has to be parsed as a subtraction, not as two statements (literal 5 followed by a unary negated -5).
I'm using LALRPOP as the parser generator (despite the name, it is LR(1) instead of LALR, afaik). LALRPOP doesn't have precedence attributes and doesn't prefer shift over reduce by default like yacc would do. I think I understand how regular operator precedence is encoded in an LR grammar by building a "chain" of rules, but I don't know how to apply that to this issue.
The expected parses would be (individual statements in brackets):
"5 - 5" → 5-5 instead of 5, -5
"5 (- 5)" → 5, -5
"- 5" → -5
"5 5" → 5, 5
How do I change the grammar such that it always prefers the longer parse?
Going through the first few pages of google results as well as stack overflow didn't yield any results for this specific problem. Most related questions need more lookahead or the result is to not allow consecutive statements without terminators.
I created a minimal sample grammar that reproduces the shift/reduce conflict (a statement in this grammar is just an expression, in the full grammar there would also be "if", "while", etc. and more levels of operator precedence, but I've omitted them for brevity). Besides unary minus, there are also other conflicts in the original grammar like print(5), which could be parsed as the identifier print and a parenthesized number (5) or a function call. There might be more conflicts like this, but all of them have the same underlying issue, that the longer sequence should be preferred, but both are currently valid, though only the first should be.
For convenience, I created a repo (checkout and cargo run). The grammar is:
use std::str::FromStr;
grammar;
match {
"+",
"-",
"(",
")",
r"[0-9]+",
// Skip whitespace
r"\s*" => { },
}
Expr: i32 = {
<l:Expr> "+" <r:Unary> => l + r,
<l:Expr> "-" <r:Unary> => l - r,
Unary,
};
Unary: i32 = {
"-" <r:Unary> => -r,
Term,
}
Term: i32 = {
Num,
"(" <Expr> ")",
};
Num: i32 = {
r"[0-9]+" => i32::from_str(<>).unwrap(),
};
Stmt: i32 = {
Expr
};
pub Stmts: Vec<i32> = {
Stmt*
};
Part of the error (full error message):
/lalrpop-shift-repro/src/test.lalrpop:37:5: 37:8: Local ambiguity detected
The problem arises after having observed the following symbols in the input:
Stmt+ Expr
At that point, if the next token is a `"-"`, then the parser can proceed in two different ways.
First, the parser could execute the production at
/lalrpop-shift-repro/src/test.lalrpop:37:5: 37:8, which would consume
the top 1 token(s) from the stack and produce a `Stmt`. This might then yield a parse tree like
Expr ╷ Stmt
├─Stmt──┤ │
├─Stmt+─┘ │
└─Stmt+──────┘
Alternatively, the parser could shift the `"-"` token and later use it to construct a `Expr`. This might
then yield a parse tree like
Stmt+ Expr "-" Unary
│ ├─Expr───────┤
│ └─Stmt───────┤
└─Stmt+────────────┘
See the LALRPOP manual for advice on making your grammar LR(1).
The issue you're going to have to confront is how to deal with function calls. I can't really give you any concrete advice based on your question, because the grammar you provide lacks any indication of the intended syntax of functions calls, but the hint that print(5) is a valid statement makes it clear that there are two distinct situations, which need to be handled separately.
Consider:
5 - 5 One statement 5 ( - 5 ) Two statements
print(-5) One statement print - 5 Two statements (presumably)
a - 5 ???
The ambiguity of the third expression could be resolved if the compiler knew whether a is a function or a variable (if we assume that functions are not first-class values, making print an invalid statement). But there aren't many ways that the parser could know that, and none of them seem very likely:
There might not be any user-defined functions. Then the lexer could be built to recognise identifier-like tokens which happen to be built-in functions (like print) and then a(-5) would be illegal since a is not a built-in function.
The names of functions and identifiers might differ in some way that the lexer can detect. For example, the language might require functions to start with a capital letter. I presume this is not the case since you wrote print rather than Print but there might be some other simple distinction, such as requiring identifiers to be a single character.
Functions must be declared as such before the first use of the function, and the parser shares the symbol table with the lexer. (I didn't search the rather inadequate documentation for the generator you're using to see if lexical feedback is practical.)
If there were an optional statement delimiter (as with Lua, for example), then you could simply require that statements which start with parentheses (usually a pretty rare case) be explicitly delimited unless they are the first statement in a block. Or there might be an optional keyword such as compute which can be used as an unambiguous statement starter and whose use is required for statements which start with a parenthesis. I presume that neither of these is the case here, since you could have used that to force 5 - 5 to be recognised as two statements (5; -5 or 5 compute - 5.)
Another unlikely possibility, again based on the print(5) example, is that function calls use a different bracket than expression grouping. In that case, a[5] (for example) would be a function call and a(5) would unambiguously be two statements.
Since I don't know the precise requirements here, I'll show a grammar (in yacc/bison syntax, although it should be easy enough to translate it) which attempts to illustrate a representative sample. It implements one statement (return) in addition to expression statements, and expressions include multiplication, subtraction, negation and single argument function calls. To force "greedy" expressions, it prohibits certain statement sequences:
statements starting with a unary operator
statements starting with an open parenthesis if the previous statement ends with an identifier. (This effectively requires that the function to be applied in a call expression be a simple identifier. Without that restriction, it becomes close to impossible to distinguish two consecutive parenthesized expressions from a single function call expression, and you then need some other way to disambiguate.)
Those rules are easy to state, but the actual implementation is annoyingly repetitive because it requires various different kinds of expressions, depending on what the first and last token in the expression is, and possibly different kinds of statements, if you have statements which might end with an expression. (return x, for example.) The formalism used by ECMAScript would be useful here, but I suspect that your parser-generator doesn't implement it -- although it's possible that its macro facility could be used to that effect, if it came with something resembling documentation. Without that, there is a lot of duplication.
In a vague attempt to generate the grammar, I used the following suffixes:
_un / _pr / _oth: starts with unary / parenthesis / other token
_id / _nid: ends / does not end with an id
The absence of a suffix is used for the union of different possibilities. There are probably more unit productions than necessary. It has not been thoroughly debugged, but it worked on a few test cases (see below):
program : block
block_id : stmt_id
| block_id stmt_oth_id
| block_nid stmt_pr_id
| block_nid stmt_oth_id
block_nid : stmt_nid
| block_id stmt_oth_nid
| block_nid stmt_pr_nid
| block_nid stmt_oth_nid
block : %empty
| block_id | block_nid
stmt_un_id : expr_un_id
stmt_un_nid : expr_un_nid
stmt_pr_id : expr_pr_id
stmt_pr_nid : expr_pr_nid
stmt_oth_id : expr_oth_id
| return_id
stmt_oth_nid : expr_oth_nid
| return_nid
stmt_id : stmt_un_id | stmt_pr_id | stmt_oth_id
stmt_nid : stmt_un_nid | stmt_pr_nid | stmt_oth_nid
return_id : "return" expr_id
return_nid : "return" expr_nid
expr_un_id : sum_un_id
expr_un_nid : sum_un_nid
expr_pr_id : sum_pr_id
expr_pr_nid : sum_pr_nid
expr_oth_id : sum_oth_id
expr_oth_nid : sum_oth_nid
expr_id : expr_un_id | expr_pr_id | expr_oth_id
expr_nid : expr_un_nid | expr_pr_nid | expr_oth_nid
expr : expr_id | expr_nid
sum_un_id : mul_un_id
| sum_un '-' mul_id
sum_un_nid : mul_un_nid
| sum_un '-' mul_nid
sum_un : sum_un_id | sum_un_nid
sum_pr_id : mul_pr_id
| sum_pr '-' mul_id
sum_pr_nid : mul_pr_nid
| sum_pr '-' mul_nid
sum_pr : sum_pr_id | sum_pr_nid
sum_oth_id : mul_oth_id
| sum_oth '-' mul_id
sum_oth_nid : mul_oth_nid
| sum_oth '-' mul_nid
sum_oth : sum_oth_id | sum_oth_nid
mul_un_id : unary_un_id
| mul_un '*' unary_id
mul_un_nid : unary_un_nid
| mul_un '*' unary_nid
mul_un : mul_un_id | mul_un_nid
mul_pr_id : mul_pr '*' unary_id
mul_pr_nid : unary_pr_nid
| mul_pr '*' unary_nid
mul_pr : mul_pr_id | mul_pr_nid
mul_oth_id : unary_oth_id
| mul_oth '*' unary_id
mul_oth_nid : unary_oth_nid
| mul_oth '*' unary_nid
mul_oth : mul_oth_id | mul_oth_nid
mul_id : mul_un_id | mul_pr_id | mul_oth_id
mul_nid : mul_un_nid | mul_pr_nid | mul_oth_nid
unary_un_id : '-' unary_id
unary_un_nid : '-' unary_nid
unary_pr_nid : term_pr_nid
unary_oth_id : term_oth_id
unary_oth_nid: term_oth_nid
unary_id : unary_un_id | unary_oth_id
unary_nid : unary_un_nid | unary_pr_nid | unary_oth_nid
term_oth_id : IDENT
term_oth_nid : NUMBER
| IDENT '(' expr ')'
term_pr_nid : '(' expr ')'
Here's a little test:
> 5-5
{ [- 5 5] }
> 5(-5)
{ 5; [~ -- 5] }
> a-5
{ [- a 5] }
> a(5)
{ [CALL a 5] }
> -7*a
{ [* [~ -- 7] a] }
> a*-7
{ [* a [~ -- 7]] }
> a-b*c
{ [- a [* b c]] }
> a*b-c
{ [- [* a b] c] }
> a*b(3)-c
{ [- [* a [CALL b 3]] c] }
> a*b-c(3)
{ [- [* a b] [CALL c 3]] }
> a*b-7(3)
{ [- [* a b] 7]; 3 }
I'm working on a GLR-parser in GNU bison and I have the following problem:
the language I'm trying to parse allows boolean expressions including relations (<,>,<=,...) and boolean composition (and, or, not). Now the problem is that the language also allows to have multiple arithmetic expressions on the right side of a relation... and they are composed using the same AND token that is used for boolean composition! This is a very dumb language-design, but I can't change it.
So you can have a > b and c which is supposed to be equivalent to (a > b) and (a > c) and you can also have a > b and c > d which is supposed to be equivalent to (a > b) and (c > d)
The S/R conflict this causes is already obvious in this example: after reading a > b with lookahead and you could either reduce the a > b to a boolean expression and wait for another boolean expression or you could shift the and and wait for another arithmetic expression.
My grammar currently looks like this:
booleanexpression
: relation
| booleanexpression TOK_AND booleanexpression
...
;
relation
: arithmeticexpression TOK_GT maxtree
...
;
maxtree
: arithmeticexpression
| maxtree TOK_AND maxtree
...
;
The language is clearly not LR(k) for any k, since the S/R conflict can't be resolved using any constant k-lookahead, because the arithmeticexpression in between can have arbitrarily many tokens. Because of that, I turned GLR-parsing on.
But when I try to parse a > b and c with this, I can see in my debug outputs, that the parser behaves like this:
it reads the a and at lookahead > it reduces the a to an arithmeticexpression
it reads the b and at lookahead and it reduces the b to an arithmeticexpression and then already to a maxtree
it reduces the a > b to a relation
it reads the c and reduces it to an arithmeticexpression
then nothing happens! The and c are apparently discarded - the debug outputs don't show any action for these tokens. Not even an error message. The corresponding if-statement doesn't exist in my AST (I still get an AST because I have error recovery).
I would think that, after reading the b, there should be 2 stacks. But then the b shouldn't be reduced. Or at least it should give me some error message ("language is ambiguous" would be okay and I have seen that message before - I don't see why it wouldn't apply here). Can anyone make sense of this?
From looking at the grammar for a while, you can tell that the main question here is whether after the next arithmeticexpression there comes
another relation token (then you should reduce)
another boolean composition (then you should shift)
a token outside of the boolean/arithmetic -expression syntax (like THEN) which would terminate the expression and you should also shift
Can you think of a different grammar that captures the situation in a better / more deterministic way? How would you approach the problem? I'm currently thinking about making the grammar more right-to-left, like
booleanexpression : relation AND booleanexpression
maxtree : arithmeticexpression AND maxtree
etc.
I think that would make bison prefer shifting and only reduce on the right first. Maybe by using different non-terminals it would allow a quasi-"lookahead" behind the arithmeticexpression...
Side note: GnuCOBOL handles this problem by just collecting all the tokens, pushing them on an intermediate stack and manually building the expression from there. That discourages me, but I cling to the hope that they did it this way because bison didn't support GLR-parsing when they started...
EDIT:
a small reproducible example
%{
#include <stdio.h>
int yylex ();
void yyerror(const char* msg);
%}
%glr-parser
%left '&'
%left '>'
%%
input: %empty | input bool '\n' {printf("\n");};
arith : 'a' | 'b' | 'c';
maxtree : arith { printf("[maxtree : arith] "); }
| maxtree '&' maxtree { printf("[maxtree : maxtree & maxtree] "); } ;
rel : arith '>' maxtree { printf("[rel : arith > maxtree] "); } ;
bool : rel { printf("[bool : rel] "); }
| bool '&' bool { printf("[bool : bool & bool] "); } ;
%%
void yyerror(const char* msg) { printf("%s\n", msg); }
int yylex () {
int c;
while ((c = getchar ()) == ' ' || c == '\t');
return c == EOF ? 0 : c;
}
int main (int argc, char** argv) {
return yyparse();
}
this one strangely does print the error message "syntax error" on input a>b&c.
Being able to simplify grammars by using precedence declarations is really handy (sometimes) [Note 1] but it doesn't play well with using GLR parsers because it can lead to early rejection of an unambiguous parse.
The idea behind precedence declarations is that they resolve ambiguities (or, more accurately, shift/reduce conflicts) using a simple one-token lookahead and a configured precedence between the possible reduction and the possible shift. If a grammar has no shift/reduce conflict, the precedence declarations won't be used, but if they are used they will be used to suppress either the shift or the reduce, depending on the (static) precedence relationship.
A Bison-generated GLR parser does not actually resolve ambiguity, but it allows possibly incorrect parses to continue to be developed until the ambiguity is resolved by the grammar. Unlike the use of precedence, this is a delayed resolution; a bit slower but a lot more powerful. (GLR parsers can produce a "parse forest" containing all possible parses. But Bison doesn't implement this feature, since it expects to be parsing programming languages and unlike human languages, programming languages cannot be ambiguous.)
In your language, it is impossible to resolve the non-determinism of the shift/reduce conflict statically, as you note yourself in the question. Your grammar is simply not LR(1), much less operator precedence, and GLR parsing is therefore a practical solution. But you have to allow GLR to do its work. Prematurely eliminating one of the plausible parses with a precedence comparison will prevent the GLR algorithm from considering it later. This will be particularly serious if you manage to eliminate the only parse which could have been correct.
In your grammar, it is impossible to define a precedence relationship between the rel productions and the & symbol, because no precedence relationship exists. In some sentences, the rel reduction needs to win; in other sentences, the shift should win. Since the grammar is not ambiguous, GLR will eventually figure out which is which, as long as both the shift and the reduce are allowed to proceed.
In your full language, both boolean and arithmetic expressions have something akin to operator precedence, but only within their respective domains. An operator precedence parser (and, equivalently, yacc/bison's precedence declarations) works by erasing the difference between different non-terminals; it cannot handle a grammar like yours in which some operator has different precedences in different domains (or between different domains).
Fortunately, this particular use of precedence declarations is only a shortcut; it does not give any additional power to the grammar and can easily and mechanically be implemented by creating new non-terminals, one for each precedence level. The alternative grammar will not be ambiguous. The classic example, which you can find in pretty well any textbook or tutorial which includes parsing arithmetic expressions, is the expr/term/factor grammar. Here I've also provided the precedence grammar for comparison:
%left '+' '-'
%left '*' '/'
%% %%
expr : term
| expr '+' term expr: expr '+' expr
| expr '-' term | expr '-' expr
term : factor
| term '*' factor | expr '*' expr
| term '/' factor | expr '/' expr
factor: ID | ID
| '(' expr ')' | '(' expr ')'
In your minimal example, there are already enough non-terminals that no new ones need to be invented, so I've just rewritten it according to the above model.
I've left the actions as I wrote them, in case the style is useful to you. Note that this style leaks memory like a sieve, but that's ok for quick tests:
%code top {
#define _GNU_SOURCE 1
}
%{
#include <ctype.h>
#include <stdio.h>
#include <string.h>
int yylex(void);
void yyerror(const char* msg);
%}
%define api.value.type { char* }
%glr-parser
%token ID
%%
input : %empty
| input bool '\n' { puts($2); }
arith : ID
maxtree : arith
| maxtree '&' arith { asprintf(&$$, "[maxtree& %s %s]", $1, $3); }
rel : arith '>' maxtree { asprintf(&$$, "[COMP %s %s]", $1, $3); }
bool : rel
| bool '&' rel { asprintf(&$$, "[AND %s %s]", $1, $3); }
%%
void yyerror(const char* msg) { printf("%s\n", msg); }
int yylex(void) {
int c;
while ((c = getchar ()) == ' ' || c == '\t');
if (isalpha(c)) {
*(yylval = strdup(" ")) = c;
return ID;
}
else return c == EOF ? 0 : c;
}
int main (int argc, char** argv) {
#if YYDEBUG
if (argc > 1 && strncmp(argv[1], "-d", 2) == 0) yydebug = 1;
#endif
return yyparse();
}
Here's a sample run. Note the warning from bison about a shift/reduce conflict. If there had been no such warning, the GLR parser would probably be unnecessary, since a grammar without conflicts is deterministic. (On the other hand, since bison's GLR implementation optimises for determinism, there is not too much cost for using a GLR parser on a deterministic language.)
$ bison -t -o glr_prec.c glr_prec.y
glr_prec.y: warning: 1 shift/reduce conflict [-Wconflicts-sr]
$ gcc -Wall -o glr_prec glr_prec.c
$ ./glr_prec
a>b
[COMP a b]
a>b & c
[COMP a [maxtree& b c]]
a>b & c>d
[AND [COMP a b] [COMP c d]]
a>b & c & c>d
[AND [COMP a [maxtree& b c]] [COMP c d]]
a>b & c>d & e
[AND [COMP a b] [COMP c [maxtree& d e]]]
$
Notes
Although precedence declarations are handy when you understand what's actually going on, there is a huge tendency for people to just cargo-cult them from some other grammar they found on the internet, and not infrequently a grammar which was also cargo-culted from somewhere else. When the precedence declarations don't work as expected, the next step is to randomly modify them in the hopes of finding a configuration which works. Sometimes that succeeds, often leaving behind unnecessary detritus which will go on to be cargo-culted again.
So, although there are circumstances in which precedence declarations really simplify grammars and the unambiguous implementation would be quite a lot more complicated (such as dangling-else resolution in languages which have many different compound statement types), I've still found myself recommending against their use.
In a recent answer to a different question, I wrote what I hope is a good explanation of the precedence algorithm (and if it isn't, please let me know how it falls short).
Welcome to the wonderful world of COBOL. I could be wrong, but you may have a few
additional problems here. An expression such as A > B AND C in COBOL is ambiguous
until you know how C was declared. Consider the following program:
IDENTIFICATION DIVISION.
PROGRAM-ID EXAMPLE.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 A PIC 9 VALUE 2.
01 B PIC 9 VALUE 1.
01 W PIC 9 VALUE 3.
88 C VALUE 3.
PROCEDURE DIVISION.
IF A > B AND C
DISPLAY 'A > B AND 88 LEVEL C is TRUE because W = ' W
ELSE
DISPLAY 'A not > B or 88 LEVEL C is not TRUE'
END-IF
DISPLAY 'A: ' A ' B: ' B ' W:' W
GOBACK
.
Output from this program is:
A > B AND 88 LEVEL C is TRUE because W = 3
A: 2 B: 1 W: 3
In essence the expression: A > B AND C is equivalent to: A > B AND W = 3. Had C
been defined in a manner similar to A and B, the semantics would
have been: A > B AND A > C, which in this case, is FALSE.
The code mentioned above works well, but I had never gotten it to work in my real project, even though I couldn't see a difference between my real project and this code.
This drove me crazy, but I just found another problem in my code, which prevented this method from working:
I had an (admittedly cargo-culted) %skeleton "lalr1.cc" in my prologue, which disabled the GLR parsing again!
I needed to replace this with
%skeleton "glr.cc"
I'm writing a grammar for a toy language in Yacc (the one packaged with Go) and I have an expected shift-reduce conflict due to the following pseudo-issue. I have to distilled the problem grammar down to the following.
start:
stmt_list
expr:
INT | IDENT | lambda | '(' expr ')' { $$ = $2 }
lambda:
'(' params ')' '{' stmt_list '}'
params:
expr | params ',' expr
stmt:
/* empty */ | expr
stmt_list:
stmt | stmt_list ';' stmt
A lambda function looks something like this:
map((v) { v * 2 }, collection)
My parser emits:
conflicts: 1 shift/reduce
Given the input:
(a)
It correctly parses an expr by the '(' expr ')' rule. However given an input of:
(a) { a }
(Which would be a lambda for the identity function, returning its input). I get:
syntax error: unexpected '{'
This is because when (a) is read, the parser is choosing to reduce it as '(' expr ')', rather than consider it to be '(' params ')'. Given this conflict is a shift-reduce and not a reduce-reduce, I'm assuming this is solvable. I just don't know how to structure the grammar to support this syntax.
EDIT | It's ugly, but I'm considering defining a token so that the lexer can recognize the ')' '{' sequence and send it through as a single token to resolve this.
EDIT 2 | Actually, better still, I'll make lambdas require syntax like ->(a, b) { a * b} in the grammar, but have the lexer emit the -> rather than it being in the actual source code.
Your analysis is indeed correct; although the grammar is not ambiguous, it is impossible for the parser to decide with the input reduced to ( <expr> and with lookahead ) whether or not the expr should be reduced to params before shifting the ) or whether the ) should be shifted as part of a lambda. If the next token were visible, the decision could be made, so the grammar LR(2), which is outside of the competence of go/yacc.
If you were using bison, you could easily solve this problem by requesting a GLR parser, but I don't believe that go/yacc provides that feature.
There is an LR(1) grammar for the language (there is always an LR(1) grammar corresponding to any LR(k) grammar for any value of k) but it is rather annoying to write by hand. The essential idea of the LR(k) to LR(1) transformation is to shift the reduction decisions k-1 tokens forward by accumulating k-1 tokens of context into each production. So in the case that k is 2, each production P: N → α will be replaced with productions TNU → Tα U for each T in FIRST(α) and each U in FOLLOW(N). [See Note 1] That leads to a considerable blow-up of non-terminals in any non-trivial grammar.
Rather than pursuing that idea, let me propose two much simpler solutions, both of which you seem to be quite close to.
First, in the grammar you present, the issue really is simply the need for a two-token lookahead when the two tokens are ){. That could easily be detected in the lexer, and leads to a solution which is still hacky but a simpler hack: Return ){ as a single token. You need to deal with intervening whitespace, etc., but it doesn't require retaining any context in the lexer. This has the added bonus that you don't need to define params as a list of exprs; they can just be a list of IDENT (if that's relevant; a comment suggests that it isn't).
The alternative, which I think is a bit cleaner, is to extend the solution you already seem to be proposing: accept a little too much and reject the errors in a semantic action. In this case, you might do something like:
start:
stmt_list
expr:
INT
| IDENT
| lambda
| '(' expr_list ')'
{ // If $2 has more than one expr, report error
$$ = $2
}
lambda:
'(' expr_list ')' '{' stmt_list '}'
{ // If anything in expr_list is not a valid param, report error
$$ = make_lambda($2, $4)
}
expr_list:
expr | expr_list ',' expr
stmt:
/* empty */ | expr
stmt_list:
stmt | stmt_list ';' stmt
Notes
That's only an outline; the complete algorithm includes the mechanism to recover the original parse tree. If k is greater than 2 then T and U are strings the the FIRSTk-1 and FOLLOWk-1 sets.
If it really is a shift-reduce conflict, and you want only the shift behavior, your parser generator may give you a way to prefer a shift vs. a reduce. This is classically how the conflict for grammar rules for "if-then-stmt" and "if-then-stmt-else-stmt" is resolved, when the if statement can also be a statement.
See http://www.gnu.org/software/bison/manual/html_node/Shift_002fReduce.html
You can get this effect two ways:
a) Count on the accidental behavior of the parsing engine.
If an LALR parser handles shifts first, and then reductions if there are no shifts, then you'll get this "prefer shift" for free. All the parser generator has to do is built the parse tables anyway, even if there is a detected conflict.
b) Enforce the accidental behavior. Design (or a get a) parser generator to accept "prefer shift on token T". Then one can supress the ambiguity. One still have to implement the parsing engine as in a) but that's pretty easy.
I think this is easier/cleaner than abusing the lexer to make strange tokens (and that doesn't always work anyway).
Obviously, you could make a preference for reductions to turn it the other way. With some extra hacking, you could make shift-vs-reduce specific the state in which the conflict occured; you can even make it specific to the pair of conflicting rules but now the parsing engine needs to keep preference data around for nonterminals. That still isn't hard. Finally, you could add a predicate for each nonterminal which is called when a shift-reduce conflict is about to occur, and it have it provide a decision.
The point is you don't have to accept "pure" LALR parsing; you can bend it easily in a variety of ways, if you are willing to modify the parser generator/engine a little bit. This gives a really good reason to understand how these tools work; then you can abuse them to your benefit.
I am trying to implement an interpreter for a programming language, and ended up stumbling upon a case where I would need to backtrack, but my parser generator (ply, a lex&yacc clone written in Python) does not allow that
Here's the rules involved:
'var_access_start : super'
'var_access_start : NAME'
'var_access_name : DOT NAME'
'var_access_idx : OPSQR expression CLSQR'
'''callargs : callargs COMMA expression
| expression
| '''
'var_access_metcall : DOT NAME LPAREN callargs RPAREN'
'''var_access_token : var_access_name
| var_access_idx
| var_access_metcall'''
'''var_access_tokens : var_access_tokens var_access_token
| var_access_token'''
'''fornew_var_access_tokens : var_access_tokens var_access_name
| var_access_tokens var_access_idx
| var_access_name
| var_access_idx'''
'type_varref : var_access_start fornew_var_access_tokens'
'hard_varref : var_access_start var_access_tokens'
'easy_varref : var_access_start'
'varref : easy_varref'
'varref : hard_varref'
'typereference : NAME'
'typereference : type_varref'
'''expression : new typereference LPAREN callargs RPAREN'''
'var_decl_empty : NAME'
'var_decl_value : NAME EQUALS expression'
'''var_decl : var_decl_empty
| var_decl_value'''
'''var_decls : var_decls COMMA var_decl
| var_decl'''
'statement : var var_decls SEMIC'
The error occurs with statements of the form
var x = new SomeGuy.SomeOtherGuy();
where SomeGuy.SomeOtherGuy would be a valid variable that stores a type (types are first class objects) - and that type has a constructor with no arguments
What happens when parsing that expression is that the parser constructs a
var_access_start = SomeGuy
var_access_metcall = . SomeOtherGuy ( )
and then finds a semicolon and ends in an error state - I would clearly like the parser to backtrack, and try constructing an expression = new typereference(SomeGuy .SomeOtherGuy) LPAREN empty_list RPAREN and then things would work because the ; would match the var statement syntax all right
However, given that PLY does not support backtracking and I definitely do not have enough experience in parser generators to actually implement it myself - is there any change I can make to my grammar to work around the issue?
I have considered using -> instead of . as the "method call" operator, but I would rather not change the language just to appease the parser.
Also, I have methods as a form of "variable reference" so you can do
myObject.someMethod().aChildOfTheResult[0].doSomeOtherThing(1,2,3).helloWorld()
but if the grammar can be reworked to achieve the same effect, that would also work for me
Thanks!
I assume that your language includes expressions other than the ones you've included in the excerpt. I'm also going to assume that new, super and var are actually terminals.
The following is only a rough outline. For readability, I'm using bison syntax with quoted literals, but I don't think you'll have any trouble converting.
You say that "types are first-class values" but your syntax explicitly precludes using a method call to return a type. In fact, it also seems to preclude a method call returning a function, but that seems odd since it would imply that methods are not first-class values, even though types are. So I've simplified the grammar by allowing expressions like:
new foo.returns_method_which_returns_type()()()
It's easy enough to add the restrictions back in, but it makes the exposition harder to follow.
The basic idea is that to avoid forcing the parser to make a premature decision; once new is encountered, it is only possible to distinguish between a method call and a constructor call from the lookahead token. So we need to make sure that the same reductions are used up to that point, which means that when the open parenthesis is encountered, we must still retain both possibilities.
primary: NAME
| "super"
;
postfixed: primary
| postfixed '.' NAME
| postfixed '[' expression ']'
| postfixed '(' call_args ')' /* PRODUCTION 1 */
;
expression: postfixed
| "new" postfixed '(' call_args ')' /* PRODUCTION 2 */
/* | other stuff not relevant here */
;
/* Your callargs allows (,,,3). This one doesn't */
call_args : /* EMPTY */
| expression_list
;
expression_list: expression
| expression_list ',' expression
;
/* Another slightly simplified production */
var_decl: NAME
| NAME '=' expression
;
var_decl_list: var_decl
| var_decl_list ',' var_decl
;
statement: "var" var_decl_list ';'
/* | other stuff not relevant here */
;
Now, take a look at PRODUCTION 1 and PRODUCTION 2, which are very similar. (Marked with comments.) These are basically the ambiguity for which you sought backtracking. However, in this grammar, there is no issue, since once a new has been encountered, the reduction of PRODUCTION 2 can only be performed when the lookahead token is , or ;, while PRODUCTION 1 can only be performed with lookahead tokens ., ( and [.
(Grammar tested with bison, just to make sure there are no conflicts.)
So I have been reading a bit on lexers, parser, interpreters and even compiling.
For a language I'm trying to implement I settled on a Recrusive Descent Parser. Since the original grammar of the language had left-recursion, I had to slightly rewrite it.
Here's a simplified version of the grammar I had (note that it's not any standard format grammar, but somewhat pseudo, I guess, it's how I found it in the documentation):
expr:
-----
expr + expr
expr - expr
expr * expr
expr / expr
( expr )
integer
identifier
To get rid of the left-recursion, I turned it into this (note the addition of the NOT operator):
expr:
-----
expr_term {+ expr}
expr_term {- expr}
expr_term {* expr}
expr_term {/ expr}
expr_term:
----------
! expr_term
( expr )
integer
identifier
And then go through my tokens using the following sub-routines (simplified pseudo-code-ish):
public string Expression()
{
string term = ExpressionTerm();
if (term != null)
{
while (PeekToken() == OperatorToken)
{
term += ReadToken() + Expression();
}
}
return term;
}
public string ExpressionTerm()
{
//PeekToken and ReadToken accordingly, otherwise return null
}
This works! The result after calling Expression is always equal to the input it was given.
This makes me wonder: If I would create AST nodes rather than a string in these subroutines, and evaluate the AST using an infix evaluator (which also keeps in mind associativity and precedence of operators, etcetera), won't I get the same result?
And if I do, then why are there so many topics covering "fixing left recursion, keeping in mind associativity and what not" when it's actually "dead simple" to solve or even a non-problem as it seems? Or is it really the structure of the resulting AST people are concerned about (rather than what it evaluates to)? Could anyone shed a light, I might be getting it all wrong as well, haha!
The shape of the AST is important, since a+(b*3) is not usually the same as (a+b)*3 and one might reasonably expect the parser to indicate which of those a+b*3 means.
Normally, the AST will actually delete parentheses. (A parse tree wouldn't, but an AST is expected to abstract away syntactic noise.) So the AST for a+(b*3) should look something like:
Sum
|
+---+---+
| |
Var Prod
| |
a +---+---+
| |
Var Const
| |
b 3
If you language obeys usual mathematical notation conventions, so will the AST for a+b*3.
An "infix evaluator" -- or what I imagine you're referring to -- is just another parser. So, yes, if you are happy to parse later, you don't have to parse now.
By the way, showing that you can put tokens back together in the order that you read them doesn't actually demonstrate much about the parser functioning. You could do that much more simply by just echoing the tokenizer's output.
The standard and easiest way to deal with expressions, mathematical or other, is with a rule hierarchy that reflects the intended associations and operator precedence:
expre = sum
sum = addend '+' sum | addend
addend = term '*' addend | term
term = '(' expre ')' | '-' integer | '+' integer | integer
Such grammars let the parse or abstract trees be directly evaluatable. You can expand the rule hierarchy to include power and bitwise operators, or make it part of the hierarchy for logical expressions with and or and comparisons.