Preferring shift over reduce in parser for language without statement terminators

Question

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).

Answer 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 }