```rust
grammar! calculator{ #![show_api]
expression = sum
sum = product ("+" product)* > add
product = value ("" value) > mult
value = ["0-9"]+ > to_digit / "(" expression ")"
pub type Digit = u32;
fn add(x: Digit, rest: Vec
fn mult(x: Digit, rest: Vec
fn todigit(rawtext: Vec
fn main() { asserteq!(calculator::parseexpression("7+(7*2)", 0).unwrap().data, 21); } ```
Add these lines in your Cargo.toml:
``` [dependencies.oak] git = "https://github.com/ptal/oak.git"
[dependencies.oak_runtime] git = "https://github.com/ptal/oak.git" path = "runtime" ```
e is a sub expression and T is the type of e. The types are only informative, it does not show unit propagation. Greedy operators do not generate "backtracking points" and consume as many characters as possible.
| Expression | Type | Precedence level | Description |
| --------------- | --------------------- |----------------- | ----------- |
| "literal" | () | 0 | Match a string literal. |
| . | char | 0 | Match any single character. |
| ["a-zA-Z-"] | char | 0 | Match a character from one of the specified classes. |
| (e) | T | 0 | Group an expression. |
| ident | Type of rule ident | 0 | Call the rule with the name ident. |
| e? | Option<T> | 1 | (Greedy) Match zero or one e. Always succeed. |
| e* | Vec<T> | 1 | (Greedy) Match zero or more e. Always succeed. |
| e+ | Vec<T> | 1 | (Greedy) Match one or more e. |
| &e | (^) | 2 | Try to match e and succeed if e succeeds. It does not consume any input. |
| !e | (^) | 2 | Try to match e and succeed if e fails. It does not consume any input. |
| e1 e2 e3 | (T1, T2, T3) | 3 | Match e1 e2 e3 in sequence. Immediately fails when one fails. |
| e > f | Return type of f | 4 | Match e and if it succeeds, call f(v) where v is the value of e. |
| e -> () | () | 4 | Force the type of e to be (). |
| e -> (^) | (^) | 4 | Force the type of e to be (^). |
| e1 / e2 / e3 | Type of any e | 5 | Match e1 e2 e3 in sequence. Immediately succeeds when one succeeds. |
(^)The full explanation of the what and why of types is available in the next section. A goal of this library is to give a type to any expression grammar. This permits to call a semantic action without naming expressions. In some cases, for example with the spacing rule spacing = [" \n\t"]*, the grammar compiler will not generate the expected type, here the rule spacing has type Vec<char> instead of () — we usually do not care about spaces. Therefore, users must annotate expressions with e -> () to force their types to be (). It works and is enough for most cases. However, we sometimes want to propagate unit type up in the expression tree because these expressions are only of syntactic interest. The fact is that e? has type Option<T> even if T = (). It is expected since Option<()> carries a boolean information about the presence of something. If we do not care, we can annotate e with (^) and the unit type will automatically be propagated, and even e1? e2* will have type (^) if e1 and e2 have type (^). In the end, the goal is really to give an expression the type that you expect it to have!
This section explains the novelties of this library and is not a tutorial to parsing expression grammar. It supposes the reader knowledgeable on the subject so if you are not, you can consult tutorial on Parsing Expression Grammar on the internet. We might provide one later.
I started this project because I had the idea of typing grammar rules. It comes from the observation that Parsing Expression Grammar (PEG) combinators are really close to traditional types: choice is a sum type, sequence is a tuple, repetition is an array,... I wondered if we could automatically generate an AST from a grammar description so both would be automatically kept in sync. It turned out that generating the AST (data type included) was hard, mostly because we need to name things and rules does not give enough information by themselves – how to name the variants of the sum type? Of course, we could annotate the expressions with names but I wanted to keep the grammar syntax as close as possible to what you could find in a text-book.
In traditional parser generators, the bridge between purely syntactic analysis and AST construction is done with semantic actions. Interaction between an expression and the user code is usually done with one of these two techniques (digit being a rule parsing an integer):
digit "+" digit { $$ = $1 + $3; } is a technique used in Yacc for example.digit:x "+" digit:y { x + y } is similar to what is used in Menhir (parser generator written in OCaml).The first technique is often discouraged because some errors can silently appear if you change the order of expression inside a rule without changing the associated action or if you make a mistake when numbering the arguments. The generated code will fail to compile if the host language is statically typed and if the two expressions have different types, but in the general case this technique is not safe. Expression labelling is better but it has the inconvenient of burdening the grammar syntax. Also note that none of these techniques help the user to build the corresponding AST, their purposes is to offer a simple interface between grammar and host code.
Using the idea of typing grammar, we can give a type to each expression and directly pass the value to the semantic action without any labelling or positional notation. The previous example becomes digit "+" digit > add with > being a "reverse function call operator", the expression digit "+" digit produces a value v of type (i32, i32) and the code generated looks like add(v). It is even smarter and will automatically unpack the tuple into function arguments, so the function add will be called with two arguments of type i32.
Cool isn't it? However the implementation was more complicated than I first thought due to expressions of type unit (()). Consider this grammar for parsing simple variable identifiers:
var_ident = !["0-9"] ["a-zA-Z0-9_"]+ spacing
spacing = [" \n\t"]*
In rule var_ident the only value of interest is the one returned by the expression ["a-zA-Z0-9_"]+ and it has type Vec<char> (note that we could use a semantic action to transform this value into a string). It is natural to think that the rule var_ident will be of type Vec<char> too. However, a trivial algorithm infers that this expression has type (char, Vec<char>, Vec<char>), the sequence has three sub expressions and thus it forms a 3-tuple. We do not care about the value of the spaces but this is not something that a computer can guess by itself so we must force the type to be unit using the arrow operator:
var_ident = !["0-9"] ["a-zA-Z0-9_"]+ spacing
spacing = [" \n\t"]* -> ()
This operator is the only annotation not directly related to parsing that we need. The new type of var_ident is now (char, Vec<char>, ()). The generator automatically reduce this type to Vec<char> thanks to a few rules:
!e or ?e) has type (). The new type is ((), Vec<char>, ()).(Vec<char>).Vec<char>.These type rewriting rules are intuitive because they produce the type the user expects! Type annotation is only needed to specify that we are not interested by the value, such as with spaces.
Implementation is not that easy due to the fact that some rules have recursive types. For example, the following grammar accept strings for which any character at position i is 'a' or 'b' if i is even and otherwise 'c' or 'd'.
a_b = ["a-b"] c_d?
c_d = ["c-d"] a_b?
This is a totally valid grammar but it can not be typed without recursive types. Let's try anyway. Say that a_b has type T and c_d has type U. We can infer that T = (char, Option<U>) for rule a_b and U = (char, Option<T>) for rule c_d. By substitution we get T = (char, Option<(char, Option<T>)) and thus T is defined by itself. It is a recursive type definition. You might think that this type is fine as long as we give an alias to the tuple types:
rust
type T = (char, Option<U>);
type U = (char, Option<T>);
However the names T and U are completely arbitrary and the user probably do not want types with random names. We would need name-annotations on expressions which is not our leitmotiv in the first place. It is cleaner and easier to let the user constructs the types by himself with semantic actions. Furthermore, here the type Option<U> introduces the necessary indirection for building recursive types but what if the grammar does not explicitly give one? We should automatically infer a type supporting recursive type which seems a lot of work for little benefit. In the end, we forbid implicit recursive types and let the user write semantic actions to build them. However recursive rules are still allowed. The difficulty was to generate a compile-time error only in the case we care about the value produced by the recursive rules. Actually, the previous grammar will be accepted by the parser generator if we are using the rule a_b below a syntactic predicate, for example the expression !a_b implies that we do not need to build the value of a_b.
A new quirk appears if we want to propagate and erase unit type in expression to obtain a smaller type (for example, ((), T) is reduced to T). If we consider the following grammar which describe the optional presence of the mut keyword on the left-hand side of a let-expression, everything works fine!
let_left = let_kw mut_kw? var_ident
let_kw = "let" spacing
mut_kw = "mut" spacing
Indeed, the type of the expression mut_kw? is Option<()>. This is expected since the type Option<()> carries a boolean information. As a rule of thumb, unit inference never erase a potential piece of information. A problematic case is the following simplified grammar describing the optional keyword return in the last statement of a function:
return_expr = return_kw? expr
return_kw = "return" spacing
In this particular case we do not care if the keyword return is present or not, it is only of syntactic interest. Using what we already know, we can use a type annotation to obtain the correct type:
return_expr = (return_kw? -> ()) expr
return_kw = "return" spacing
It breaks our hopes to have a clean grammar and because it is nested, this is a bit difficult to understand at a first sight. This is why we have introduced a new type (^) called the "invisible" type. It is a unit type that can not be composed within another type, it becomes invisible in tuple type for example. The grammar then becomes:
return_expr = return_kw? expr
return_kw = "return" spacing -> (^)
The type of return_expr is the type of expr as expected. The circumflex symbol in (^) indicates a bottom up propagation of unit in expression. The propagation is only stopped if a value with another type is encountered. The expression return_kw? return_kw? has type (^), it has been propagated across Option<(^)> and ((^), (^)) types.
That is for the story of typing parsing expressions but don't be sad! It continues in the issues tracker...
For the moment my priority is to stabilize/test things and to add a decent error reporting mechanism (#63), probably something based on the article Error reporting in parsing expression grammars. Next I want more static analysis to prevent grammar design error such as in "=" / "==" (can you find what's wrong?) Here some other wanted features:
Spanned<T> structure to get location information (#13).e1 > A / e2 > B with A and B being variants (#41, #53, #54).A shortcoming to cleanly achieve these objectives with the Rust compiler is that we can only access item definitions declared inside the procedural macro. It probably means that, for the moment, compositionality would come at the cost of some run-time verifications (or no inter-grammar analysis at all).