Add documentation for infix operators

hugo/content/docs/reference/grammar-language.md → hugo/content/docs/reference/grammar-language/_index.md

@@ -370,6 +370,21 @@ Element<isRoot>:
 
 The parser will always exclude alternatives whose guard conditions evaluate to `false`. All other alternatives remain possible options for the parser to choose from.
 
+### Infix operators
+
+[Infix operators](/docs/reference/grammar-language/infix-operators) can be defined using the `infix` keyword. This new syntax allows to define operators with different precedence levels and associativity in a more readable way. For more information on infix operators, please refer to the [dedicated documentation page](/docs/reference/grammar-language/infix-operators/syntactical-implementation). Be aware that the `infix` notation is syntactic sugar. You can do it also the [manual way using parser rules](/docs/reference/grammar-language/infix-operators/manual-implementation).
+
+```langium
+Expression: BinaryExpr;
+
+infix BinaryExpr on PrimaryExpression:
+    right assoc '^'
+    > '*' | '/'
+    > '+' | '-'
+    ;
+
+PrimaryExpression: '(' expr=Expression ')' | value=Number;
+```
 
 ### More Examples
 

hugo/content/docs/reference/grammar-language/infix-operators/_index.md

@@ -0,0 +1,49 @@
+---
+title: "Infix Operators"
+weight: 125
+---
+
+Infix operators are binary operators - they require two operands and an operator in between them. For example, in the expression `a + b`, `+` is an infix operator with operands `a` and `b`.
+
+## Grammar Ambiguities
+
+With infix operator we are confronted with grammar ambiguities.
+
+Ambiguities are a problem for the parsing process, because the parser needs to be able to determine the structure of an expression unambiguously.
+
+For example, consider these expressions:
+
+```plain
+a + b * c
+a - b - c
+```
+
+### Ambiguity between different operators
+
+Without additional rules, the first expression can be interpreted in two different ways:
+
+1. As `(a + b) * c`, where addition is performed first, followed by multiplication.
+2. As `a + (b * c)`, where multiplication is performed first, followed by addition.
+
+Solution: The parser needs to know the **precedence** of the operators. In this case, multiplication has higher precedence than addition, so the correct interpretation is `a + (b * c)`. A precedence of an operator is higher, lower or equal to another operator's precedence.
+
+### Ambiguity between same operators
+
+The second expression can also be interpreted in two different ways:
+
+1. As `(a - b) - c`, where the first subtraction is performed first.
+2. As `a - (b - c)`, where the second subtraction is performed first.
+
+Solution: The parser needs to know the **associativity** of the operator. In this case, subtraction is left-associative, so the correct interpretation is `(a - b) - c`. An operator can be left-associative, right-associative or non-associative. A way to remember what is what:
+Imagine a operand between two same operators (like `... - b - ...`), which operator is executed first? If the left one is executed first, the operator is left-associative. If the right one is executed first, the operator is right-associative. If neither can be executed first (like in `a < b < c`), the operator is non-associative.
+
+Operator candidates for right-associativity are usually assignment operators (e.g., `=`) and exponentiation operators (e.g., `^`).
+
+## Implementation
+
+In order to embed precedence and associativity rules into the parsing process, we can use a technique called **precedence climbing** (also known as operator-precedence parsing). Precedence climbing is a recursive parsing technique that allows us to handle infix operators with different precedences and associativities in a straightforward manner.
+
+Independent of the used parser generator or language framework, this technique can be often implemented using grammar rules. In Langium, you have two options to implement precedence climbing:
+
+* using [non-terminal rules](/docs/reference/grammar-language/infix-operators/manual-implementation)
+* using the [infix syntax](/docs/reference/grammar-language/infix-operators/syntactical-implementation)

hugo/content/docs/reference/grammar-language/infix-operators/manual-implementation.md

@@ -0,0 +1,70 @@
+---
+title: "Using non-terminal rules"
+weight: 100
+---
+
+Infix operators can also be implemented using non-terminal rules. This approach provides more flexibility and allows for better handling of operator precedence and associativity.
+
+## Operator table
+
+Let's implement a simple expression grammar with the following operators:
+
+| Operator | Precedence | Associativity |
+|----------|------------|---------------|
+| `+`      | 1          | Left          |
+| `-`      | 1          | Left          |
+| `*`      | 2          | Left          |
+| `/`      | 2          | Left          |
+| `^`      | 3          | Right         |
+
+## Grammar rules
+
+```langium
+Expression:
+    Addition;
+
+Addition infers Expression:
+    Multiplication ({infer BinaryExpression.left=current} operator=('+' | '-') right=Multiplication)*;
+
+Multiplication infers Expression:
+    Exponentiation ({infer BinaryExpression.left=current} operator=('*' | '/') right=Exponentiation)*;
+
+Exponentiation infers Expression:
+    Primary ({infer BinaryExpression.left=current} operator='^' right=Exponentiation)?;
+
+Primary infers Expression:
+    '(' Expression ')'
+    | ... //prefix, literals, identifiers
+    ;
+```
+
+## Explanation
+
+### Precedence
+
+Precedence is handled by creating a hierarchy of non-terminal rules. Each rule corresponds to a level of precedence, with higher-precedence operators being defined in rules that are called by lower-precedence rules. For example, `Addition` calls `Multiplication`, which in turn calls `Exponentiation`. This ensures that multiplication and division are evaluated before addition and subtraction, and exponentiation is evaluated before both.
+
+### Associativity
+
+Associativity is handled by three patterns. They make sure that operators are grouped correctly based on their associativity.
+
+#### Pattern 1 (Left Associative):
+
+```langium
+Current infers Expression:
+    Next ({infer BinaryExpression.left=current} operator=('op1' | 'op2' | ...) right=Next)*;
+```
+
+#### Pattern 2 (Right Associative):
+
+```langium
+Current infers Expression:
+    Next ({infer BinaryExpression.left=current} operator=('op1'| 'op2' | ...) right=Current)?;
+```
+
+#### Pattern 3 (Non-Associative):
+
+```langium
+Current infers Expression:
+    Next ({infer BinaryExpression.left=current} operator=('op1' | 'op2' | ...) right=Next)?;
+```

hugo/content/docs/reference/grammar-language/infix-operators/syntactical-implementation.md

@@ -0,0 +1,69 @@
+---
+title: "Using the infix syntax"
+weight: 200
+---
+
+## Operator table
+
+Let's implement a simple expression grammar with the following operators:
+
+| Operator | Precedence | Associativity |
+|----------|------------|---------------|
+| `+`      | 1          | Left          |
+| `-`      | 1          | Left          |
+| `*`      | 2          | Left          |
+| `/`      | 2          | Left          |
+| `^`      | 3          | Right         |
+
+## Grammar rules
+
+```langium
+Expression: BinaryExpr;
+
+infix BinaryExpr on PrimaryExpression:
+    right assoc '^'
+    > '*' | '/'
+    > '+' | '-'
+    ;
+
+PrimaryExpression: '(' expr=Expression ')' | value=Number;
+```
+
+In addition to better readability, the new notation also makes use of **performance optimizations** to speed up expression parsing by roughly 50% compared to the typical way of writing expressions.
+
+### Primary expression
+
+The `PrimaryExpression` rule defines the basic building blocks of our expressions, which can be (for example) a parenthesized expression, an unary expression, or a number literal.
+
+```langium
+Expression: BinaryExpr;
+
+infix BinaryExpr on PrimaryExpression:
+    ...
+    ;
+
+PrimaryExpression: '(' expr=Expression ')' | '-' value=PrimaryExpression | value=Number | ...;
+```
+
+### Precedence
+
+Use the `>` operator to define precedence levels. Operators listed after a `>` have lower precedence than those before it. In the example above, `^` has the highest precedence, followed by `*` and `/`, and finally `+` and `-` with the lowest precedence.
+
+```langium
+infix BinaryExpr on ...:
+    A > B > C
+    //A has higher precedence than B, B higher than C
+    ;
+```
+
+If you have multiple operators with the same precedence, list them on the same line separated by `|`.
+
+### Associativity
+
+The default associativity for infix operators is left associative. To specify right associativity, use the `assoc` keyword preceded by `right` before the operator.
+
+```langium
+infix BinaryExpr on ...:
+    ...> right assoc '^' >...
+    ;
+```

hugo/static/prism/langium-prism.js

@@ -18,7 +18,7 @@ Prism.languages.langium = {
         greedy: true
     },
     keyword: {
-        pattern: /\b(interface|fragment|terminal|boolean|current|extends|grammar|returns|bigint|hidden|import|infers|number|string|entry|false|infer|Date|true|type|with)\b/
+        pattern: /\b(interface|fragment|terminal|boolean|current|extends|grammar|returns|bigint|hidden|import|infers|number|string|entry|false|infer|Date|true|type|with|on|infix|left|right|assoc)\b/
     },
     property: {
         pattern: /\b[a-z][\w]*(?==|\?=|\+=|\??:|>)\b/