What if adjacency were a binary operator?

What if this were a real, compile time type-safe expression:

2025 July 19   // → LocalDate 

That’s the idea behind binding expressions -- a compiler plugin for Java that explores what it would be like if adjacency were a binary operator. In a nutshell, it lets adjacent expressions bind based on their static types, to form a new expression.

Type-directed expression binding

With binding expressions, adjacency is used as a syntactic trigger for a process called expression binding, where adjacent expressions are resolved through methods defined on their types.

Here are some examples of binding expressions in Java with the Manifold compiler plugin:

2025 July 19        // → LocalDate
299.8M m/s          // → Velocity
1 to 10             // → Range<Integer>
Meet Alice Tuesday at 3pm  // → CalendarEvent

A pair of adjacent expressions is a candidate for binding. If the LHS type defines:

<R> LR prefixBind(R right);

...or the RHS type defines:

<L> RL postfixBind(L left);

...then the compiler applies the appropriate binding. These bindings nest and compose, and the compiler attempts to reduce the entire series of expressions into a single, type-safe expression.

Example: LocalDates as composable expressions

Consider the expression:

LocalDate date = 2025 July 19;

The compiler reduces this expression by evaluating adjacent pairs. Let’s say July is an enum:

public enum Month {
  January, February, March, /* ... */

  public LocalMonthDay prefixBind(Integer day) {
    return new LocalMonthDay(this, day);
  }

  public LocalYearMonth postfixBind(Integer year) {
    return new LocalYearMonth(this, year);
  }
}

Now suppose LocalMonthDay defines:

public LocalDate postfixBind(Integer year) {
  return LocalDate.of(year, this.month, this.day);
}

The expression reduces like this:

2025 July 19
⇒ July.postfixBind(2025) // → LocalYearMonth
⇒ [retreat]              // → error: No binding with `19`
⇒ July.prefixBind(19)    // → LocalMonthDay
⇒ .postfixBind(2025)     // → LocalDate

Although the reduction algorithm favors left-to-right binding, it systematically retreats from failed paths and continues exploring alternative reductions until a valid one is found. This isn’t parser-style backtracking — instead, it's a structured search that reduces adjacent operand pairs using available binding methods. In this case, the initial attempt to bind 2025 July succeeds, but the resulting intermediate expression cannot bind with 19, forcing the algorithm to retreat and try a different reduction. Binding July 19 succeeds, yielding a LocalMonthDay, which can then bind with 2025 to produce a LocalDate.

Why bother?

Binding expressions give you a type-safe and non-invasive way to define DSLs or literal grammars directly in Java, without modifying base types or introducing macros.

Going back to the date example:

LocalDate date = 2025 July 19;

The Integer type (2025) doesn’t need to know anything about LocalMonthDay or LocalDate. Instead, the logic lives in the Month and LocalMonthDay types via pre/postfixBind methods. This keeps your core types clean and allows you to add domain-specific semantics via adjacent types.

You can build:

• Unit systems (e.g., 299.8M m/s)
• Natural-language DSLs
• Domain-specific literal syntax (e.g., currencies, time spans, ranges)

All of these are possible with static type safety and zero runtime magic.

Experimental usage

The Manifold project makes interesting use of binding expressions. Here are some examples:

• Science: The manifold-science library implements units using binding expressions and arithmetic & relational operators across the full spectrum of SI quantities, providing strong type safety, clearer code, and prevention of unit-related errors.

• Ranges: The Range API uses binding expressions with binding constants like to, enabling more natural representations of ranges and sequences.

• Vectors: Experimental vector classes in the manifold.science.vector package support vector math directly within expressions, e.g., 1.2m E + 5.7m NW.

Tooling note: The IntelliJ plugin for Manifold supports binding expressions natively, with live feedback and resolution as you type.

Downsides

Binding expressions are powerful and flexible, but there are trade-offs to consider:

• Parsing complexity: Adjacency is a two-stage parsing problem. The initial, untyped stage parses with static precedence rules. Because binding is type-directed, expression grouping isn't fully resolved until attribution. The algorithm for solving a binding series is nontrivial.

• Flexibility vs. discipline: Allowing types to define how adjacent values compose shifts the boundary between syntax and semantics in a way that may feel a little unsafe. The key distinction here is that binding expressions are grounded in static types -- the compiler decides what can bind based on concrete, declared rules. But yes, in the wrong hands, it could get a bit sporty.

• Cognitive overhead: While binding expressions can produce more natural, readable syntax, combining them with a conventional programming language can initially cause confusion -- much like when lambdas were first introduced to Java. They challenged familiar patterns, but eventually settled in.

Still Experimental

Binding expressions have been part of Manifold for several years, but they remain somewhat experimental. There’s still room to grow. For example, compile-time formatting rules could verify compile-time constant expressions, such as validating that July 19 is a real date in 2025. Future improvements might include support for separators and punctuation, binding statements, specialization of the reduction algorithm, and more.

If you're curious, you can explore the implementation in the Manifold repo.