Rethinking Syntax: Binding by Adjacency
github.comThe drawback is that building an AST now requires a symbol table and resolving imports, possibly performing type inference and whatnot. It constitutes a higher barrier for various types of tooling. You really want your programming language to avoid becoming context-sensitive in that way.
It’s similar for the human reader: The examples are only intelligible to the reader incidentally, due to the names used and some natural-text conventions. In the general case, you have a seemingly random token sequence where you have no idea what binds to what, without looking up the type definitions or having an IDE present the expression in some structured way again.
Furthermore, in typical code you don’t have the case of constant values so often. You’ll rather have things like:
nextYear thisMonth.previous() lastDayOf(thisMonth.previous())
Double.parse(speedInput) m/s
startPos to (startPos + length - 1)
Schedule contacts.select(contactId) inputForm.getDateTime()> The drawback is that building an AST now requires a symbol table
Well, yes and no. During AST building a binding expression resolves as an untyped polyadic expression. Only later during the compiler's type attribution phase does a binding expression's structure resolve based on the operand types.
https://github.com/manifold-systems/manifold/tree/master/man...
> in typical code you don’t have the case of constant values so often.
Agreed. It's not really useful with inlined expressions:
but if you write it like:Schedule contacts.select(contactId) inputForm.getDateTime()
But, honestly, I can't say I personally use it that way ;)var plumber = contacts.select(contactId) var date = inputForm.getDateTime() var building = findLocation(warehouse) Schedule plumber on date at buildingInitially, I wrote it as a science extension to Java: https://github.com/manifold-systems/manifold/tree/master/man...
> This isn’t parser-style backtracking
How is this different from backtracking? You're doing a depth-first search over possible interpretations. The grammar is just expressed in the type system instead of usual spec formats.
Critiques in other comments are accurate. This is a tooling nightmare, but also probably a nightmare to read. Consider an expression like
2026 March 10 to 13
Isn't it obvious?
It's the range from 1773100800 down to 13.
Author here.
Yes, technically this is a form of backtracking, similar to what a parser does. The key difference is that the search is drastically constrained by the type system: reductions are only attempted where the types actually support a binding operator. Unlike a parser exploring all grammar possibilities, this mechanism prunes most candidates automatically, so the compiler efficiently "solves" the expression rather than blindly exploring every syntactic alternative.
Here is the high-level explanation of the mechanism:
https://github.com/manifold-systems/manifold/tree/master/man...
But the short answer is that it’s not parser-style backtracking over a grammar.
The Java parser still produces a normal AST for the sequence of tokens. What happens afterward is a type-directed binding phase where adjacent expressions may bind if their types agree on a binding operator. The compiler effectively reduces the expression by forming larger typed expressions until it reaches a stable form.
The algorithm favors left associativity, but since a type can implement the binding operator as either the left or right operand, the overall structure of the expression can emerge in different ways depending on the participating types.
So rather than exploring grammar productions, the compiler is solving a set of type-compatible reductions across the expression.
For example:
reduces roughly like this:2026 March 10
And if `Month` binds with `Range<Integer>`:(2026 (March 10)) → March.postfixBind(2026) // → LocalYearMonth → [retreat] // → no binding with 10 → March.prefixBind(10) // → LocalMonthDay → .postfixBind(2026) // → LocalDate
can reduce as:2026 March 10 to 13
The meaning is therefore determined entirely by which types participate in binding e.g., `LocalDate`, `Month`, `Integer`, `Range`, etc. and which reductions they define.(2026 (March ((10 to) 13)))If a competing interpretation exists but the types don’t support the necessary bindings, it simply never forms.
In that sense it behaves less like a traditional parser and more like a typed reduction system layered on top of the Java AST.
What if these were real, type-safe expressions in Java:
2025 July 19 // → LocalDate
300M m/s // → Velocity
1 to 10 // → Range<Int>
Schedule Alice Tues 3pm // → CalendarEvent
Details here: https://github.com/manifold-systems/manifold/blob/master/doc...
Information that might be of interest to someone here:
The formal name for the “empty” binary infix operator that gets implied in the AST when doing this, is the “juxtaposition” (or “juxtapose”, or “juxt”) operator. The implicit multiplication operator between `3` and `a` in the polynomial expression `3a + 4`, and the implicit function-application operator in the Lambda-calculus expression `f x y`, are both instances of an implied juxtaposition operator (with different semantics for it in each of the two cases, as befits each type of algebra/calculus.)
Mathematica has Infix [0], which expresses the adjacency with a ~ (because Mathematica reserves pure blankspace for multiplication). But it works fine to do eg. `"hello"~StringJoin~" world"`; I was always surprised we could only have the predefined operators in many other languages and we couldn't define our own.
This seems like a great attempt. I would be worried about how much parsing and backtracking might be required to infer the infix precedence in a totally general system (like garden-path sentences[1]) or actually ambiguous parse trees (which is cured by adopting some rule like right precedence and parens, but what rule you pick makes some 'natural language' constructions work over others).
Haskell supports user-defined operators (made up of symbols) and also lets you use functions in infix position by surrounding the name in backticks, e.g.
rather than2 `plus` 3plus 2 3In Postgres you can define custom operators via `create operator`[0]
A lot of custom types end up using this [1].-- infix select a <!!!> b; -- prefix select <||> a;
[0] https://www.postgresql.org/docs/current/sql-createoperator.h... [1] https://www.postgresql.org/docs/current/functions-geometry.h...select @-@ '[(0,0),(1,0),(1,1)]'::path; -- 2Similarly, Agda has a well-typed mixfix operator syntax – you define a function like (_foo_bar_baz) and can automatically write "X foo Y bar Z baz". It does mean that the operator parser has to be extensible at runtime, but it's not a huge cost for a dependently-typed language.
Bjarne Stroustrup wrote a paper about adding overloading for the "whitespace operator" in C++, but in his case it was a joke: https://stroustrup.com/whitespace98.pdf
I don't think this is useful in complex situations/expressions. Structure has to be encoded in the same place as meaning somehow. Natural language does it by using an extraordinarily large set of signifiers. That's not feasible for a formal language.
You could of course affix all lemmata with structural information, as free word order languages do, but that's introducing syntactic structure via the backdoor.
An old paper on the expressiveness of the programming languages [1] had to add an implicit binary operator into whitespace to make Haskell not be ten times more expressive than most imperative languages.
[1] https://www.researchgate.net/publication/2743686_Are_Ours_Re...
So, yes, it can be done and it was done. Yes, expressiveness rises. No, reading comprehension of such languages does not suffer. Yes, it has to have a lot of scaffolding.
Sorry for this sounds absurd, but with diffusion language models, who generate text non-linearly (from the few that I get, they relate terms without a simpler order), I wonder if new syntactic ideas will come up.
I like the fend calculator that uses similar syntax.
Maybe with a Java string templates:
var myDate = MAGIC"2025 July 19"StringTemplates were withdrawn.
I'm sorry, but that sounds like it would be a debugging nightmare when it doesn't work right.
God I can't believe I'm gonna be that guy, but I feel like in some of these situations one should just forward the text to an LLM and call it a day.
Congratulations, you reinvented yet another stack language.
No, stack languages can’t achieve this as described.
If you added a function to the examples, you could do a few of them, e.g.:
But even this breaks down when you get to something like “Meet Alice Tuesday at 3pm”. Sure, you could contort things to make it resemble the concept, but it’d be a stretch at best.2025 July 19 date 299.8 M m / s velocity