They are isomorphic in the strong sense that their logical interpretations are identical. Applying Curry-Howard, a function type is an implication, so a curried function with type A -> B -> C is equivalent to an implication that says "If A, then if B, then C." Likewise, a tuple is a conjunction, so a non-curried function with type (A, B) -> C is equivalent to the logic statement (A /\ B) -> C, i.e., "If A and B then C." Both logical statements are equivalent, i.e., have the same truth tables.

However, as the article outlines, there are differences (both positive and negative) to using functions with these types. Curried functions allow for partial application, leading to elegant definitions, e.g., in Haskell, we can define a function that sums over lists as sum = foldl (+) 0 where we leave out foldl's final list argument, giving us a function expecting a list that performs the behavior we expect. However, this style of programming can lead to weird games and unweildy code because of the positional nature of curried functions, e.g., having to use function combinators such as Haskell's flip function (with type (A -> B -> C) -> B -> A -> C) to juggle arguments you do not want to fill to the end of the parameter list.

That's a fair point, they are all isomorphic.

The distinction is mostly semantic so you could say they are the same. But I thought it makes sense to emphasize that the former is a feature of function types, and the latter is still technically single-parameter.

I suppose one real difference is that you cannot feed a tuple into a parameter list function. Like:

fn do_something(name: &str, age: u32) { ... }

let person = ("Alice", 40);

do_something(person); // doesn't compile

Probably just that having parameter-lists as a specific special feature makes them distinct from tuple types. So you may end up with packing/unpacking features to convert between them, and a function being generic over its number of parameters is distinct from it being generic over its input types. On the other hand you can more easily do stuff like named args or default values.

The parameter list forces the individual arguments to be visible at the call site. You cannot separate the packaging of the argument list from invoking the function (barring special syntactic or library support by the language). It also affects how singleton tuples behave in your language.

The article is about programmer ergonomics of a language. Two languages can have substantially different ergonomics even when there is a straightforward mapping between the two.

It's not that they are meaningfully different. It's just acknowledging if you really want currying, you can say 'why not just use a single parameter of tuple type'.

Then there's an implication of 'sure, but that doesn't actually help much if it's not standar' and then it's not addressed further.

Presumably creating a different class for parameter lists allows you to extend it with operations that aren't natural to tuples, like named arguments.

The tuple style can't be curried (in Haskell).

I completely agree with the points in this article and have come to the same conclusion after using languages that default to unary curried functions.

> I'd also love to hear if you know any (dis)advantages of curried functions other than the ones mentioned.

I think it fundamentally boils down to the curried style being _implicit_ partial application, whereas a syntax for partial application is _explicit_. And as if often the case, being explicit is clearer. If you see something like

    let f = foobinade a b

in a curried language then you don't immediately know if `f` is the result of foobinading `a` and `b` or if `f` is `foobinade` partially applied to some of its arguments. Without currying you'd either write

    let f = foobinade(a, b)

or

    let f = foobinade(a, b, $) // (using the syntax in the blog post)

and now it's immediately explicitly clear which of the two cases we're in.

This clarity not only helps humans, it also help compilers give better error messages. In a curried languages, if a function is mistakenly applied to too few arguments then the compiler can't always immediately detect the error. For instance, if `foobinate` takes 3 arguments, then `let f = foobinade a b` doesn't give rise to any errors, whereas a compiler can immediately detect the error in `let f = foobinade(a, b)`.

A syntax for partial application offers the same practical benefits of currying without the downsides (albeit loosing some of the theoretical simplicity).

  f = foobinade a b
  g = foobinadd c d

    let result =
        input
            |> foobinade a b
            |> barbalyze c d

    let f = foobinade a b >> barbalyze c d
    let result = f input

    let f = barbalyze(c, d, foobinade(a, b, $))
    let result = f(input)

    let result = barbalyze(c, d, foobinade(a, b, input))

  let result = (barbalyze(c, d, $) . foobinade(a, b, $)) input

  let result = input
    |> foobinade(a, b, $)
    |> barbalyze(c, d, $)

  let foos = foobinate(a, b, input)
  let bars = barbakize(c, d, foos)

A benefit to using the currying style is that you can do work in the intermediate steps and use that later. It is not simply a 'cool' way to define functions. Imagine a logging framework:

  (log configuration identifier level format-string arg0 arg1 ... argN)
  

After each partial application step you can do more and more work narrowing the scope of what you return from subsequent functions.

  ;; Preprocessing the configuration is possible
  ;; Imagine all logging is turned off, now you can return a noop
  (partial log conf)
  ;; You can look up the identifier in the configuration to determine what the logger function should look like
  (partial log conf id)
  ;; You could return a noop function if the level is not enabled for the particular id
  (partial log config id level)
  ;; Pre-parsing the format string is now possible
  (partial log conf id level "%time - %id")
  

In many codebases I've seen a large amount of code is literally just to emulate this process with multiple classes, where you're performing work and then caching it somewhere. In simpler cases you can consolidate all of that in a function call and use partial application. Without some heroic work by the compiler you simply cannot do that in an imperative style.

One "feature of currying" in Haskell that isn't mentioned in the fine article is that parts of the function may not be dependent on the last argument(s) and only needs to be evaluated once over many application of the last argument(s) which can be very useful when partially applied functions are passed to higher-order functions.

Functions can be done explicitly written to do this or it can be achieved through compiler optimisation.

Currying was recently removed from Coalton: https://coalton-lang.github.io/20260312-coalton0p2/#fixed-ar...

I couldn't agree more. Having spent a lot of time with a language with currying like this recently, it seems very obviously a misfeature.

1. Looking at a function call, you can't tell if it's returning data, or a function from some unknown number of arguments to data, without carefully examining both its declaration and its call site

2. Writing a function call, you can accidentally get a function rather than data if you leave off an argument; coupled with pervasive type inference, this can lead to some really tiresome compiler errors

3. Functions which return functions look just like functions which take more arguments and return data (card-carrying functional programmers might argue these are really the same thing, but semantically, they aren't at all - in what sense is make_string_comparator_for_locale "really" a function which takes a locale and a string and returns a function from string to ordering?)

3a. Because of point 3, our codebase has a trivial wrapper to put round functions when your function actually returns a function (so make_string_comparator_for_locale has type like Locale -> Function<string -> string -> order>), so now if you actually want to return a function, there's boilerplate at the return and call sites that wouldn't be there in a less 'concise' language!

I think programming languages have a tendency to pick up cute features that give you a little dopamine kick when you use them, but that aren't actually good for the health of a substantial codebase. I think academic and hobby languages, and so functional languages, are particularly prone to this. I think implicit currying is one of these features.

I'm biased here since the easy currying is by far my favourite feature in Haskell (it always bothers me that I have to explicitly create a lamba in Lisps) but the arguments in the article don't convince me, what with the synctactic overhead for the "tuple style".

I'd got a step further and say that in business software, named parameters are preferable for all but the smallest functions.

Using curried OR tuple arg lists requires remembering the name of an argument by its position. This saves room on the screen but is mental overhead.

The fact is that arguments do always have names anyway and you always have to know what they are.

One language that uses the tuple argument convention described in the article is Standard ML. In Standard ML, like OCaml and Haskell, all functions take exactly one argument. However, while OCaml and Haskell prefer to curry the arguments, Standard ML does not.

There is one situation, however, where Standard ML prefers currying: higher-order functions. To take one example, the type signature of `map` (for mapping over lists) is `val map : ('a -> 'b) -> 'a list -> 'b list`. Because the signature is given in this way, one can "stage" the higher-order function argument and represent the function "increment all elements in the list" as `map (fn n => n + 1)`.

That being said, because of the value restriction [0], currying is less powerful because variables defined using partial application cannot be used polymorphically.

[0] http://mlton.org/ValueRestriction

From the article:

    length = foldr (+) 0 . map (const 1)
    length2d = foldr (+) 0 . map length

    -- and the proposed syntax the author calls more readable:
    length = foldr((+), 0, $) . map(const(1), $)
    length2d = foldr((+), 0, $) . map(length, $)

But I don't understand. Why does the author think it's confusing to partially apply foldr and map but not (+), (.), const, and length? Applied consistently:

    length = (.)(foldr((+)($, $), 0, $), map(const(1, $), $), $)
    length2d = (.)(foldr((+)($, $), 0, $), map(length($), $), $)

And clearly no-one thinks this strawman is clearer. Further, it's impossible to make it 100% consistent: any function you write with polymorphic result could instantiate as a function needing more arguments. I think currying is the better default.

The Roc devs came to a similar conclusion: https://www.roc-lang.org/faq#curried-functions

(Side note: if you're reading this Roc devs, could you add a table of contents?)

I agree with this article. Tuples nicely unified multiple return values and multiple parameters. FWIW Scala and Virgil both support the _ syntax for the placeholder in a partial application.

    def add(x: int, y: int) -> int { return x + y; }
    def add3 = add(_, 3);

Or more simply, reusing some built-in functions:

    def add3 = int.+(_, 3);

    { add(it, 3) } // Kotiln
    add(_, 3) // Scala

    { add(subtract(it, 2), 3) } // Kotlin
    // add(subtract(_, 2), 3) // no, this means adding 3 to the function `add(subtract(_, 2)`
    x => { add(subtract(x, 2), 3) } // Scala

    fun x => add(subtract(x, 2), 3) // Virgil

There are good ideas in functional languages that other languages have borrowed, but there are bad ideas too: currying, function call syntax without parentheses, Hindley-Milner type inference, and laziness by default (Haskell) are experiments that new languages shouldn’t copy.

I like currying because it's fun and cool, but found myself nodding along throughout the whole article. I've taken for granted that declaring and using curried functions with nice associativity (i.e., avoiding lots of parentheses) is as ergonomic as partial application syntax gets, but I'm glad to have that assumption challenged.

The "hole" syntax for partial application with dollar signs is a really creative alternative that seems much nicer. Does anyone know of any languages that actually do it that way? I'd love to try it out and see if it's actually nicer in practice.

I completely agree. Giving the first parameter of a function special treatment only makes sense in a limited subset of cases, while forcing an artificial asymmetry in the general case that I find unergonomic.

1. Such bad examples :( Tuples are data types you have to destruct, in every language. Somebody please show me a language where this doesn't require a tuple-to-function-argument translation:

  sayHi name age = "Hi I'm " ++ name ++ " and I'm " ++ show age
  people = [("Alice", 70), ("Bob", 30), ("Charlotte", 40)]
  -- ERROR: sayHi is String -> Int -> String, a person is (String, Int)
  conversation = intercalate "\n" (map sayHi people)

In python you have `*people` to destruct the tuple into separate arguments, or pattern matching. In C-languages you have structs you have to destruct.

2. And performance, you'd think a slow-down affecting every single function call would be high-up on the optimization wish list, right? That's why it's implemented in basically every compiler, including non-fp compilers. Here's GHC authors in 2004 declaring that obviously the optimization is in "any decent compiler". https://simonmar.github.io/bib/papers/eval-apply.pdf

3. Type errors, the only place where currying is actually bad, is not even mentioned directly. Accidentally passing a different number of arguments compared to what you expected will result in a compiler error.

Some very powerful and generic languages will happily support lots of weird code you throw at them instead of erroring out. Others will errors out on things you'd expect them to handle just fine.

Here's Haskell supporting something most people would never want to use, giving it a proper type, and causing a confusing type error in any surrounding code when you leave out a parentheis around `+`:

  foldl (+) 0 [1,2,3] :: Num a => a
  foldl + 0 [1,2,3]
    :: (Foldable t, Num a1, Num ((b -> a2 -> b) -> b -> t a2 -> b),
        Num ([a1] -> (b -> a2 -> b) -> b -> t a2 -> b)) =>
       (b -> a2 -> b) -> b -> t a2 -> b

Is it bad that it has figured out that you (apparently) wanted to add things of type `(b -> a2 -> b) -> b -> t a2 -> b` as if they were numbers, and done what you told it to do? Drop it into any gpt of choice and it'll find the mistake for you right away.

A bunch of Scheme implementations define little-known syntax for partial application[0] that lets you put limits on how many arguments have to be provided at each application step. Using the article's add example:

  (define (((add x) y) z) (+ x y z))
  (define add1 (add 1))
  (define add3 (add1 2))
  (add3 3) ; => 6

it gets tedious with lots of single-argument cases like the above, but in cases where you know you're going be calling a function a lot with, say, the first three arguments always the same and the fourth varying, it can be cleaner than a function of three arguments that returns an anonymous lambda of one argument.

  (define ((foo a b c) d)
    (do-stuff))
  (for-each (foo 1 2 3) '(x y z))

vs

  (define (foo a b c)
    (lambda (d) (do-stuff)))
  (for-each (foo 1 2 3) '(x y z))

There's also a commonly supported placeholder syntax[1]:

    (define inc (cut + 1 <>))
    (inc 2) ; => 3
    (define (foo a b c d) (do-stuff))
    (for-each (cut foo 1 2 3 <>) '(x y z))

And assorted ways to define or adapt functions to make fully curried ones when desired. I like the "make it easy to do something complicated or esoteric when needed, but don't make it the default to avoid confusion" approach.

[0]: https://srfi.schemers.org/srfi-219/srfi-219.html

[1]: https://srfi.schemers.org/srfi-26/srfi-26.html

Here’s an article I wrote a while ago about a hypothetical language feature I call “folded application”, that makes parameter-list style and folded style equivalent.

https://jonathanwarden.com/implicit-currying-and-folded-appl...

With a language like Forth, you know that you can use a stack for data and apply functions on that data. With currying it you put functions on a stack instead. This makes it weird. But you also obscure the dataflow.

With the most successful functional programing language Excel, the dataflow is fully exposed. Which makes it easy.

Certain functional programming languages prefer the passing of just one data-item from one function to the next. One parameter in and one parameter out. And for this to work with more values, it needs to use functions as an output. It is unnecessary cognitive burden. And APL programmers would love it.

Let's make an apple pie as an example. You give the apple and butter and flour to the cook. The cursed curry version would be "use knife for cutting, add cutting board, add apple, stand near table, use hand. Bowl, add table, put, flour, mix, cut, knife butter, mixer, put, press, shape, cut_apple." etc..

A case for currying:

In languages in which every function is unary but there is a convenience syntax for writing "multiargument" functions that produces curried functions, so that the type functions of type "a -> b -> c" can be written as if their type was "a b -> c", but which also have tuples such that "multiargument" functions could equally conveniently be written as having type "(a, b) -> c", and where the syntax for calling each type of function is equally straightforward in situations that don't require "partial application" (where the curried form has a natural added utility), people overwhelming use the syntax that produces curried functions.

People only predominantly use uncurried multiargument functions in languages which make writing and/or calling curried functions significant syntactic overhead.

The article lists two arguments against Currying:

  1) "performance is a bit of a concern"
  2) "curried function types have a weird shape"

2 is followed by single example of how it doesn't work the way the author would expect it to in Haskell.

It's not a strong case in my opinion. Dismissed.

I also think there’s an interesting effect when cool functional language features like currying and closures are adopted by imperative languages. They make it way too easy to create state in a way that makes you FEEL like you’re writing beautiful pure functions. Of course, in a functional language everything IS pure and this is just how things work. But in an imperative language you can trick yourself into thinking you’ve gotten away with something. At one point I stored practically all state in local variables captured by closures. It was a dark time.

If you're looking for this argument in a language closer to home, it's basically the opposite of your IDE's style guide:

If I write this Java:

  pair.map((a, b) -> Foo.merge(a, b));

My IDE flashes up with Lambda can be replaced with method reference and gives me

  pair.map(Foo::merge);

(TFA does not seem to be arguing against the idea of partial-function-application itself, as much as he wants languages to be explicit about using the full lambda terms and function-call-parentheses.)

Okay, but if you combine the curried and tuple styles, and add a dash of runtime function pointers, you can solve the expression problem. [1]

[1]: https://gavinhoward.com/2025/04/how-i-solved-the-expression-...

> curried functions often don't compose nicely

Same for imperative languages with "parameter list" style. In python, with

def f(a, b): return c, d

def g(k, l): return m, n

you can't do

f(g(1,2))

but have to use

f(*g(1,2))

what is analogical to uncurry, but operate on value rather than function.

TBH I can't name a language where such f(g(1,2)) would work.

  #!/usr/bin/env perl
  use v5.36;
  
  sub f($a, $b) {
    return ($a+1, $b+1);
  }
  
  sub g($k, $l) {
    return ($k+1, $l+1);
  }
  
  say for f(g(1,2));

  3
  4

I've long been thinking the same thing. In many fields of mathematics the placeholder $ from the OP is often written •, i.e. partial function application is written as f(a, b, •). I've always found it weird that most functional languages, particularly heavily math-inspired ones like Haskell, deviate from that. Yes, there are isomorphisms left and right but at the end of the day you have to settle on one category and one syntax. A function f: A × B -> C is simply not the same thing as a function f: A -> B -> C. Stop treating it like it is.

That's a very good point, I never thought really about how this relates to the execution model & graph reduction and such. Do you have an example of a function where this can make a difference? I might add something to the article about it.

It's also a question of whether this is exclusive to a curried definition or if such an optimization may also apply to partial application with a special operator like in the article. I think it could, but the compiler might need to do some extra work?

  where

    go [] = z

    go (x : xs) = f x (go xs)

    [] -> 0

    (x : xs) = x + go xs

> explicitly written to do this

In that case I want the signature of "this function pre-computes, then returns another function" and "this function takes two arguments" to be different, to show intent.

> achieved through compiler optimisation

Haskell is different in that its evaluation ordering allows this. But in strict evaluation languages, this is much harder, or even forbidden by language semantics.

Here's what Yaron Minsky (an OCaml guy) has to say:

> starting from scratch, I’d avoid partial application as the default way of building multi-argument functions.

https://discuss.ocaml.org/t/reason-general-function-syntax-d...

> 3. Better type errors. With currying, writing (f 1 2) instead of (f 1 2 3) silently produces a partial application. The compiler happily infers a function type like :s -> :t and moves on. The real error only surfaces later, when that unexpected function value finally clashes with an incompatible type, often far from the actual mistake. With fixed arity, a missing argument is caught right where it happens.

'Putting things' (multi-argument function calls, in this case) 'in-band doesn't make them go away, but it does successfully hide them from your tooling', part 422.

> Simplicity: Every function takes exactly one input and produces exactly one output. No exceptions. If you didn’t care about the input or output, you used Unit, and we made special syntax for that.

Seems like a disaster to use s-expressions for a language like that. I love s-expressions but they only make sense for variadic languages. The entire point of them is to quickly delimit how many arguments are passed.

In say Haskell `f x y z` is the same thing as `(((f x) y) z)`. That is definitely not the case with s-expressions; braces don't delimit; they denote function application. It's like saying that `f(x,y,z)` being the same as `f(x)(y)(z)` which it really isn't. The point of s-expressions is that you often find yourself calling functions with many arguments that are themselves a result of a function application, at that point `foo(a)(g(a,b), h(x,y))` just becomes easier to parse as ((foo a) (g a b) (h x y))`.

    (f x y z)

    (f . (x . (y . (z . ())))

    partial2 : (((a, b) -> z), a) -> (b -> z)
    partial3 : (((a, b, c) -> z), a) -> ((b, c) -> z)
    partial4 : (((a, b, c, d) -> z), a) -> ((b, c, d) -> z)
    ...

    ($define! $partial
        ($vau (f first) env
            ($lambda rest
                (eval (list* f first rest) env))))

    ($define! f ($lambda (x y z) (+ x y z)))
    (f 3 2 1)
    => 6
    
    ($define! g ($partial f 3))
    (g 2 1)
    => 6
    
    ($define! h ($partial g 2))
    (h 1)
    => 6

    ($define! i ($partial h 1))
    (i)
    => 6

    class Partial full first rest | full first -> rest where
        partial :: (full -> z, first) -> (rest -> z)
        
    instance Partial ((a,b)) a b where
        partial (f, a) = \b -> f (a, b)
        
    instance Partial ((a, b, c)) a ((b, c)) where
        partial (f, a) = \(b, c) -> f (a, b, c)
        
    instance Partial ((a, b, c, d)) a ((b, c, d)) where
        partial (f, a) = \(b, c, d) -> f (a, b, c, d)

    ...

Thanks for sharing, interesting to see that people writing functional languages also experience the same issues in practice. And they give some reasons I didn't think about.

That's so cool. I already liked Coalton, and after this change I think it's definitely going to be even better. Can't wait to try it.

> in what sense is make_string_comparator_for_locale "really" a function which takes a locale and a string and returns a function from string to ordering?

In the sense that "make_string_comparator" is not a useful concept. Being able to make a "string comparator" is inherently a function of being able to compare strings, and carving out a bespoke concept for some variation of this universal idea adds complexity that is neither necessary nor particularly useful. At the extreme, that's how you end up with Enterprise-style OO codebases full of useless nouns like "FooAdapter" and "BarFactory".

The alternative is to have a consistent, systematic way to turn verbs into nouns. In English we have gerunds. I don't have to say "the sport where you ski" and "the activity where you write", I can just say "skiing" and "writing". In functional programming we have lambdas. On top of that, curried functions are just a sort of convenient contraction to make the common case smoother. And hey, maybe the contraction isn't worth the learning curve or usability edge-cases, but the function it's serving is still important!

> Because of point 3, our codebase has a trivial wrapper to put round functions when your function actually returns a function

That seems either completely self-inflicted, or a limitation of whatever language you're using. I've worked on a number of codebases in Haskell, OCaml and a couple of Lisps, and I have never seen or wanted anything remotely like this.

> I think programming languages have a tendency to pick up cute features that give you a little dopamine kick when you use them, but that aren't actually good for the health of a substantial codebase.

That's not the case with Haskell.

Haskell has a tendency to pick up features that have deep theoretical reasoning and "mathematical beauty". Of course, that doesn't always correlate with codebase health very well either, and there's a segment of the community that is very vocal about dropping features because of that.

Anyway, the case here is that a superficial kind of mathematical beauty seems to conflict with a deeper case of it.

I want to agree, but there is the tension that in business code, what you pass as arguments is very often already named like the parameter, so having to indicate the parameter name in the call leads to a lot of redundancy. And if you’re using domain types judiciously, the types are typically also different, hence (in a statically-typed language) there is already a reduced risk of passing the wrong parameter.

Maybe there could be a rule that parameters have to be named only if their type doesn’t already disambiguate them and if there isn’t some concordance between the naming in the argument expression and the parameter, or something along those lines. But the ergonomics of that might be annoying as well.

    fn compute_thing(cost: whatever, num_widgets: whatever) -> Whatever;

    let cost = …;
    let num_widgets = …;
    let result = compute_thing(num_widgets, cost);

  let warn_user ~message = ... (* the ~ makes this a named parameter *)

  let error = "fatal error!!" in
  warn_user ~message:error; (* different names, have to specify both *)

  let message = "fatal error!!" in
  warn_user ~message; (* same names, elided *)

> Why does the author think it's confusing to partially apply foldr and map but not (+), (.), const, and length?

Neither of these functions is being partially applied in the code you cited. While the placeholder $ can be used to indicate all "free slots" of a function, you would only have to use it in partial applications of that function. (Analogous to how in mathematics the abstract index notation for tensors[0] is only really useful when you start contracting tensors, etc. Otherwise, the plain objects/tensors without indices are much easier to write & read.)

Specifically:

- (+) was already a function of two arguments, so usage of $ is unnecessary since (+)($, $) == (+). Similarly with the length function (a function of 1 argument): length($) == length.

- Function composition was being used as a binary operator between two functions. You just replaced the infix notation with prefix notation.

- I read const(1) as the function that maps everything to 1. I.e. `const` is a function of one argument x, which returns a function that always returns x. Once again, no need to indicate slots there.

[0]: See https://en.wikipedia.org/wiki/Abstract_index_notation and https://math.stackexchange.com/questions/455478/what-is-the-...

  (f . g) x = f (g x)

  const x y = x

In SML I believe. I never used SML but from how I understand it in ML all functions technically take one argument, which may be a tuple. In Haskell and Ocaml, all functions technically take one argument and just return a function that takes one argument again.

I never understood why the latter was so popular. Just for automatic implitic partial application which honestly should just have explicit syntax. In Scheme one simply uses the `(cut f x y)` operator which does a partial application and returns a function that consumes the remaining arguments which is far more explicit. But since Scheme is dynamically typed implicit partial application would be a disaster but it's not like in OCaml and Haskell the error messages at times can't be confusing.

I don't get simulating it with tuples either to be honest. Nothing wrong with just letting functions take multiple arguments and that's it. In Rust they oddly take multiple arguments as expect, but they can return tuples to simulate returning multiple arguments whereas in Scheme they just return multiple arguments. There's a difference between returning one argument which is a tuple of multiple arguments, and actually returning multiple arguments.

I think automatic implicit partial application, like almost anything “implicit” is bad. But in Haskell or Ocaml or even Rust it has to be a syntactic macro, it can't just be a normal function because no easy variadic functions which to be fair is incredibly difficult without dynamic typing and in practice just passing some kind of sequence is what you really want.