trans :: (b -> a) -> (c -> a -> c) -> c -> b -> c
trans f reduce c = reduce c . f
mapping :: (a -> b) -> Transducer b a
mapping f xf r a = xf r (f a)
Transducer a b
b -> [a]
Calling Clojure "dynamically typed" in this context (or any context), is confusing, as it is more of a mashup of a few ideas from functional and OO languages than a typical dynamically typed language. For example, Clojure does not have dynamic dispatch (except for multimethods, which are a limited form of dynamic dispatch) other than that offered by OO polymorphism (interfaces/protocols). In other words, it lacks the most important mechanism that lends dynamically typed languages like JavaScript and Ruby their power.
It is a language that, like Java/C#/Go, is based on interfaces, which are then mixed with some functional concepts. Unlike the aforementioned OO languages, Clojure usually uses only a handful of such abstractions (or interfaces; or protocols). So, while the translation to Haskell requires such concepts as type classes and higher-rank types, this has nothing to do with dynamic typing, and a lot to do with plain old OO polymorphism.
Personally I find it less confusing that dynamic typing is a small and comparatively well-defined concept, than mixing it in with aspects of polymorphism and dynamic dispatch. Dynamic dispatch doesn't seem to me to have much to do with dynamic typing; it's a fundamental tool of expression in C++ and Java, and those are both statically-typed languages.
I'm curious why you think multimethods are more limited than dynamic dispatch. It seems to me that their expressiveness is a strict superset of dynamic dispatch. Am I missing something?
Well, yes, but that has little to do with the way Clojure abstractions work; namely, they're not based on dynamic dispatch, but on OO-style polymorphism.
But BTW, your definition is not entirely complete, and the distinction between statically typed and dynamically typed is not always so clear cut when you're not talking about extremes such as Haskell and JavaScript.
Statically typed languages like Java, C++, C# and Scala can, and do have runtime type errors because they allow casting. They also all have type tags (well, optional in C++). I.e., most statically typed languages don't attempt to eliminate all type errors at compile time. Clojure indeed does very little static type checks (I think only function arity is checked).
Even in Haskell values must be tagged with types, and the type tags are inspected at runtime. Otherwise, pattern matching wouldn't work (pattern matching is always based on type reflection).
> I'm curious why you think multimethods are more limited than dynamic dispatch.
Because methods can't (or rarely do) "appear out of nowhere" or get installed at runtime as they do in, say, JavaScript or Groovy.
Multimethods are actually a rather powerful form of dynamic dispatch. From the context, I think what you're referring to is late binding, which is when an identifier is resolved to a storage location / function implementation at runtime rather than at compile time. It's easy to get them confused, since late binding gives you dynamic dispatch "for free", but it is possible to have dynamic dispatch with early binding (as in C++, for example).
> Calling Clojure "dynamically typed" in this context (or any context), is confusing, as it is more of a mashup of a few ideas from functional and OO languages than a typical dynamically typed language.
A language's type system (or lack thereof) has nothing at all to do with dynamicity of dispatch nor binding.
I think you haven't spent much time using Clojure.
Your phrase "it is more of a mashup of a few ideas from functional and OO languages" seems intended to downplay the language as nothing important. By that metric, Ruby and Javascript are both "just" mashups of lisp/scheme, perl, smalltalk and self.
Clojure can be just as dynamic as JS & Ruby. On the JVM, protocols are implemented in terms of Java interfaces, because that's how you get fast dispatch, however, protocols share little in common with "standard" OO. There's no implementation inheritance, a protocol can be extended to any type (except for a few limitations caused by the JVM, those limitations don't apply to other implementations, like CLJS).
For example: If I implement the ISeq data structure, I can use instances of my ISeq implementation in code that was written for lets say list processing (such as a function that uses ``(first val)``. The implementation is looked up at runtime. My program compiles, even if I call ``(first 4)``, it will lead in an error at runtime however, since the number 4 is not a sequence. Java is fundamentally different. It is checked at compile time whether the ``val`` does adhere to the interface. This is what makes it static.