Why are some programming languages Turing complete but lack some abilities of other languages?

Question Detail: 

I came across an odd problem when writing an interpreter that (should) hooks to external programs/functions: Functions in 'C' and 'C++' can't hook variadic functions, e.g. I can't make a function that calls 'printf' with the exact same arguments that it got, and instead has to call an alternate version that take a variadic object. This is very problematic since I want to be able to make an object that hold an anonymous hook.

So, I thought that this was weird since Forth, JavaScript, and perhaps a plethora of other languages can do this very easily without having to resort to assembly language/machine code. Since other languages can do this so easily, does that mean that the class of problems that each programming language can solve actually varies by language, even though these languages are all Turing complete?

Asked By : Mr. Minty Fresh

Best Answer from StackOverflow

Question Source : http://cs.stackexchange.com/questions/63961

Answered By : chi

Turing complete languages can compute the same set of functions $\mathbb{N}^k \rightarrow \mathbb{N}$, which is the set of general recursive partial functions. That's it.

This says nothing about the language features. A Turing Machine has very limited compositional features. The untyped $\lambda$-calculus is far more compositional, but lacks many features commonly found in modern languages.

Turing completeness tells nothing about having types, built in arrays/integers/dictionaries, input/output capabilities, network access, multithreading, dynamic allocation, ...

Just because Java does not have feature X (say, macros, higher-rank types, or dependent types), it does not suddenly stop being Turing complete.

Turing completeness and language expressiveness are two different notions.