Regarding the Int / BigInt distinction, other issues besides performance, which haven't historically been prominent considerations in new language designs, are interoperability and transparency. In the current design, a Vector{Int} always has the same in-memory representation as it would in C or Fortran – you can take a pointer to the first array element and pass it to a library function using the C ABI and it will just work. You also know exactly how your data is represented and can reason about it. You know, for example, that a Vector{Int} definitely does not require any additional heap allocation besides the inline Int values and that arithmetic operations on Ints will just be machine arithmetic ops. I think that the transparency of the C data and performance models has been one of the major reasons for C's long-lived success. One of the design goals of Julia is to have similarly transparent data and performance models.
IMHO it is total fail to have int be dependent on the machine architecture. C99 fixed this behavior with types for specific sizes so people could finally write portable code. Julia should adopt 64bit integers by default given its intended audience and the reality that even some phones have 64bit processors. int64_t works on 32bit processors too, but with a performance penalty. Having the range of a variable depend on the machine architecture really went out of style a long time ago.
We considered that, but even though 64-bit ints work on 32-bit machines, they are dog slow. Insisting that integers are 64-bit everywhere is basically saying that you want slow for loops, slow array indexing – slow everything – on 32-bit systems. Clearly that's unacceptable in a language that is meant to be fast. So Julia has Int32 and Int64 when you want a specific bit size and Int is always the same size as your pointers. This arrangement is considerably simpler to deal with than C's "integers are whatever size I want them to be! [evil cackle]" approach. In particular, default integers and pointers are always the same size – which is not always the case in C (I'm looking at you, Win64) – so there's only one system-dependent size to worry about.
