Here is an example of the difference Toivo refers to (I think):
julia> foo{T<:Real}(a::Array{T},b::T) = T foo (generic function with 1 method) julia> bar(a::Array{Real},b::Real) = Real bar (generic function with 1 method) julia> aR = Real[1,2]; aI = Int[1,2]; julia> foo(aR, 5) ERROR: no method foo(Array{Real,1}, Int64) julia> foo(aI, 5) Int64 julia> bar(aR, 5) Real When calling foo(aR, 5), then T is set to Real. Now in case of parameterized functions this means that typeof(b)===T, i.e. typeof(b) must be Real. (which in this case is never possible as Real is an abstract type). This contrasts to bar where only the weaker constraint typeof(b)<:Real is needed, i.e. a isa relation. Thus, Toivo's complaint is that in function definitions :: usually means `isa` whereas for parameterized functions it means type equality `===`. However, I think this realisation does not make the :: situation worse than it already is. :: has different meanings depending on context: ditto when in function declarations, then in function bodies it can also be a sub-type-assert, or a type declaration of a variable in the sense of check-and-convert (if check fails). So, three meanings of :: are possible. As an aside, in the issue about "function return type declarations" https://github.com/JuliaLang/julia/issues/1090 it is suggested to add syntax like f(a)::Int = 5 to declare that f returns an Int. The discussion there suggests that there :: will have the check-and-convert semantics. Thus a line like this could contain all three meanings of :: f{T<:Real}((a::Array{T},b::T,c::Integer)::Complex = ... ! On Fri, 2014-05-16 at 08:15, tomas.lyc...@gmail.com wrote: >> But do you agree that the usage of x::T as a formal parameter is quite > different when T is a type parameter compared to when it is a plain type? > > I'm not 100% sure I grok what you're getting at, but *if *what you're > asking is whether I see a difference between foo(x::Real) and > foo{T<:Real}(x::Array{T}), then really no - I don't. > > I just the latter as shorthand for defining a function with a whole bunch > of methods - foo(x::Array{Int64}), foo(x::Array{Float64}), etc etc - with > the same Julia implementation. They will still, just as the former for > foo(x::Int64) and foo(x::Float64), be compiled to different versions, > strongly typed to the runtime type of the argument, and I could get exactly > the same behavior without parametric methods by copy-pasting the > implementation and using different specific type signatures. I'd need one > for every subtype of Real, so of course this isn't feasible in practice, > but the way I look at it the difference is really mainly syntactic sugar. > > The possibility to do diagonal dispatch with the help of type parameters is > also syntactic sugar - I could just as easily define bar(x::Int64, > y::Int64) etc for all real types, but with no methods for bar that take > arguments of different kinds, as define bar{T<:Real}(x::T, y::T). Again, > this would mean an insane amount of code duplication, so I'm really glad I > don't *have* to code this way, but I certainly could if I for some wicked > reason wanted to. > > There is of course one thing that differs profoundly: if you define > foo{T<:Real}(x::Array{T}) and then someone else comes, later on, and > defines a new subtype to Real, your definition just works. Had you done it > without type parameters, it of course wouldn't have worked without also > adding a specific implementation for foo(x::Array{MyNewRealType}). > > // Tomas > > On Thursday, May 15, 2014 10:03:12 PM UTC+2, Kevin Squire wrote: >> >> FWIW, I really appreciate you pointing out the different uses of :: Toivo. >> Along with the different meanings of parameterizations in types and >> functions, this is another area I haven't been clear about (and I wasn't >> even aware of it until you pointed it out). >> >> Cheers! >> Kevin >> >> >> On Thu, May 15, 2014 at 11:49 AM, Toivo Henningsson >> <toiv...@gmail.com<javascript:> >> > wrote: >> >>> >>> >>> On Thursday, 15 May 2014 10:59:07 UTC+2, Tomas Lycken wrote: >>>> >>>> it silently uses :: in a different sense than anywhere else in the >>>>> language >>>> >>>> >>>> I started writing a reply here, but realized it would be more >>>> instructive to have it as an IJulia notebook, where we can actually >>>> inspect >>>> the values of various statements along the way - take a look here instead: >>>> http://nbviewer.ipython.org/github/tlycken/IJulia-Notebooks/blob/master/ >>>> A%20more%20thorough%20look%20at%20Julia's%20%22double% >>>> 20colon%22%20syntax.ipynb >>>> >>>> I hope it makes things a little clearer. I tried to base it on the >>>> relevant section on `::` in the manual (http://docs.julialang.org/en/ >>>> latest/manual/types/#type-declarations) and expand it with more >>>> examples etc, so I hope it's possible to see the connections. >>>> >>> >>> / Toivo >>> >> >> --