I know you probably want a solution in Perl 5, but here is one in Perl 6, because it hapepns to be very short:
$ perl6 -e 'say [\+] 0, 1, 3, 2'
0 1 4 6
Enclosing an infix operator like + with square brackets applies it to a list, as if you had written 0 + 1 + 4 + 6. The [\infix] for also returns the intermediate results.
Mnemonic: the [\ has the shape of a triangle, just like the list of expressions that is generated from it:
0 + 1
0 + 1 + 4
0 + 1 + 4 + 6
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