Erlang Dialyzer integer ranges

Question

-module(test).
-export([f/0, g/0]).

-spec f() -> RESULT when
      RESULT :: 0..12 .

-spec g() -> RESULT when
      RESULT :: 0..13 .

f () -> 100 .

g () -> 100 .

Running dialyzer (and typer) only the function f is caught.

dialyzer test.erl
Checking whether the PLT /Users/ben/.dialyzer_plt is up-to-date... yes
Proceeding with analysis...
test.erl:4: Invalid type specification for function test:f/0. The success typing is () -> 100
 done in 0m0.53s
done (warnings were emitted)

the same with typer

typer test.erl
typer: Error in contract of function test:f/0
         The contract is: () -> RESULT when RESULT :: 0..12
         but the inferred signature is: () -> 100

Is this "expected" behaviour?

Hood

Answer 1

Yes it does seem to be "expected". Looking at the source code here It tests against the value of

-define(SET_LIMIT, 13).

in the test

t_from_range(X, Y) when is_integer(X), is_integer(Y) ->
  case ((Y - X) < ?SET_LIMIT) of 
    true -> t_integers(lists:seq(X, Y));
    false ->
      case X >= 0 of
    false -> 
      if Y < 0 -> ?integer_neg;
         true -> t_integer()
      end;
    true ->
      if Y =< ?MAX_BYTE, X >= 1 -> ?int_range(1, ?MAX_BYTE);
         Y =< ?MAX_BYTE -> t_byte();
         Y =< ?MAX_CHAR, X >= 1 -> ?int_range(1, ?MAX_CHAR);
         Y =< ?MAX_CHAR -> t_char();
         X >= 1         -> ?integer_pos;
         X >= 0         -> ?integer_non_neg
      end
      end
  end;

IMHO this seems dangerous, and does not provide any real guarantees. It should definitely be documented clearly. there is passing reference on the learn you some Erlang website.

A range of integers. For example, if you wanted to represent a number of months in a year, the range 1..12 could be defined. Note that Dialyzer reserves the right to expand this range into a bigger one.

But nothing official on the front page of google using the keywords dialyzer integer ranges

Edit... looking a bit closer you can see that if you try:

-module(test).
-export([h/0]).

-spec h() -> RESULT when
      RESULT :: 1..13 .

h () -> 100 .

Dialyzer will catch the error! (Typer will not) ...

Hood

Answer 2

Yes, it is "expected" behaviour. Or rather "accepted".

Disclaimers:

1. Dialyzer never promised to catch all the errors.
2. Code like the above is fairly artificial.

Explanation:

Dialyzer's designers have decided to use over-approximations like this to (among other reasons) make the tool's type inference analysis terminate (reach a fix-point) when analysing recursive functions (the internal steps really look like this: "factorial's base case works for 0, so it's recursive case also works for 1, so it also works for 2, so it also works for 3, [...], so it works for 12, ok so it also works for any char(), but it also works for char_range + 1 so it works for all integers()").

It is fairly rare that this (arbitrary indeed) limit becomes critical, and then again, Dialyzer never promised to report anything...

Ancon