Exercise 2

I add output and then run it to see it execute.
There is peace of my code with output:

increments([Head | Tail]) -> increments(Head, Tail).

increments(_, []) ->
    io:format("~n"),
    true;
increments(N, [Head | Tail]) when Head == N + 1 ->
    io:format("~p", [Head]),
    if length(Tail) > 0 -> io:format(", ");
       true -> io:format("|")
    end,
    increments(Head, Tail);
increments(_, _) -> false.

Erlang
(page 88)
code/CustomGenerators/erlang/pbt/test/prop_generators.erl

I would like to share inner step calculation while gathering values (by groups of 10). I was confused a litter how is the calculation going.

I have inserted an expression to print the parameters.

prop_collect2() ->
    ?FORALL(Bin, (binary()),
            (collect(to_range(10, byte_size(Bin)),
                     is_binary(Bin)))).

%%%%%%%%%%%%%%%
%%% Helpers %%%
%%%%%%%%%%%%%%%
to_range(M, N) ->
    Base = N div M,
    io:format("~2B = ~2B div ~B | {~2B, ~B} = {~2B * ~B, (~B + 1)*~B~n",
              [Base, N, M, Base * M, (Base + 1) * M, Base, M, Base, M]),
    {Base * M, (Base + 1) * M}.

Command:
rebar3 proper​ -p prop_collect2

Output (with the intermediate calculations):

 0 =   0 div 10 | { 0, 10} = { 0 * 10, (0 + 1)*10
. 0 =  1 div 10 | { 0, 10} = { 0 * 10, (0 + 1)*10
. 0 =  0 div 10 | { 0, 10} = { 0 * 10, (0 + 1)*10
. 0 =  0 div 10 | { 0, 10} = { 0 * 10, (0 + 1)*10
...
. 3 = 38 div 10 | {30, 40} = { 3 * 10, (3 + 1)*10
. 3 = 33 div 10 | {30, 40} = { 3 * 10, (3 + 1)*10
. 1 = 15 div 10 | {10, 20} = { 1 * 10, (1 + 1)*10
. 2 = 22 div 10 | {20, 30} = { 2 * 10, (2 + 1)*10

OK: Passed 100 test(s).

56.00% {0,10}
28.00% {10,20}
 9.00% {20,30}
 7.00% {30,40}
===>
1/1 properties passed

Erlang
(page 89)
code/CustomGenerators/erlang/pbt/test/prop_generators.erl

While running property based test prop_dupes you will get the same logging info.

prop_dupes() ->
 ?FORALL(KV, list({key(), val()}),
        begin
     M = maps:from_list(KV),
     _ = [maps:get(K, M) || {K, _V} <- KV], % crash if K's not in map
     collect(
       {dupes, to_range(5, length(KV) - length(lists:ukeysort(1,KV)))},
       true
     )
  end).


%%%%%%%%%%%%%%%
%%% Helpers %%%
%%%%%%%%%%%%%%%
key() -> integer().
val() -> term().

to_range(M, N) ->
    Base = N div M,
    io:format("~2B = ~2B div ~B | {~2B, ~2B} = {~2B * ~B, (~B + 1)*~B~n",
              [Base, N, M, Base * M, (Base + 1) * M, Base, M, Base, M]),
    {Base * M, (Base + 1) * M}.

Full code project

maps:from_list/1
maps:get/2
lists:ukeysort/2
length/1