this clause cannot match because of different types/sizes - erlang

Question

i tried to implement binary_search in erlang :
binary_search(X , List) ->
case {is_number(x) , is_list(List)} of
{false , false} -> {error};
{false , true} -> {error} ;
{true , false} -> {error} ;
{true , true} ->
Length = length(List) ,
case Length of
0 -> {false};
1 -> case lists:member(X , List) of
true -> {true};
false -> {false}
end ;
_ ->
Middle = (Length + 1) div 2 ,
case X >= Middle of
true -> binary_search(X , lists:sublist(List , Middle , Length));
false -> binary_search(X , lists:sublist(List , 1 , Middle))
end
end
end .
However when i try to compile it , i get the following error : "this clause cannot match because of different types/sizes" in the two lines :
{true , false} -> {error} ;
{true , true} ->

Answer 1

is_number(x) will always return false since you made a typo: x instead of X, an atom instead of a variable.
BTW, I don't know what you are experiencing, but the whole code can be written as:
binary_search(X , [_|_] = List) when is_number(X) ->
{lists:member(X,List)};
binary_search(_,_) -> {error}.

Answer 2

Context: The OP's post appears to be a learning example -- an attempt to understand binary search in Erlang -- and is treated as one below (hence the calls to io:format/2 each iteration of the inner function). In production lists:member/2 should be used as noted by Steve Vinoski in a comment below, or lists:member/2 guarded by a function head as in Pascal's answer. What follows is a manual implementation of binary search.
Pascal is correct about the typo, but this code has more fundamental problems. Instead of just finding the typo let's see if we can obviate the need for this nested case checking entirely.
(The code as written above won't work anyway because X should not represent the value of an index, but rather the value that is held at that index, so Middle will likely never match X. Also, there is another issue: you don't cover all the base cases (cases in which you should stop recursing). So the inner function below covers them all up front as matches within the function head, so it is more obvious how the search works. Note the Middle + 1 when X > Value, by the way; contemplate why this is necessary.)
Two main notes on Erlang style
First: If you receive the wrong sort of data, just crash, don't return an error. With that in mind, consider using a guard.
Second: If you find yourself doing lots of cases, you can usually simplify your life by making them named functions. This gives you two advantages:
A much better crash report than you will get within nested case expressions.
A named, pure function can be tested and even formally verified rather easily if it is small enough -- which is also pretty cool. (As a side note, the religion of testing tests my patience and sanity at times, but when you have pure functions you actually can test at least those parts of your program -- so distilling out as much of this sort of thing as possible is a big win.)
Below I do both, and this should obviate the issue you ran into as well as make things a bit easier to read/sort through mentally:
%% Don't return errors, just crash.
%% Only check the data on entry.
%% Guarantee the data is sorted, as this is fundamental to binary search.
binary_search(X, List)
when is_number(X),
is_list(List) ->
bs(X, lists:sort(List)).
%% Get all of our obvious base cases out of the way as matches.
%% Note the lack of type checking; its already been done.
bs(_, []) -> false;
bs(X, [X]) -> true;
bs(X, [_]) -> false;
bs(X, List) ->
ok = io:format("bs(~p, ~p)~n", [X, List]),
Length = length(List),
Middle = (Length + 1) div 2,
Value = lists:nth(Middle, List),
% This is one of those rare times I find an 'if' to be more
% clear in meaning than a 'case'.
if
X == Value -> true;
X > Value -> bs(X, lists:sublist(List, Middle + 1, Length));
X < Value -> bs(X, lists:sublist(List, 1, Middle))
end.