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# Sequential Programming

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## The Erlang Shell

Most operating systems have a command interpreter or shell, UNIX and Linux have many, Windows has the command prompt, powershell and more. Erlang has its own shell where bits of Erlang code can be written directly, and be evaluated to see what happens (see the `shell` manual page in STDLIB).

Start the Erlang shell (in Linux or UNIX) by starting a shell or command interpreter in your operating system and typing `erl`. You will see something like this.

    $ erl
    Erlang R15B (erts-5.9.1) [source] [smp:8:8] [rq:8] [async-threads:0] [hipe] [kernel-poll:false]

    Eshell V5.9.1  (abort with ^G)
    1>

Type `2 + 5.` in the shell and then press Enter (carriage return). Notice that you tell the shell you are done entering code by finishing with a full stop `.` and a carriage return.

    1> 2 + 5.
    7
    2>

As shown, the Erlang shell numbers the lines that can be entered, (as 1> 2>) and that it correctly says that 2 + 5 is 7. If you make writing mistakes in the shell, you can delete with the backspace key, as in most shells. There are many more editing commands in the shell (see tty - A command line interface in ERTS User's Guide).

(Notice that many line numbers given by the shell in the following examples are out of sequence. This is because this tutorial was written and code-tested in separate sessions).

Here is a bit more complex calculation:

    2> (42 + 77) * 66 / 3.
    2618.0

Notice the use of brackets, the multiplication operator `*`, and the division operator `/`, as in normal arithmetic (see Expressions).

Press Control-C to shut down the Erlang system and the Erlang shell.

The following output is shown:

    BREAK: (a)bort (c)ontinue (p)roc info (i)nfo (l)oaded
           (v)ersion (k)ill (D)b-tables (d)istribution
    a
    $

Type `a` to leave the Erlang system.

Another way to shut down the Erlang system is by entering `halt/0`:

    3> halt().
    $

## Modules and Functions

A programming language is not much use if you only can run code from the shell. So here is a small Erlang program. Enter it into a file named `tut.erl` using a suitable text editor. The file name `tut.erl` is important, and also that it is in the same directory as the one where you started `erl`). If you are lucky your editor has an Erlang mode that makes it easier for you to enter and format your code nicely (see The Erlang mode for Emacs in Tools User's Guide), but you can manage perfectly well without. Here is the code to enter:

    -module(tut).
    -export([double/1]).

    double(X) ->
        2 * X.

It is not hard to guess that this program doubles the value of numbers. The first two lines of the code are described later. Let us compile the program. This can be done in an Erlang shell as follows, where `c` means compile:

    3> c(tut).
    {ok,tut}

The `{ok,tut}` means that the compilation is OK. If it says `error` it means that there is some mistake in the text that you entered. Additional error messages gives an idea to what is wrong so you can modify the text and then try to compile the program again.

Now run the program:

    4> tut:double(10).
    20

As expected, double of 10 is 20.

Now let us get back to the first two lines of the code. Erlang programs are written in files. Each file contains an Erlang module. The first line of code in the module is the module name (see Modules):

    -module(tut).

Thus, the module is called tut. Notice the full stop `.` at the end of the line. The files which are used to store the module must have the same name as the module but with the extension `.erl`. In this case the file name is `tut.erl`. When using a function in another module, the syntax `module_name:function_name(arguments)` is used. So the following means call function `double` in module `tut` with argument `10`.

    4> tut:double(10).

The second line says that the module `tut` contains a function called `double`, which takes one argument (`X` in our example):

    -export([double/1]).

The second line also says that this function can be called from outside the module `tut`. More about this later. Again, notice the `.` at the end of the line.

Now for a more complicated example, the factorial of a number. For example, the factorial of 4 is 4 3 2 * 1, which equals 24.

Enter the following code in a file named `tut1.erl`:

    -module(tut1).
    -export([fac/1]).

    fac(1) ->
        1;
    fac(N) ->
        N * fac(N - 1).

So this is a module, called `tut1` that contains a function called `fac>`, which takes one argument, `N`.

The first part says that the factorial of 1 is 1.:

    fac(1) ->
        1;

Notice that this part ends with a semicolon `;` that indicates that there is more of the function `fac>` to come.

The second part says that the factorial of N is N multiplied by the factorial of N - 1:

    fac(N) ->
        N * fac(N - 1).

Notice that this part ends with a `.` saying that there are no more parts of this function.

Compile the file:

    5> c(tut1).
    {ok,tut1}

And now calculate the factorial of 4.

    6> tut1:fac(4).
    24

Here the function `fac>` in module `tut1` is called with argument `4`.

A function can have many arguments. Let us expand the module `tut1` with the function to multiply two numbers:

    -module(tut1).
    -export([fac/1, mult/2]).

    fac(1) ->
        1;
    fac(N) ->
        N * fac(N - 1).

    mult(X, Y) ->
        X * Y.

Notice that it is also required to expand the `-export` line with the information that there is another function `mult` with two arguments.

Compile:

    7> c(tut1).
    {ok,tut1}

Try out the new function `mult`:

    8> tut1:mult(3,4).
    12

In this example the numbers are integers and the arguments in the functions in the code `N`, `X`, and `Y` are called variables. Variables must start with a capital letter (see Variables). Examples of variables are `Number`, `ShoeSize`, and `Age`.

## Atoms

Atom is another data type in Erlang. Atoms start with a small letter (see Atom), for example, `charles`, `centimeter`, and `inch`. Atoms are simply names, nothing else. They are not like variables, which can have a value.

Enter the next program in a file named `tut2.erl`). It can be useful for converting from inches to centimeters and conversely:

    -module(tut2).
    -export([convert/2]).

    convert(M, inch) ->
        M / 2.54;

    convert(N, centimeter) ->
        N * 2.54.

Compile:

    9> c(tut2).
    {ok,tut2}

Test:

    10> tut2:convert(3, inch).
    1.1811023622047243
    11> tut2:convert(7, centimeter).
    17.78

Notice the introduction of decimals (floating point numbers) without any explanation. Hopefully you can cope with that.

Let us see what happens if something other than `centimeter` or `inch` is entered in the `convert` function:

    12> tut2:convert(3, miles).
    ** exception error: no function clause matching tut2:convert(3,miles) (tut2.erl, line 4)

The two parts of the `convert` function are called its clauses. As shown, `miles` is not part of either of the clauses. The Erlang system cannot match either of the clauses so an error message `function_clause` is returned. The shell formats the error message nicely, but the error tuple is saved in the shell's history list and can be output by the shell command `v/1`:

    13> v(12).
    {'EXIT',{function_clause,[{tut2,convert,
                                    [3,miles],
                                    [{file,"tut2.erl"},{line,4}]},
                              {erl_eval,do_apply,6,
                                        [{file,"erl_eval.erl"},{line,677}]},
                              {shell,exprs,7,[{file,"shell.erl"},{line,687}]},
                              {shell,eval_exprs,7,[{file,"shell.erl"},{line,642}]},
                              {shell,eval_loop,3,
                                     [{file,"shell.erl"},{line,627}]}]}}

## Tuples

Now the `tut2` program is hardly good programming style. Consider:

    tut2:convert(3, inch).

Does this mean that 3 is in inches? Or does it mean that 3 is in centimeters and is to be converted to inches? Erlang has a way to group things together to make things more understandable. These are called tuples and are surrounded by curly brackets, `{` and `}`.

So, `{inch,3}` denotes 3 inches and `{centimeter,5}` denotes 5 centimeters. Now let us write a new program that converts centimeters to inches and conversely. Enter the following code in a file called `tut3.erl`):

    -module(tut3).
    -export([convert_length/1]).

    convert_length({centimeter, X}) ->
        {inch, X / 2.54};
    convert_length({inch, Y}) ->
        {centimeter, Y * 2.54}.

Compile and test:

    14> c(tut3).
    {ok,tut3}
    15> tut3:convert_length({inch, 5}).
    {centimeter,12.7}
    16> tut3:convert_length(tut3:convert_length({inch, 5})).
    {inch,5.0}

Notice on line 16 that 5 inches is converted to centimeters and back again and reassuringly get back to the original value. That is, the argument to a function can be the result of another function. Consider how line 16 (above) works. The argument given to the function `{inch,5}` is first matched against the first head clause of `convert_length`, that is, `convert_length({centimeter,X})`. It can be seen that `{centimeter,X}` does not match `{inch,5}` (the head is the bit before the `->`). This having failed, let us try the head of the next clause that is, `convert_length({inch,Y})`. This matches, and `Y` gets the value 5.

Tuples can have more than two parts, in fact as many parts as you want, and contain any valid Erlang term. For example, to represent the temperature of various cities of the world:

    {moscow, {c, -10}}
    {cape_town, {f, 70}}
    {paris, {f, 28}}

Tuples have a fixed number of items in them. Each item in a tuple is called an element. In the tuple `{moscow,{c,-10}}`, element 1 is `moscow` and element 2 is `{c,-10}`. Here `c` represents Celsius and `f` Fahrenheit.

## Lists

Whereas tuples group things together, it is also needed to represent lists of things. Lists in Erlang are surrounded by square brackets, `[` and `]`. For example, a list of the temperatures of various cities in the world can be:

    [{moscow, {c, -10}}, {cape_town, {f, 70}}, {stockholm, {c, -4}},
     {paris, {f, 28}}, {london, {f, 36}}]

Notice that this list was so long that it did not fit on one line. This does not matter, Erlang allows line breaks at all "sensible places" but not, for example, in the middle of atoms, integers, and others.

A useful way of looking at parts of lists, is by using `|`. This is best explained by an example using the shell:

    17> [First |TheRest] = [1,2,3,4,5].
    [1,2,3,4,5]
    18> First.
    1
    19> TheRest.
    [2,3,4,5]

To separate the first elements of the list from the rest of the list, `|` is used. `First` has got value `1` and `TheRest` has got the value `[2,3,4,5]`.

Another example:

    20> [E1, E2 | R] = [1,2,3,4,5,6,7].
    [1,2,3,4,5,6,7]
    21> E1.
    1
    22> E2.
    2
    23> R.
    [3,4,5,6,7]

Here you see the use of `|` to get the first two elements from the list. If you try to get more elements from the list than there are elements in the list, an error is returned. Notice also the special case of the list with no elements, `[]`:

    24> [A, B | C] = [1, 2].
    [1,2]
    25> A.
    1
    26> B.
    2
    27> C.
    []

In the previous examples, new variable names are used, instead of reusing the old ones: `First`, `TheRest`, `E1`, `E2`, `R`, `A`, `B`, and `C`. The reason for this is that a variable can only be given a value once in its context (scope). More about this later.

The following example shows how to find the length of a list. Enter the following code in a file named `tut4.erl`:

    -module(tut4).

    -export([list_length/1]).

    list_length([]) ->
        0;
    list_length([First | Rest]) ->
        1 + list_length(Rest).

Compile and test:

    28> c(tut4).
    {ok,tut4}
    29> tut4:list_length([1,2,3,4,5,6,7]).
    7

Explanation:

    list_length([]) ->
        0;

The length of an empty list is obviously 0.

    list_length([First | Rest]) ->
        1 + list_length(Rest).

The length of a list with the first element `First` and the remaining elements `Rest` is 1 + the length of `Rest`.

(Advanced readers only: This is not tail recursive, there is a better way to write this function.)

In general, tuples are used where "records" or "structs" are used in other languages. Also, lists are used when representing things with varying sizes, that is, where linked lists are used in other languages.

Erlang does not have a string data type. Instead, strings can be represented by lists of Unicode characters. This implies for example that the list `[97,98,99]` is equivalent to `"abc"`. The Erlang shell is "clever" and guesses what list you mean and outputs it in what it thinks is the most appropriate form, for example:

    30> [97,98,99].
    "abc"

## Maps

Maps are a set of key to value associations. These associations are encapsulated with `#{` and `}`. To create an association from `"key"` to value `42`:

    > #{ "key" => 42 }.
    #{"key" => 42}

Let us jump straight into the deep end with an example using some interesting features.

The following example shows how to calculate alpha blending using maps to reference color and alpha channels. Enter the code in a file named `color.erl`):

    -module(color).

    -export([new/4, blend/2]).

    -define(is_channel(V), (is_float(V) andalso V >= 0.0 andalso V =< 1.0)).

    new(R,G,B,A) when ?is_channel(R), ?is_channel(G),
                      ?is_channel(B), ?is_channel(A) ->
        #{red => R, green => G, blue => B, alpha => A}.

    blend(Src,Dst) ->
        blend(Src,Dst,alpha(Src,Dst)).

    blend(Src,Dst,Alpha) when Alpha > 0.0 ->
        Dst#{
            red   := red(Src,Dst) / Alpha,
            green := green(Src,Dst) / Alpha,
            blue  := blue(Src,Dst) / Alpha,
            alpha := Alpha
        };
    blend(_,Dst,_) ->
        Dst#{
            red   := 0.0,
            green := 0.0,
            blue  := 0.0,
            alpha := 0.0
        }.

    alpha(#{alpha := SA}, #{alpha := DA}) ->
        SA + DA*(1.0 - SA).

    red(#{red := SV, alpha := SA}, #{red := DV, alpha := DA}) ->
        SV*SA + DV*DA*(1.0 - SA).
    green(#{green := SV, alpha := SA}, #{green := DV, alpha := DA}) ->
        SV*SA + DV*DA*(1.0 - SA).
    blue(#{blue := SV, alpha := SA}, #{blue := DV, alpha := DA}) ->
        SV*SA + DV*DA*(1.0 - SA).

Compile and test:

    > c(color).
    {ok,color}
    > C1 = color:new(0.3,0.4,0.5,1.0).
    #{alpha => 1.0,blue => 0.5,green => 0.4,red => 0.3}
    > C2 = color:new(1.0,0.8,0.1,0.3).
    #{alpha => 0.3,blue => 0.1,green => 0.8,red => 1.0}
    > color:blend(C1,C2).
    #{alpha => 1.0,blue => 0.5,green => 0.4,red => 0.3}
    > color:blend(C2,C1).
    #{alpha => 1.0,blue => 0.38,green => 0.52,red => 0.51}

This example warrants some explanation:

    -define(is_channel(V), (is_float(V) andalso V >= 0.0 andalso V =< 1.0)).

First a macro `is_channel` is defined to help with the guard tests. This is only here for convenience and to reduce syntax cluttering. For more information about macros, see The Preprocessor.

    new(R,G,B,A) when ?is_channel(R), ?is_channel(G),
                      ?is_channel(B), ?is_channel(A) ->
        #{red => R, green => G, blue => B, alpha => A}.

The function `new/4` creates a new map term and lets the keys `red`, `green`, `blue`, and `alpha` be associated with an initial value. In this case, only float values between and including 0.0 and 1.0 are allowed, as ensured by the `?is_channel/1` macro for each argument. Only the `=>` operator is allowed when creating a new map.

By calling `blend/2` on any color term created by `new/4`, the resulting color can be calculated as determined by the two map terms.

The first thing `blend/2` does is to calculate the resulting alpha channel:

    alpha(#{alpha := SA}, #{alpha := DA}) ->
        SA + DA*(1.0 - SA).

The value associated with key `alpha` is fetched for both arguments using the `:=` operator. The other keys in the map are ignored, only the key `alpha` is required and checked for.

This is also the case for functions `red/2`, `blue/2`, and `green/2`.

    red(#{red := SV, alpha := SA}, #{red := DV, alpha := DA}) ->
        SV*SA + DV*DA*(1.0 - SA).

The difference here is that a check is made for two keys in each map argument. The other keys are ignored.

Finally, let us return the resulting color in `blend/3`:

    blend(Src,Dst,Alpha) when Alpha > 0.0 ->
        Dst#{
            red   := red(Src,Dst) / Alpha,
            green := green(Src,Dst) / Alpha,
            blue  := blue(Src,Dst) / Alpha,
            alpha := Alpha
        };

The `Dst` map is updated with new channel values. The syntax for updating an existing key with a new value is with the `:=` operator.

## Standard Modules and Manual Pages

Erlang has many standard modules to help you do things. For example, the module `io` contains many functions that help in doing formatted input/output. To look up information about standard modules, the command `h(..)` can be used at the erlang shell. Try the erlang shell command:

    1> h(io).

    	io

        Standard I/O server interface functions.

        This module provides an interface to standard Erlang I/O servers. The output
        functions all return `ok` if they are successful, or exit if they are not.
         ...

If this does not work on your system, the documentation is included as HTML in the Erlang/OTP release. You can also read the documentation as HTML or download it as epub from <www.erlang.org/doc>.

## Writing Output to a Terminal

It is nice to be able to do formatted output in examples, so the next example shows a simple way to use the `io:format/2` function. Like all other exported functions, you can test the `io:format/2` function in the shell:

    31> io:format("hello world~n", []).
    hello world
    ok
    32> io:format("this outputs one Erlang term: ~w~n", [hello]).
    this outputs one Erlang term: hello
    ok
    33> io:format("this outputs two Erlang terms: ~w~w~n", [hello, world]).
    this outputs two Erlang terms: helloworld
    ok
    34> io:format("this outputs two Erlang terms: ~w ~w~n", [hello, world]).
    this outputs two Erlang terms: hello world
    ok

The function `io:format/2` (that is, `format` with two arguments) takes two lists. The first one is nearly always a list written between `" "`. This list is printed out as it is, except that each `~w` is replaced by a term taken in order from the second list. Each ~n is replaced by a new line. The `io:format/2` function itself returns the atom `ok` if everything goes as planned. Like other functions in Erlang, it crashes if an error occurs. This is not a fault in Erlang, it is a deliberate policy. Erlang has sophisticated mechanisms to handle errors which are shown later. As an exercise, try to make `io:format/2` crash, it should not be difficult. But notice that although `io:format/2` crashes, the Erlang shell itself does not crash.

## A Larger Example

Now for a larger example to consolidate what you have learnt so far. Assume that you have a list of temperature readings from a number of cities in the world. Some of them are in Celsius and some in Fahrenheit (as in the previous list). First let us convert them all to Celsius, then let us print the data neatly.

    %% This module is in file tut5.erl

    -module(tut5).
    -export([format_temps/1]).

    %% Only this function is exported
    format_temps([])->                        % No output for an empty list
        ok;
    format_temps([City | Rest]) ->
        print_temp(convert_to_celsius(City)),
        format_temps(Rest).

    convert_to_celsius({Name, {c, Temp}}) ->  % No conversion needed
        {Name, {c, Temp}};
    convert_to_celsius({Name, {f, Temp}}) ->  % Do the conversion
        {Name, {c, (Temp - 32) * 5 / 9}}.

    print_temp({Name, {c, Temp}}) ->
        io:format("~-15w ~w c~n", [Name, Temp]).

    35> c(tut5).
    {ok,tut5}
    36> tut5:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    moscow          -10 c
    cape_town       21.11111111111111 c
    stockholm       -4 c
    paris           -2.2222222222222223 c
    london          2.2222222222222223 c
    ok

Before looking at how this program works, notice that a few comments are added to the code. A comment starts with a %-character and goes on to the end of the line. Notice also that the `-export([format_temps/1]).` line only includes the function `format_temps/1`. The other functions are local functions, that is, they are not visible from outside the module `tut5`.

Notice also that when testing the program from the shell, the input is spread over two lines as the line was too long.

When `format_temps` is called the first time, `City` gets the value `{moscow,{c,-10}}` and `Rest` is the rest of the list. So the function `print_temp(convert_to_celsius({moscow,{c,-10}}))` is called.

Here is a function call as `convert_to_celsius({moscow,{c,-10}})` as the argument to the function `print_temp`. When function calls are nested like this, they execute (evaluate) from the inside out. That is, first `convert_to_celsius({moscow,{c,-10}})` is evaluated, which gives the value `{moscow,{c,-10}}` as the temperature is already in Celsius. Then `print_temp({moscow,{c,-10}})` is evaluated. The function `convert_to_celsius` works in a similar way to the `convert_length` function in the previous example.

`print_temp` simply calls `io:format` in a similar way to what has been described above. Notice that `~-15w` says to print the "term" with a field length (width) of 15 and left justify it. (see `io:fwrite/1` manual page in STDLIB).

Now `format_temps(Rest)` is called with the rest of the list as an argument. This way of doing things is similar to the loop constructs in other languages. (Yes, this is recursion, but do not let that worry you.) So the same `format_temps` function is called again, this time `City` gets the value `{cape_town,{f,70}}` and the same procedure is repeated as before. This is done until the list becomes empty, that is [], which causes the first clause `format_temps([])` to match. This simply returns (results in) the atom `ok`, so the program ends.

## Matching, Guards, and Scope of Variables

It can be useful to find the maximum and minimum temperature in lists like this. Before extending the program to do this, let us look at functions for finding the maximum value of the elements in a list:

    -module(tut6).
    -export([list_max/1]).

    list_max([Head|Rest]) ->
       list_max(Rest, Head).

    list_max([], Res) ->
        Res;
    list_max([Head|Rest], Result_so_far) when Head > Result_so_far ->
        list_max(Rest, Head);
    list_max([Head|Rest], Result_so_far)  ->
        list_max(Rest, Result_so_far).

    37> c(tut6).
    {ok,tut6}
    38> tut6:list_max([1,2,3,4,5,7,4,3,2,1]).
    7

First notice that two functions have the same name, `list_max`. However, each of these takes a different number of arguments (parameters). In Erlang these are regarded as completely different functions. Where you need to distinguish between these functions, you write Name/Arity, where Name is the function name and Arity is the number of arguments, in this case `list_max/1` and `list_max/2`.

In this example you walk through a list "carrying" a value, in this case `Result_so_far`. `list_max/1` simply assumes that the max value of the list is the head of the list and calls `list_max/2` with the rest of the list and the value of the head of the list. In the above this would be `list_max([2,3,4,5,7,4,3,2,1],1)`. If you tried to use `list_max/1` with an empty list or tried to use it with something that is not a list at all, you would cause an error. Notice that the Erlang philosophy is not to handle errors of this type in the function they occur, but to do so elsewhere. More about this later.

In `list_max/2`, you walk down the list and use `Head` instead of `Result_so_far` when `Head` > `Result_so_far`. `when` is a special word used before the -> in the function to say that you only use this part of the function if the test that follows is true. A test of this type is called guard. If the guard is false (that is, the guard fails), the next part of the function is tried. In this case, if `Head` is not greater than `Result_so_far`, then it must be smaller or equal to it. This means that a guard on the next part of the function is not needed.

Some useful operators in guards are:

- `<` less than
- `>` greater than
- `==` equal
- `>=` greater or equal
- `=<` less or equal
- `/=` not equal

(see Guard Sequences).

To change the above program to one that works out the minimum value of the element in a list, you only need to write < instead of >. (But it would be wise to change the name of the function to `list_min`.)

Earlier it was mentioned that a variable can only be given a value once in its scope. In the above you see that `Result_so_far` is given several values. This is OK since every time you call `list_max/2` you create a new scope and one can regard `Result_so_far` as a different variable in each scope.

Another way of creating and giving a variable a value is by using the match operator = . So if you write `M = 5`, a variable called `M` is created with the value 5. If, in the same scope, you then write `M = 6`, an error is returned. Try this out in the shell:

    39> M = 5.
    5
    40> M = 6.
    ** exception error: no match of right hand side value 6
    41> M = M + 1.
    ** exception error: no match of right hand side value 6
    42> N = M + 1.
    6

The use of the match operator is particularly useful for pulling apart Erlang terms and creating new ones.

    43> {X, Y} = {paris, {f, 28}}.
    {paris,{f,28}}
    44> X.
    paris
    45> Y.
    {f,28}

Here `X` gets the value `paris` and `Y` the value `{f,28}`.

If you try to do the same again with another city, an error is returned:

    46> {X, Y} = {london, {f, 36}}.
    ** exception error: no match of right hand side value {london,{f,36}}

Variables can also be used to improve the readability of programs. For example, in function `list_max/2` above, you can write:

    list_max([Head|Rest], Result_so_far) when Head > Result_so_far ->
        New_result_far = Head,
        list_max(Rest, New_result_far);

This is possibly a little clearer.

## More About Lists

Remember that the `|` operator can be used to get the head of a list:

    47> [M1|T1] = [paris, london, rome].
    [paris,london,rome]
    48> M1.
    paris
    49> T1.
    [london,rome]

The `|` operator can also be used to add a head to a list:

    50> L1 = [madrid | T1].
    [madrid,london,rome]
    51> L1.
    [madrid,london,rome]

Now an example of this when working with lists - reversing the order of a list:

    -module(tut8).

    -export([reverse/1]).

    reverse(List) ->
        reverse(List, []).

    reverse([Head | Rest], Reversed_List) ->
        reverse(Rest, [Head | Reversed_List]);
    reverse([], Reversed_List) ->
        Reversed_List.

    52> c(tut8).
    {ok,tut8}
    53> tut8:reverse([1,2,3]).
    [3,2,1]

Consider how `Reversed_List` is built. It starts as [], then successively the heads are taken off of the list to be reversed and added to the the `Reversed_List`, as shown in the following:

    reverse([1|2,3], []) =>
        reverse([2,3], [1|[]])

    reverse([2|3], [1]) =>
        reverse([3], [2|[1]])

    reverse([3|[]], [2,1]) =>
        reverse([], [3|[2,1]])

    reverse([], [3,2,1]) =>
        [3,2,1]

The module `lists` contains many functions for manipulating lists, for example, for reversing them. So before writing a list-manipulating function it is a good idea to check if one not already is written for you (see the `lists` manual page in STDLIB).

Now let us get back to the cities and temperatures, but take a more structured approach this time. First let us convert the whole list to Celsius as follows:

    -module(tut7).
    -export([format_temps/1]).

    format_temps(List_of_cities) ->
        convert_list_to_c(List_of_cities).

    convert_list_to_c([{Name, {f, F}} | Rest]) ->
        Converted_City = {Name, {c, (F -32)* 5 / 9}},
        [Converted_City | convert_list_to_c(Rest)];

    convert_list_to_c([City | Rest]) ->
        [City | convert_list_to_c(Rest)];

    convert_list_to_c([]) ->
        [].

Test the function:

    54> c(tut7).
    {ok, tut7}.
    55> tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    [{moscow,{c,-10}},
     {cape_town,{c,21.11111111111111}},
     {stockholm,{c,-4}},
     {paris,{c,-2.2222222222222223}},
     {london,{c,2.2222222222222223}}]

Explanation:

    format_temps(List_of_cities) ->
        convert_list_to_c(List_of_cities).

Here `format_temps/1` calls `convert_list_to_c/1`. `convert_list_to_c/1` takes off the head of the `List_of_cities`, converts it to Celsius if needed. The `|` operator is used to add the (maybe) converted to the converted rest of the list:

    [Converted_City | convert_list_to_c(Rest)];

or:

    [City | convert_list_to_c(Rest)];

This is done until the end of the list is reached, that is, the list is empty:

    convert_list_to_c([]) ->
        [].

Now when the list is converted, a function to print it is added:

    -module(tut7).
    -export([format_temps/1]).

    format_temps(List_of_cities) ->
        Converted_List = convert_list_to_c(List_of_cities),
        print_temp(Converted_List).

    convert_list_to_c([{Name, {f, F}} | Rest]) ->
        Converted_City = {Name, {c, (F -32)* 5 / 9}},
        [Converted_City | convert_list_to_c(Rest)];

    convert_list_to_c([City | Rest]) ->
        [City | convert_list_to_c(Rest)];

    convert_list_to_c([]) ->
        [].

    print_temp([{Name, {c, Temp}} | Rest]) ->
        io:format("~-15w ~w c~n", [Name, Temp]),
        print_temp(Rest);
    print_temp([]) ->
        ok.

    56> c(tut7).
    {ok,tut7}
    57> tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    moscow          -10 c
    cape_town       21.11111111111111 c
    stockholm       -4 c
    paris           -2.2222222222222223 c
    london          2.2222222222222223 c
    ok

Now a function has to be added to find the cities with the maximum and minimum temperatures. The following program is not the most efficient way of doing this as you walk through the list of cities four times. But it is better to first strive for clarity and correctness and to make programs efficient only if needed.

    -module(tut7).
    -export([format_temps/1]).

    format_temps(List_of_cities) ->
        Converted_List = convert_list_to_c(List_of_cities),
        print_temp(Converted_List),
        {Max_city, Min_city} = find_max_and_min(Converted_List),
        print_max_and_min(Max_city, Min_city).

    convert_list_to_c([{Name, {f, Temp}} | Rest]) ->
        Converted_City = {Name, {c, (Temp -32)* 5 / 9}},
        [Converted_City | convert_list_to_c(Rest)];

    convert_list_to_c([City | Rest]) ->
        [City | convert_list_to_c(Rest)];

    convert_list_to_c([]) ->
        [].

    print_temp([{Name, {c, Temp}} | Rest]) ->
        io:format("~-15w ~w c~n", [Name, Temp]),
        print_temp(Rest);
    print_temp([]) ->
        ok.

    find_max_and_min([City | Rest]) ->
        find_max_and_min(Rest, City, City).

    find_max_and_min([{Name, {c, Temp}} | Rest],
             {Max_Name, {c, Max_Temp}},
             {Min_Name, {c, Min_Temp}}) ->
        if
            Temp > Max_Temp ->
                Max_City = {Name, {c, Temp}};           % Change
            true ->
                Max_City = {Max_Name, {c, Max_Temp}} % Unchanged
        end,
        if
             Temp < Min_Temp ->
                Min_City = {Name, {c, Temp}};           % Change
            true ->
                Min_City = {Min_Name, {c, Min_Temp}} % Unchanged
        end,
        find_max_and_min(Rest, Max_City, Min_City);

    find_max_and_min([], Max_City, Min_City) ->
        {Max_City, Min_City}.

    print_max_and_min({Max_name, {c, Max_temp}}, {Min_name, {c, Min_temp}}) ->
        io:format("Max temperature was ~w c in ~w~n", [Max_temp, Max_name]),
        io:format("Min temperature was ~w c in ~w~n", [Min_temp, Min_name]).

    58> c(tut7).
    {ok, tut7}
    59> tut7:format_temps([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    moscow          -10 c
    cape_town       21.11111111111111 c
    stockholm       -4 c
    paris           -2.2222222222222223 c
    london          2.2222222222222223 c
    Max temperature was 21.11111111111111 c in cape_town
    Min temperature was -10 c in moscow
    ok

## If and Case

The function `find_max_and_min` works out the maximum and minimum temperature. A new construct, `if`, is introduced here. If works as follows:

    if
        Condition 1 ->
            Action 1;
        Condition 2 ->
            Action 2;
        Condition 3 ->
            Action 3;
        Condition 4 ->
            Action 4
    end

Notice that there is no `;` before `end`. Conditions do the same as guards, that is, tests that succeed or fail. Erlang starts at the top and tests until it finds a condition that succeeds. Then it evaluates (performs) the action following the condition and ignores all other conditions and actions before the `end`. If no condition matches, a run-time failure occurs. A condition that always succeeds is the atom `true`. This is often used last in an `if`, meaning, do the action following the `true` if all other conditions have failed.

The following is a short program to show the workings of `if`.

    -module(tut9).
    -export([test_if/2]).

    test_if(A, B) ->
        if
            A == 5 ->
                io:format("A == 5~n", []),
                a_equals_5;
            B == 6 ->
                io:format("B == 6~n", []),
                b_equals_6;
            A == 2, B == 3 ->                      %That is A equals 2 and B equals 3
                io:format("A == 2, B == 3~n", []),
                a_equals_2_b_equals_3;
            A == 1 ; B == 7 ->                     %That is A equals 1 or B equals 7
                io:format("A == 1 ; B == 7~n", []),
                a_equals_1_or_b_equals_7
        end.

Testing this program gives:

    60> c(tut9).
    {ok,tut9}
    61> tut9:test_if(5,33).
    A == 5
    a_equals_5
    62> tut9:test_if(33,6).
    B == 6
    b_equals_6
    63> tut9:test_if(2, 3).
    A == 2, B == 3
    a_equals_2_b_equals_3
    64> tut9:test_if(1, 33).
    A == 1 ; B == 7
    a_equals_1_or_b_equals_7
    65> tut9:test_if(33, 7).
    A == 1 ; B == 7
    a_equals_1_or_b_equals_7
    66> tut9:test_if(33, 33).
    ** exception error: no true branch found when evaluating an if expression
         in function  tut9:test_if/2 (tut9.erl, line 5)

Notice that `tut9:test_if(33,33)` does not cause any condition to succeed. This leads to the run time error `if_clause`, here nicely formatted by the shell. See Guard Sequences for details of the many guard tests available.

`case` is another construct in Erlang. Recall that the `convert_length` function was written as:

    convert_length({centimeter, X}) ->
        {inch, X / 2.54};
    convert_length({inch, Y}) ->
        {centimeter, Y * 2.54}.

The same program can also be written as:

    -module(tut10).
    -export([convert_length/1]).

    convert_length(Length) ->
        case Length of
            {centimeter, X} ->
                {inch, X / 2.54};
            {inch, Y} ->
                {centimeter, Y * 2.54}
        end.

    67> c(tut10).
    {ok,tut10}
    68> tut10:convert_length({inch, 6}).
    {centimeter,15.24}
    69> tut10:convert_length({centimeter, 2.5}).
    {inch,0.984251968503937}

Both `case` and `if` have return values, that is, in the above example `case` returned either `{inch,X/2.54}` or `{centimeter,Y*2.54}`. The behaviour of `case` can also be modified by using guards. The following example clarifies this. It tells us the length of a month, given the year. The year must be known, since February has 29 days in a leap year.

    -module(tut11).
    -export([month_length/2]).

    month_length(Year, Month) ->
        %% All years divisible by 400 are leap
        %% Years divisible by 100 are not leap (except the 400 rule above)
        %% Years divisible by 4 are leap (except the 100 rule above)
        Leap = if
            trunc(Year / 400) * 400 == Year ->
                leap;
            trunc(Year / 100) * 100 == Year ->
                not_leap;
            trunc(Year / 4) * 4 == Year ->
                leap;
            true ->
                not_leap
        end,
        case Month of
            sep -> 30;
            apr -> 30;
            jun -> 30;
            nov -> 30;
            feb when Leap == leap -> 29;
            feb -> 28;
            jan -> 31;
            mar -> 31;
            may -> 31;
            jul -> 31;
            aug -> 31;
            oct -> 31;
            dec -> 31
        end.

    70> c(tut11).
    {ok,tut11}
    71> tut11:month_length(2004, feb).
    29
    72> tut11:month_length(2003, feb).
    28
    73> tut11:month_length(1947, aug).
    31

## Built-In Functions (BIFs)

BIFs are functions that for some reason are built-in to the Erlang virtual machine. BIFs often implement functionality that is impossible or is too inefficient to implement in Erlang. Some BIFs can be called using the function name only but they are by default belonging to the `erlang` module. For example, the call to the BIF `trunc` below is equivalent to a call to `erlang:trunc`.

As shown, first it is checked if a year is leap. If a year is divisible by 400, it is a leap year. To determine this, first divide the year by 400 and use the BIF `trunc` (more about this later) to cut off any decimals. Then multiply by 400 again and see if the same value is returned again. For example, year 2004:

    2004 / 400 = 5.01
    trunc(5.01) = 5
    5 * 400 = 2000

2000 is not the same as 2004, so 2004 is not divisible by 400. Year 2000:

    2000 / 400 = 5.0
    trunc(5.0) = 5
    5 * 400 = 2000

That is, a leap year. The next two `trunc`-tests evaluate if the year is divisible by 100 or 4 in the same way. The first `if` returns `leap` or `not_leap`, which lands up in the variable `Leap`. This variable is used in the guard for `feb` in the following `case` that tells us how long the month is.

This example showed the use of `trunc`. It is easier to use the Erlang operator `rem` that gives the remainder after division, for example:

    74> 2004 rem 400.
    4

So instead of writing:

    trunc(Year / 400) * 400 == Year ->
        leap;

it can be written:

    Year rem 400 == 0 ->
        leap;

There are many other BIFs such as `trunc`. Only a few BIFs can be used in guards, and you cannot use functions you have defined yourself in guards. (see Guard Sequences) (For advanced readers: This is to ensure that guards do not have side effects.) Let us play with a few of these functions in the shell:

    75> trunc(5.6).
    5
    76> round(5.6).
    6
    77> length([a,b,c,d]).
    4
    78> float(5).
    5.0
    79> is_atom(hello).
    true
    80> is_atom("hello").
    false
    81> is_tuple({paris, {c, 30}}).
    true
    82> is_tuple([paris, {c, 30}]).
    false

All of these can be used in guards. Now for some BIFs that cannot be used in guards:

    83> atom_to_list(hello).
    "hello"
    84> list_to_atom("goodbye").
    goodbye
    85> integer_to_list(22).
    "22"

These three BIFs do conversions that would be difficult (or impossible) to do in Erlang.

## Higher-Order Functions (Funs)

Erlang, like most modern functional programming languages, has higher-order functions. Here is an example using the shell:

    86> Xf = fun(X) -> X * 2 end.
    #Fun<erl_eval.5.123085357>
    87> Xf(5).
    10

Here is defined a function that doubles the value of a number and assigned this function to a variable. Thus `Xf(5)` returns value 10. Two useful functions when working with lists are `foreach` and `map`, which are defined as follows:

    foreach(Fun, [First|Rest]) ->
        Fun(First),
        foreach(Fun, Rest);
    foreach(Fun, []) ->
        ok.

    map(Fun, [First|Rest]) ->
        [Fun(First)|map(Fun,Rest)];
    map(Fun, []) ->
        [].

These two functions are provided in the standard module `lists`. `foreach` takes a list and applies a fun to every element in the list. `map` creates a new list by applying a fun to every element in a list. Going back to the shell, `map` is used and a fun to add 3 to every element of a list:

    88> Add_3 = fun(X) -> X + 3 end.
    #Fun<erl_eval.5.123085357>
    89> lists:map(Add_3, [1,2,3]).
    [4,5,6]

Let us (again) print the temperatures in a list of cities:

    90> Print_City = fun({City, {X, Temp}}) -> io:format("~-15w ~w ~w~n",
    [City, X, Temp]) end.
    #Fun<erl_eval.5.123085357>
    91> lists:foreach(Print_City, [{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    moscow          c -10
    cape_town       f 70
    stockholm       c -4
    paris           f 28
    london          f 36
    ok

Let us now define a fun that can be used to go through a list of cities and temperatures and transform them all to Celsius.

    -module(tut13).

    -export([convert_list_to_c/1]).

    convert_to_c({Name, {f, Temp}}) ->
        {Name, {c, trunc((Temp - 32) * 5 / 9)}};
    convert_to_c({Name, {c, Temp}}) ->
        {Name, {c, Temp}}.

    convert_list_to_c(List) ->
        lists:map(fun convert_to_c/1, List).

    92> tut13:convert_list_to_c([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    [{moscow,{c,-10}},
     {cape_town,{c,21}},
     {stockholm,{c,-4}},
     {paris,{c,-2}},
     {london,{c,2}}]

The `convert_to_c` function is the same as before, but here it is used as a fun:

    lists:map(fun convert_to_c/1, List)

When a function defined elsewhere is used as a fun, it can be referred to as `Function/Arity` (remember that `Arity` = number of arguments). So in the `map`-call `lists:map(fun convert_to_c/1, List)` is written. As shown, `convert_list_to_c` becomes much shorter and easier to understand.

The standard module `lists` also contains a function `sort(Fun, List)` where `Fun` is a fun with two arguments. This fun returns `true` if the first argument is less than the second argument, or else `false`. Sorting is added to the `convert_list_to_c`:

    -module(tut13).

    -export([convert_list_to_c/1]).

    convert_to_c({Name, {f, Temp}}) ->
        {Name, {c, trunc((Temp - 32) * 5 / 9)}};
    convert_to_c({Name, {c, Temp}}) ->
        {Name, {c, Temp}}.

    convert_list_to_c(List) ->
        New_list = lists:map(fun convert_to_c/1, List),
        lists:sort(fun({_, {c, Temp1}}, {_, {c, Temp2}}) ->
                           Temp1 < Temp2 end, New_list).

    93> c(tut13).
    {ok,tut13}
    94> tut13:convert_list_to_c([{moscow, {c, -10}}, {cape_town, {f, 70}},
    {stockholm, {c, -4}}, {paris, {f, 28}}, {london, {f, 36}}]).
    [{moscow,{c,-10}},
     {stockholm,{c,-4}},
     {paris,{c,-2}},
     {london,{c,2}},
     {cape_town,{c,21}}]

In `sort` the fun is used:

    fun({_, {c, Temp1}}, {_, {c, Temp2}}) -> Temp1 < Temp2 end,

Here the concept of an anonymous variable `_` is introduced. This is simply shorthand for a variable that gets a value, but the value is ignored. This can be used anywhere suitable, not just in funs. `Temp1 < Temp2` returns `true` if `Temp1` is less than `Temp2`.

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