This section introduces functional objects (Funs). That is a new data type introduced in Erlang 4.4. Functions which takes Funs as arguments, or which return Funs are called higher order functions.
Funs encourages us to encapsulate common patterns of design into functional forms called higher order functions. These functions not only shortens programs, but also produce clearer programs because the intended meaning of the program is explicitly rather than implicitly stated.
The concepts of higher order functions and procedural abstraction are introduced with two brief examples.
If we want to double every element in a list, we could write a function named double
:
double([H|T]) -> [2*H|double(T)]; double([]) -> []
This function obviously doubles the argument entered as input as follows:
> double([1,2,3,4]). [2,4,6,8]
We now add the function add_one
, which adds one to every element in a list:
add_one([H|T]) -> [H+1|add_one(T)]; add_one([]) -> [].
These functions, double
and add_one
, have a very similar structure. We can exploit this fact and write a function map
which expresses this similarity:
map(F, [H|T]) -> [F(H)|map(F, T)]; map(F, []) -> [].
We can now express the functions double
and add_one
in terms of map
as follows:
double(L) -> map(fun(X) -> 2*X end, L). add_one(L) -> map(fun(X) -> 1 + X end, L).
map(F, List)
is a function which takes a function F
and a list L
as arguments and
returns the new list which is obtained by applying F
to each of the elements in L
.
The process of abstracting out the common features of a number of different programs is called procedural abstraction. Procedural abstraction can be used in order to write several different functions which have a similar structure, but differ only in some minor detail. This is done as follows:
This example illustrates procedural abstraction. Initially, we show the following two examples written as conventional functions:
print_list(Stream, [H|T]) -> io:format(Stream, "~p~n", [H]), print_list(Stream, T); print_on_list(Stream, []) -> true.
broadcast(Msg, [Pid|Pids]) -> Pid ! Msg, broadcast(Msg, Pids); broadcast(_, []) -> true.
Both these functions have a very similar structure. They both iterate over a list doing something to each element in the list. The "something" has to be carried round as an extra argument to the function which does this.
The function foreach
expresses this similarity:
foreach(F, [H|T]) -> F(H), foreach(F, T); foreach(F, []) -> ok.
Using foreach
, print_on_list
becomes:
foreach(fun(H) -> io:format(S, "~p~n~,[H]) end, L)
broadcast
becomes:
foreach(fun(Pid) -> Pid ! M end, L)
foreach
is evaluated for its side-effect and not its value. foreach(Fun ,L)
calls Fun(X)
for each element X
in L
and the processing occurs in the order in which the elements were defined in L
. map
does not define the order in which its elements are processed.
Programming with higher order functions, such as map
and foreach
, has a number of advantages:
foreach(fun(X) ->
clearly indicates that the intention of this program is to do something to each element in the list L
. We also know that the function which is passed as the first argument of foreach
takes one argument X
, which will be successively bound to each of the elements in L
.
Funs are written with the syntax:
F = fun (Arg1, Arg2, ... ArgN) -> ... end
This creates an anonymous function of N
arguments and binds it to the variable F
.
If we have already written a function in the same module and wish to pass this function as an argument, we can use the following syntax:
F = fun FunctionName/Arity
With this form of function reference, the function which is referred to does not need to be exported from the module.
We can also refer to a function defined in a different module with the following syntax:
F = {Module, FunctionName}
In this case, the function must be exported from the module in question.
The follow program illustrates the different ways of creating Funs:
-module(fun_test). -export([t1/0, t2/0, t3/0, t4/0, double/1]). -import(lists, [map/2]). t1() -> map(fun(X) -> 2 * X end, [1,2,3,4,5]). t2() -> map(fun double/1, [1,2,3,4,5]). t3() -> map({?MODULE, double}, [1,2,3,4,5]). double(X) -> X * 2.
We can evaluate the fun F
with the syntax:
F(Arg1, Arg2, ..., Argn)
To check whether a term is a Fun, use the test function/1
in a guard. Example:
f(F, Args) when function(F) -> apply(F, Args); f(N, _) when integer(N) -> N.
Funs are a distinct type. The BIFs erlang:fun_info/1,2 can be used to retrieve information about a fun, and the BIF erlang:fun_to_list/1 returns a textual representation of a fun. The check_process_code/2 BIF returns true if the process contains funs that depend on the old version of a module.
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In OTP R5 and earlier releases, funs were represented using tuples. |
The scope rules for variables which occur in Funs are as follows:
The following examples illustrate these rules:
print_list(File, List) -> {ok, Stream} = file:open(File, write), foreach(fun(X) -> io:format(Stream,"~p~n",[X]) end, List), file:close(Stream).
In the above example, the variable X
which is defined in the head of the Fun is a new variable. The value of the variable Stream
which is used within within the Fun gets its value from the
file:open
line.
Since any variable which occurs in the head of a Fun is considered a new variable it would be equally valid to write:
print_list(File, List) -> {ok, Stream} = file:open(File, write), foreach(fun(File) -> io:format(Stream,"~p~n",[File]) end, List), file:close(Stream).
In this example, File
is used as the new variable instead of X
. This is rather silly since code in the body of the Fun cannot refer to the variable File
which is defined outside the Fun. Compiling this example will yield the diagnostic:
./FileName.erl:Line: Warning: variable 'File' shadowed in 'lambda head'
This reminds us that the variable File
which is defined inside the Fun collides with the variable File
which is defined outside the Fun.
The rules for importing variables into a Fun has the consequence that certain pattern matching operations have to be moved into guard expressions and cannot be written in the head of the Fun. For example, we might write the following code if we intend the first clause of F
to be evaluated when the value of its argument is Y
:
f(...) -> Y = ... map(fun(X) when X == Y -> ; (_) -> ... end, ...) ...
instead of
f(...) -> Y = ... map(fun(Y) -> ; (_) -> ... end, ...) ...
The following examples show a dialogue with the Erlang shell. All the higher order functions discussed are exported from the module lists
.
map(F, [H|T]) -> [F(H)|map(F, T)]; map(F, []) -> [].
map
takes a function of one argument and a list of terms. It returns the list obtained by applying the function to every argument in the list.
1> Double = fun(X) -> 2 * X end. #Fun<erl_eval> 2> lists:map(Double, [1,2,3,4,5]). [2,4,6,8,10]
When a new Fun is defined in the shell, the value of the Fun is printed as Fun#<erl_eval>
any(Pred, [H|T]) -> case Pred(H) of true -> true; false -> any(Pred, T) end; any(Pred, []) -> false.
any
takes a predicate P
of one argument and a list of terms. A predicate is a function which returns true
or false
. any
is true if there is a term X
in the list such that P(X)
is true
.
We define a predicate Big(X)
which is true
if its argument is greater that 10.
3> Big = fun(X) -> if X > 10 -> true; true -> false end end. #Fun<erl_eval> 4> lists:any(Big, [1,2,3,4]). false. 5> lists:any(Big, [1,2,3,12,5]). true.
all(Pred, [H|T]) -> case Pred(H) of true -> all(Pred, T); false -> false end; all(Pred, []) -> true.
all
has the same arguments as any
. It is true if the predicate applied to all elements in the list is true.
6> lists:all(Big, [1,2,3,4,12,6]). false 7> lists:all(Big, [12,13,14,15]). true
foreach(F, [H|T]) -> F(H), foreach(F, T); foreach(F, []) -> ok.
foreach
takes a function of one argument and a list of terms. The function is applied to each argument in the list. foreach
returns ok
. It is used for its side-effect only.
8> lists:foreach(fun(X) -> io:format("~w~n",[X]) end, [1,2,3,4]). 1 2 3 4 true
foldl(F, Accu, [Hd|Tail]) -> foldl(F, F(Hd, Accu), Tail); foldl(F, Accu, []) -> Accu.
foldl
takes a function of two arguments, an accumulator and a list. The function is called with two arguments. The first argument is the successive elements in the list, the second argument is the accumulator. The function must return a new accumulator which is used the next time the function is called.
If we have a list of lists L = ["I","like","Erlang"]
, then we can sum the lengths of all the strings in L
as follows:
9> L = ["I","like","Erlang"]. ["I","like","Erlang"] 10> lists:foldl(fun(X, Sum) -> length(X) + Sum end, 0, L). 11
foldl
works like a while
loop in an imperative language:
L = ["I","like","Erlang"], Sum = 0, while( L != []){ Sum += length(head(L)), L = tail(L) end
mapfoldl(F, Accu0, [Hd|Tail]) -> {R,Accu1} = F(Hd, Accu0), {Rs,Accu2} = mapfoldl(F, Accu1, Tail), {[R|Rs], Accu2}; mapfoldl(F, Accu, []) -> {[], Accu}.
mapfoldl
simultaneously maps and folds over a list. The following example shows how to change all letters in L
to upper case and count them.
First upcase:
11> Upcase = fun(X) when $a =< X, X =< $z -> X + $A - $a; (X) -> X end. #Fun<erl_eval> 12> Upcase_word = fun(X) -> lists:map(Upcase, X) end. #Fun<erl_eval> 13> Upcase_word("Erlang"). "ERLANG" 14> lists:map(Upcase_word, L). ["I","LIKE","ERLANG"]
Now we can do the fold and the map at the same time:
14> lists:mapfoldl(fun(Word, Sum) -> 14> {Upcase_word(Word), Sum + length(Word)} 14> end, 0, L). {["I","LIKE","ERLANG"],11}
filter(F, [H|T]) -> case F(H) of true -> [H|filter(F, T)]; false -> filter(F, T) end; filter(F, []) -> [].
filter
takes a predicate of one argument and a list and returns all element in the list which satisfy the predicate.
15> lists:filter(Big, [500,12,2,45,6,7]). [500,12,45]
When we combine maps and filters we can write very succinct and obviously correct code. For example, suppose we want to define a set difference function. We want to define diff(L1, L2)
to be the difference between the lists L1
and L2
.
This is the list of all elements in L1 which are not contained in L2. This code can be written as follows:
diff(L1, L2) -> filter(fun(X) -> not member(X, L2) end, L1).
The AND intersection of the list L1
and L2
is also easily defined:
intersection(L1,L2) -> filter(fun(X) -> member(X,L1) end, L2).
takewhile(Pred, [H|T]) -> case Pred(H) of true -> [H|takewhile(Pred, T)]; false -> [] end; takewhile(Pred, []) -> [].
takewhile(P, L)
takes elements X
from a list L
as long as the predicate P(X)
is true.
16> lists:takewhile(Big, [200,500,45,5,3,45,6]). [200,500,45]
dropwhile(Pred, [H|T]) -> case Pred(H) of true -> dropwhile(Pred, T); false -> [H|T] end; dropwhile(Pred, []) -> [].
dropwhile
is the complement of takewhile
.
17> lists:dropwhile(Big, [200,500,45,5,3,45,6]). [5,3,45,6]
splitlist(Pred, L) -> splitlist(Pred, L, []). splitlist(Pred, [H|T], L) -> case Pred(H) of true -> splitlist(Pred, T, [H|L]); false -> {reverse(L), [H|T]} end; splitlist(Pred, [], L) -> {reverse(L), []}.
splitlist(P, L)
splits the list L
into the two sub-lists {L1, L2}
, where L = takewhile(P, L)
and L2 = dropwhile(P, L)
.
18> lists:splitlist(Big, [200,500,45,5,3,45,6]). {[200,500,45],[5,3,45,6]}
first(Pred, [H|T]) -> case Pred(H) of true -> {true, H}; false -> first(Pred, T) end; first(Pred, []) -> false.
first
returns {true, R}
, where R
is the first element in a list satisfying a predicate or false
:
19> lists:first(Big, [1,2,45,6,123]). {true,45} 20> lists:first(Big, [1,2,4,5]). false
So far, this section has only described functions which take Funs as arguments. It is also possible to write more powerful functions which themselves return Funs. The following examples illustrate these type of functions.
Adder(X)
is a function which, given X
, returns a new function G
such that G(K)
returns K + X
.
21> Adder = fun(X) -> fun(Y) -> X + Y end end. #Fun<erl_eval> 22> Add6 = Adder(6). #Fun<erl_eval> 23> Add6(10). 16
The idea is to write something like:
-module(lazy). -export([ints_from/1]). ints_from(N) -> fun() -> [N|ints_from(N+1)] end.
Then we can proceed as follows:
24> XX = lazy:ints_from(1). #Fun<lazy> 25> XX(). [1|#Fun<lazy>] 26> hd(XX()). 1 27> Y = tl(XX()). #Fun<lazy> 28> hd(Y()). 2
etc. - this is an example of "lazy embedding"
The following examples show parsers of the following type:
Parser(Toks) -> {ok, Tree, Toks1} | fail
Toks
is the list of tokens to be parsed. A successful parse returns {ok, Tree, Toks1}
, where Tree
is a parse tree and Toks1
is a tail of Tree
which contains symbols encountered after the structure which was correctly parsed. Otherwise fail
is returned.
The example which follows illustrates a simple, functional parser which parses the grammar:
(a | b) & (c | d)
The following code defines a function pconst(X)
in the module funparse
, which returns a Fun which parses a list of tokens.
pconst(X) -> fun (T) -> case T of [X|T1] -> {ok, {const, X}, T1}; _ -> fail end end.
This function can be used as follows:
29> P1 = funparse:pconst(a). #Fun<hof> 30> P1([a,b,c]). {ok,{const,a},[b,c]} 31> P1([x,y,z]). fail
Next, we define the two higher order functions pand
and por
which combine primitive parsers to produce more complex parsers. Firstly pand
:
pand(P1, P2) -> fun (T) -> case P1(T) of {ok, R1, T1} -> case P2(T1) of {ok, R2, T2} -> {ok, {'and', R1, R2}}; fail -> fail end; fail -> fail end end.
Given a parser P1
for grammar G1
, and a parser P2
for grammar G2
, pand(P1, P2)
returns a parser for the grammar which consists of sequences of tokens which satisfy G1
followed by sequences of tokens which satisfy G2
.
por(P1, P2)
returns a parser for the language described by the grammar G1
or G2
.
por(P1, P2) -> fun (T) -> case P1(T) of {ok, R, T1} -> {ok, {'or',1,R}, T1}; fail -> case P2(T) of {ok, R1, T1} -> {ok, {'or',2,R1}, T1}; fail -> fail end end end.
The original problem was to parse the grammar (a | b) & (c | d)
. The following code addresses this problem:
grammar() -> pand( por(pconst(a), pconst(b)), por(pconst(c), pconst(d))).
The following code adds a parser interface to the grammar:
parse(List) -> (grammar())(List).
We can test this parser as follows:
32> funparse:parse([a,c]). {ok,{'and',{'or',1,{const,a}},{'or',1,{const,c}}}} 33> funparse:parse([a,d]). {ok,{'and',{'or',1,{const,a}},{'or',2,{const,d}}}} 34> funparse:parse([b,c]). {ok,{'and',{'or',2,{const,b}},{'or',1,{const,c}}}} 35> funparse:parse([b,d]). {ok,{'and',{'or',2,{const,b}},{'or',2,{const,d}}}} 36> funparse:parse([a,b]). fail