std.functional

Functions that manipulate other functions.

This module provides functions for compile time function composition. These functions are helpful when constructing predicates for the algorithms in std.algorithm or std.range.

License:

Boost License 1.0.

Authors:

Andrei Alexandrescu

Source

std/functional.d

template unaryFun(alias fun, string parmName = "a")

Transforms a string representing an expression into a unary function. The string must either use symbol name a as the parameter or provide the symbol via the parmName argument.

Parameters:

fun	a string or a callable
parmName	the name of the parameter if fun is a string. Defaults to "a".

Returns:

If fun is a string, a new single parameter function If fun is not a string, an alias to fun.

Examples:

// Strings are compiled into functions:
alias isEven = unaryFun!("(a & 1) == 0");
assert(isEven(2) && !isEven(1));

template binaryFun(alias fun, string parm1Name = "a", string parm2Name = "b")

Transforms a string representing an expression into a binary function. The string must either use symbol names a and b as the parameters or provide the symbols via the parm1Name and parm2Name arguments.

Parameters:

fun	a string or a callable
parm1Name	the name of the first parameter if fun is a string. Defaults to "a".
parm2Name	the name of the second parameter if fun is a string. Defaults to "b".

Returns:

If fun is not a string, binaryFun aliases itself away to fun.

Examples:

alias less = binaryFun!("a < b");
assert(less(1, 2) && !less(2, 1));
alias greater = binaryFun!("a > b");
assert(!greater("1", "2") && greater("2", "1"));

alias lessThan = safeOp!"<".safeOp(T0, T1)(auto ref T0 a, auto ref T1 b);

Predicate that returns a < b. Correctly compares signed and unsigned integers, ie. -1 < 2U.

Examples:

assert(lessThan(2, 3));
assert(lessThan(2U, 3U));
assert(lessThan(2, 3.0));
assert(lessThan(-2, 3U));
assert(lessThan(2, 3U));
assert(!lessThan(3U, -2));
assert(!lessThan(3U, 2));
assert(!lessThan(0, 0));
assert(!lessThan(0U, 0));
assert(!lessThan(0, 0U));

alias greaterThan = safeOp!">".safeOp(T0, T1)(auto ref T0 a, auto ref T1 b);

Predicate that returns a > b. Correctly compares signed and unsigned integers, ie. 2U > -1.

Examples:

assert(!greaterThan(2, 3));
assert(!greaterThan(2U, 3U));
assert(!greaterThan(2, 3.0));
assert(!greaterThan(-2, 3U));
assert(!greaterThan(2, 3U));
assert(greaterThan(3U, -2));
assert(greaterThan(3U, 2));
assert(!greaterThan(0, 0));
assert(!greaterThan(0U, 0));
assert(!greaterThan(0, 0U));

alias equalTo = safeOp!"==".safeOp(T0, T1)(auto ref T0 a, auto ref T1 b);

Predicate that returns a == b. Correctly compares signed and unsigned integers, ie. !(-1 == ~0U).

Examples:

assert(equalTo(0U, 0));
assert(equalTo(0, 0U));
assert(!equalTo(-1, ~0U));

template reverseArgs(alias pred)

N-ary predicate that reverses the order of arguments, e.g., given pred(a, b, c), returns pred(c, b, a).

Parameters:

pred	A callable

Returns:

A function which calls pred after reversing the given parameters

Examples:

alias gt = reverseArgs!(binaryFun!("a < b"));
assert(gt(2, 1) && !gt(1, 1));

Examples:

int x = 42;
bool xyz(int a, int b) { return a * x < b / x; }
auto foo = &xyz;
foo(4, 5);
alias zyx = reverseArgs!(foo);
writeln(zyx(5, 4)); // foo(4, 5)

Examples:

alias gt = reverseArgs!(binaryFun!("a < b"));
assert(gt(2, 1) && !gt(1, 1));
int x = 42;
bool xyz(int a, int b) { return a * x < b / x; }
auto foo = &xyz;
foo(4, 5);
alias zyx = reverseArgs!(foo);
writeln(zyx(5, 4)); // foo(4, 5)

Examples:

int abc(int a, int b, int c) { return a * b + c; }
alias cba = reverseArgs!abc;
writeln(abc(91, 17, 32)); // cba(32, 17, 91)

Examples:

int a(int a) { return a * 2; }
alias _a = reverseArgs!a;
writeln(a(2)); // _a(2)

Examples:

int b() { return 4; }
alias _b = reverseArgs!b;
writeln(b()); // _b()

template not(alias pred)

Negates predicate pred.

Parameters:

pred	A string or a callable

Returns:

A function which calls pred and returns the logical negation of its return value.

Examples:

import std.algorithm.searching : find;
import std.functional;
import std.uni : isWhite;
string a = "   Hello, world!";
writeln(find!(not!isWhite)(a)); // "Hello, world!"

template partial(alias fun, alias arg)

Partially applies fun by tying its first argument to arg.

Parameters:

fun	A callable
arg	The first argument to apply to fun

Returns:

A new function which calls fun with arg plus the passed parameters.

Examples:

int fun(int a, int b) { return a + b; }
alias fun5 = partial!(fun, 5);
writeln(fun5(6)); // 11
// Note that in most cases you'd use an alias instead of a value
// assignment. Using an alias allows you to partially evaluate template
// functions without committing to a particular type of the function.

auto curry(alias F)()
Constraints: if (isCallable!F && Parameters!F.length);

auto curry(T)(T t)
Constraints: if (isCallable!T && Parameters!T.length);

Takes a function of (potentially) many arguments, and returns a function taking one argument and returns a callable taking the rest. f(x, y) == curry(f)(x)(y)

Parameters:

F	a function taking at least one argument
T t	a callable object whose opCall takes at least 1 object

Returns:

A single parameter callable object

Examples:

int f(int x, int y, int z)
{
    return x + y + z;
}
auto cf = curry!f;
auto cf1 = cf(1);
auto cf2 = cf(2);

writeln(cf1(2)(3)); // f(1, 2, 3)
writeln(cf2(2)(3)); // f(2, 2, 3)

Examples:

//works with callable structs too
struct S
{
    int w;
    int opCall(int x, int y, int z)
    {
        return w + x + y + z;
    }
}

S s;
s.w = 5;

auto cs = curry(s);
auto cs1 = cs(1);
auto cs2 = cs(2);

writeln(cs1(2)(3)); // s(1, 2, 3)
writeln(cs1(2)(3)); // (1 + 2 + 3 + 5)
writeln(cs2(2)(3)); // s(2, 2, 3)

template adjoin(F...) if (F.length == 1)

template adjoin(F...) if (F.length > 1)

Takes multiple functions and adjoins them together.

Parameters:

F	the call-able(s) to adjoin

Returns:

A new function which returns a std.typecons.Tuple. Each of the elements of the tuple will be the return values of F.

Note

In the special case where only a single function is provided (F.length == 1), adjoin simply aliases to the single passed function (F[0]).

Examples:

import std.functional, std.typecons : Tuple;
static bool f1(int a) { return a != 0; }
static int f2(int a) { return a / 2; }
auto x = adjoin!(f1, f2)(5);
assert(is(typeof(x) == Tuple!(bool, int)));
assert(x[0] == true && x[1] == 2);

template compose(fun...) if (fun.length > 0)

Composes passed-in functions fun[0], fun[1], ....

Parameters:

fun	the call-able(s) or string(s) to compose into one function

Returns:

A new function f(x) that in turn returns fun[0](fun[1](...(x)))....

See Also:

pipe

Examples:

import std.algorithm.comparison : equal;
import std.algorithm.iteration : map;
import std.array : split;
import std.conv : to;

// First split a string in whitespace-separated tokens and then
// convert each token into an integer
assert(compose!(map!(to!(int)), split)("1 2 3").equal([1, 2, 3]));

template pipe(fun...)

Pipes functions in sequence. Offers the same functionality as compose, but with functions specified in reverse order. This may lead to more readable code in some situation because the order of execution is the same as lexical order.

Parameters:

fun	the call-able(s) or string(s) to compose into one function

Returns:

A new function f(x) that in turn returns fun[$-1](...fun[1](fun[0](x)))....

Example

// Read an entire text file, split the resulting string in
// whitespace-separated tokens, and then convert each token into an
// integer
int[] a = pipe!(readText, split, map!(to!(int)))("file.txt");

See Also:

compose

Examples:

import std.conv : to;
string foo(int a) { return to!(string)(a); }
int bar(string a) { return to!(int)(a) + 1; }
double baz(int a) { return a + 0.5; }
writeln(compose!(baz, bar, foo)(1)); // 2.5
writeln(pipe!(foo, bar, baz)(1)); // 2.5

writeln(compose!(baz, `to!(int)(a) + 1`, foo)(1)); // 2.5
writeln(compose!(baz, bar)("1"[])); // 2.5

writeln(compose!(baz, bar)("1")); // 2.5

writeln(compose!(`a + 0.5`, `to!(int)(a) + 1`, foo)(1)); // 2.5

ReturnType!fun memoize(alias fun)(Parameters!fun args);

ReturnType!fun memoize(alias fun, uint maxSize)(Parameters!fun args);

Memoizes a function so as to avoid repeated computation. The memoization structure is a hash table keyed by a tuple of the function's arguments. There is a speed gain if the function is repeatedly called with the same arguments and is more expensive than a hash table lookup. For more information on memoization, refer to this book chapter.

Example

double transmogrify(int a, string b)
{
   ... expensive computation ...
}
alias fastTransmogrify = memoize!transmogrify;
unittest
{
    auto slow = transmogrify(2, "hello");
    auto fast = fastTransmogrify(2, "hello");
    assert(slow == fast);
}

Parameters:

fun	the call-able to memozie
maxSize	The maximum size of the GC buffer to hold the return values

Returns:

A new function which calls fun and caches its return values.

Note

Technically the memoized function should be pure because memoize assumes it will always return the same result for a given tuple of arguments. However, memoize does not enforce that because sometimes it is useful to memoize an impure function, too.

Examples:

To memoize a recursive function, simply insert the memoized call in lieu of the plain recursive call. For example, to transform the exponential-time Fibonacci implementation into a linear-time computation:

ulong fib(ulong n) @safe nothrow
{
    return n < 2 ? n : memoize!fib(n - 2) + memoize!fib(n - 1);
}
writeln(fib(10)); // 55

Examples:

To improve the speed of the factorial function,

ulong fact(ulong n) @safe
{
    return n < 2 ? 1 : n * memoize!fact(n - 1);
}
writeln(fact(10)); // 3628800

Examples:

This memoizes all values of fact up to the largest argument. To only cache the final result, move memoize outside the function as shown below.

ulong factImpl(ulong n) @safe
{
    return n < 2 ? 1 : n * factImpl(n - 1);
}
alias fact = memoize!factImpl;
writeln(fact(10)); // 3628800

Examples:

When the maxSize parameter is specified, memoize will used a fixed size hash table to limit the number of cached entries.

ulong fact(ulong n)
{
    // Memoize no more than 8 values
    return n < 2 ? 1 : n * memoize!(fact, 8)(n - 1);
}
writeln(fact(8)); // 40320
// using more entries than maxSize will overwrite existing entries
writeln(fact(10)); // 3628800

auto toDelegate(F)(auto ref F fp)
Constraints: if (isCallable!F);

Convert a callable to a delegate with the same parameter list and return type, avoiding heap allocations and use of auxiliary storage.

Parameters:

F fp	a function pointer or an aggregate type with opCall defined.

Returns:

A delegate with the context pointer pointing to nothing.

Example

void doStuff() {
    writeln("Hello, world.");
}

void runDelegate(void delegate() myDelegate) {
    myDelegate();
}

auto delegateToPass = toDelegate(&doStuff);
runDelegate(delegateToPass);  // Calls doStuff, prints "Hello, world."

Bugs:

• Does not work with @safe functions.
• Ignores C-style / D-style variadic arguments.

Examples:

static int inc(ref uint num) {
    num++;
    return 8675309;
}

uint myNum = 0;
auto incMyNumDel = toDelegate(&inc);
auto returnVal = incMyNumDel(myNum);
writeln(myNum); // 1

template forward(args...)

Forwards function arguments while keeping out, ref, and lazy on the parameters.

Parameters:

args	a parameter list or an std.meta.AliasSeq.

Returns:

An AliasSeq of args with out, ref, and lazy saved.

Examples:

class C
{
    static int foo(int n) { return 1; }
    static int foo(ref int n) { return 2; }
}

// with forward
int bar()(auto ref int x) { return C.foo(forward!x); }

// without forward
int baz()(auto ref int x) { return C.foo(x); }

int i;
writeln(bar(1)); // 1
writeln(bar(i)); // 2

writeln(baz(1)); // 2
writeln(baz(i)); // 2

Examples:

void foo(int n, ref string s) { s = null; foreach (i; 0 .. n) s ~= "Hello"; }

// forwards all arguments which are bound to parameter tuple
void bar(Args...)(auto ref Args args) { return foo(forward!args); }

// forwards all arguments with swapping order
void baz(Args...)(auto ref Args args) { return foo(forward!args[$/2..$], forward!args[0..$/2]); }

string s;
bar(1, s);
writeln(s); // "Hello"
baz(s, 2);
writeln(s); // "HelloHello"

Examples:

struct X {
    int i;
    this(this)
    {
        ++i;
    }
}

struct Y
{
    private X x_;
    this()(auto ref X x)
    {
        x_ = forward!x;
    }
}

struct Z
{
    private const X x_;
    this()(auto ref X x)
    {
        x_ = forward!x;
    }
    this()(auto const ref X x)
    {
        x_ = forward!x;
    }
}

X x;
const X cx;
auto constX = (){ const X x; return x; };
static assert(__traits(compiles, { Y y = x; }));
static assert(__traits(compiles, { Y y = X(); }));
static assert(!__traits(compiles, { Y y = cx; }));
static assert(!__traits(compiles, { Y y = constX(); }));
static assert(__traits(compiles, { Z z = x; }));
static assert(__traits(compiles, { Z z = X(); }));
static assert(__traits(compiles, { Z z = cx; }));
static assert(__traits(compiles, { Z z = constX(); }));


Y y1 = x;
// ref lvalue, copy
writeln(y1.x_.i); // 1
Y y2 = X();
// rvalue, move
writeln(y2.x_.i); // 0

Z z1 = x;
// ref lvalue, copy
writeln(z1.x_.i); // 1
Z z2 = X();
// rvalue, move
writeln(z2.x_.i); // 0
Z z3 = cx;
// ref const lvalue, copy
writeln(z3.x_.i); // 1
Z z4 = constX();
// const rvalue, copy
writeln(z4.x_.i); // 1