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# Templates Revisited

by Walter Bright, http://www.digitalmars.com/d

> What I am going to tell you about is what we teach our programming students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my programming students don't understand it... That is because I don't understand it. Nobody does. Richard Deeman

Contents

1. Abstract
2. Similarities
3. Argument Syntax
4. Template Definition Syntax
5. Template Declaration, Definition, and Export
6. Template Parameters
7. Specialization
8. Two Level Name Lookup
9. Template Recursion
10. Substitution Failure Is Not An Error (SFINAE)
11. Template Metaprogramming With Floats
12. Template Metaprogramming With Strings
13. Regular Expression Compiler
14. More Template Metaprogramming
15. References
16. Acknowledgements

## Abstract

Templates in C++ have evolved from little more than token substitution into a programming language in itself. Many useful aspects of C++ templates have been discovered rather than designed. A side effect of this is that C++ templates are often criticized for having an awkward syntax, many arcane rules, and being very difficult to implement properly. What might templates look like if one takes a step back, looks at what templates can do and what uses they are put to, and redesign them? Can templates be powerful, aesthetically pleasing, easy to explain and straightforward to implement? This article takes a look at an alternative design of templates in the D Programming Language [1].

## Similarities

- compile time semantics
- function templates
- class templates
- type parameters
- value parameters
- template parameters
- partial and explicit specialization
- type deduction
- implicit function template instantiation
- SFINAE (Substitution Failure Is Not An Error)

## Argument Syntax

The first thing that comes to mind is the use of < > to enclose parameter lists and argument lists. < > has a couple serious problem, however. They are ambiguous with operators <, >, and >>. This means that expressions like:

    a<b,c>d;

and:

    a<b<c>>d;

are syntactically ambiguous, both to the compiler and the programmer. If you run across a<b,c>d; in unfamiliar code, you've got to slog through an arbitrarily large amount of declarations and .h files to figure out if it is a template or not. How much effort has been expended by programmers, compiler writers, and language standard writers to deal with this?

There's got to be a better way. D solves it by noticing that ! is not used as a binary operator, so replacing:

    a<b,c>

with:

    a!(b,c)

is syntactically unambiguous. This makes it easy to parse, easy to generate reasonable error messages for, and makes it easy for someone inspecting the code to determine that yes, a must be a template.

## Template Definition Syntax

C++ can define two broad types of templates: class templates, and function templates. Each template is written independently, even if they are closely related:

    template<class T, class U> class Bar { ... };

    template<class T, class U> T foo(T t, U u) { ... }

    template<class T, class U> static T abc;

POD (Plain Old Data, as in C style) structs bring together related data declarations, classes bring together related data and function declarations, but there's nothing to logically group together templates that are to be instantiated together. In D, we can write:

    template Foo(T, U)
    {
        class Bar { ... }

        T foo(T t, U u) { ... }

        T abc;

        typedef T* Footype; // any declarations can be templated
    }

The Foo forms a name space for the templates, which are accessed by, for example:

    Foo!(int,char).Bar b;
    Foo!(int,char).foo(1,2);
    Foo!(int,char).abc = 3;

Of course, this can get a little tedious, so one can use an alias for a particular instantiation:

    alias f = Foo!(int,char);
    f.Bar b;
    f.foo(1,2);
    f.abc = 3;

For class templates, there's an even simpler syntax. A class is defined like:

    class Abc
    {
        int t;
        ...
    }

This can be turned into a template by just adding a parameter list:

    class Abc(T)
    {
        T t;
        ...
    }

## Template Declaration, Definition, and Export

C++ templates can be in the form of a template declaration, a template definition, and an exported template. Because D has a true module system, rather than textual #include files, there are only template definitions in D. The need for template declarations and export is irrelevant. For example, given a template definition in module A:

    module A;

    template Foo(T)
    {
        T bar;
    }

it can be accessed from module B like:

    module B;

    import A;

    void test()
    {
        A.Foo!(int).bar = 3;
    }

As usual, an alias can be used to simplify access:

    module B;

    import A;
    alias bar = A.Foo!(int).bar;

    void test()
    {
        bar = 3;
    }

## Template Parameters

C++ template parameters can be:

- types
- integral values
- static/global addresses
- template names

D template parameters can be:

- types
- integral values
- floating point values
- string literals
- templates
- or any symbol

Each can have default values, and type parameters can have (a limited form of) constraints:

    class B { ... }
    interface I { ... }

    class Foo(
        R,            // R can be any type
        P:P*,         // P must be a pointer type
        T:int,        // T must be int type
        S:T*,         // S must be pointer to T
        C:B,          // C must be of class B or derived
                      // from B
        U:I,          // U must be interface I, or any interface
                      // or class which has interface I in its
                      // inheritance tree
        string str = "hello",
                      // string literal,
                      // default is "hello"
        alias A = B   // A is any symbol
                      // (including template symbols),
                      // defaulting to B
        )
    {
        ...
    }

## Specialization

Partial and explicit specialization work as they do in C++, except that there is no notion of a ‘primary’ template. All the templates with the same name are examined upon template instantiation, and the one with the best fit of arguments to parameters is instantiated.

    template Foo(T) ...
    template Foo(T:T*) ...
    template Foo(T, U:T) ...
    template Foo(T, U) ...
    template Foo(T, U:int) ...

    Foo!(long)       // picks Foo(T)
    Foo!(long[])     // picks Foo(T), T is long[]
    Foo!(int*)       // picks Foo(T*), T is int
    Foo!(long,long)  // picks Foo(T, U:T)
    Foo!(long,short) // picks Foo(T, U)
    Foo!(long,int)   // picks Foo(T, U:int)
    Foo!(int,int)    // ambiguous - Foo(T, U:T)
                     // or Foo(T, U:int)

## Two Level Name Lookup

C++ has some unusual rules for name lookup inside templates, such as not looking inside base classes, not allowing scoped redeclaration of template parameter names, and not considering overloads that happen after the point of definition (this example is derived from one in the C++98 Standard):

    int g(double d) { return 1; }

    typedef double A;

    template<class T> struct B
    {
        typedef int A;
    };

    template<class T> struct X : B<T>
    {
        A a;              // a has type double
        int T;            // error, T redeclared
        int foo()
        {
            char T;       // error, T redeclared
            return g(1);  // always returns 1
        }
    };

    int g(int i) { return 2; }  // this definition not seen by X

Scoped lookup rules in D match the rules for the rest of the language:

    int g(double d) { return 1; }

    alias A = double;

    class B(T)
    {
        alias A = int;
    }

    class X(T) : B!(T)
    {
        A a;             // a has type int
        int T;           // ok, T redeclared as int
        int foo()
        {
            char T;      // ok, T redeclared as char
            return g(1); // always returns 2
        }
    };

    int g(int i) { return 2; }  // functions can be forward referenced

## Template Recursion

Template recursion combined with specialization means that C++ templates actually form a programming language, although certainly an odd one. Consider a set of templates that computes a factorial at run time. Like "hello world" programs, factorial is the canonical example of template metaprogramming:

    template<int n> class factorial
    {
        public:
            enum
            {
                result = n * factorial<n - 1>::result
            };
    };

    template<> class factorial<1>
    {
        public:
            enum { result = 1 };
    };

    void test()
    {
        // prints 24
        printf("%d\n", factorial<4>::result);
    }

Recursion works as well in D, though with significantly less typing:

    template factorial(int n)
    {
        const factorial = n * factorial!(n-1);
    }

    template factorial(int n : 1)
    {
        const factorial = 1;
    }

    void test()
    {
        writeln(factorial!(4));  // prints 24
    }

Through using the static if construct it can be done in just one template:

    template factorial(int n)
    {
        static if (n == 1)
            const factorial = 1;
        else
            const factorial = n * factorial!(n-1);
    }

reducing 13 lines of code to an arguably much cleaner 7 lines. static ifs are the equivalent of C++'s #if. But #if cannot access template arguments, so all template conditional compilation must be handled with partial and explicitly specialized templates. static if dramatically simplifies such constructions.

D can make this even simpler. Value generating templates such as the factorial one are possible, but it's easier to just write a function that can be computed at compile time:

    int factorial(int n)
    {
        if (n == 1)
            return 1;
        else
            return n * factorial(n - 1);
    }

    static int x = factorial(5);  // x is statically initialized to 120

## Substitution Failure Is Not An Error (SFINAE)

This determines if the template's argument type is a function, from "C++ Templates: The Complete Guide", Vandevoorde & Josuttis pg. 353:

    template<U> class IsFunctionT
    {
        private:
            typedef char One;
            typedef struct { char a[2]; } Two;
            template static One test(...);
            template static Two test(U (*)[1]);
        public:
            enum
            {
                Yes = sizeof(IsFunctionT::test(0)) == 1
            };
    };

    void test()
    {
        typedef int (fp)(int);

        assert(IsFunctionT<fp>::Yes == 1);
    }

Template IsFunctionT relies on two side effects to achieve its result. First, it relies on arrays of functions being an invalid C++ type. Thus, if U is a function type, the second test will not be selected since to do so would cause an error (SFINAE (Substitution Failure Is Not An Error)). The first test will be selected. If U is not a function type, the second test is a better fit than ... . Next, it is determined which test was selected by examining the size of the return value, i.e. sizeof(One) or sizeof(Two). Unfortunately, template metaprogramming in C++ often seems to be relying on side effects rather than being able to expressly code what is desired.

In D this can be written:

    template IsFunctionT(T)
    {
        static if (is(T[]))
            const int IsFunctionT = 0;
        else
            const int IsFunctionT = 1;
    }

    void test()
    {
        alias int fp(int);

        assert(IsFunctionT!(fp) == 1);
    }

The is(T[]) is the equivalent of SFINAE (Substitution Failure Is Not An Error). It tries to build an array of T, and if T is a function type, it is an array of functions. Since this is an invalid type, the T[] fails and is(T[]) returns false.

Although SFINAE (Substitution Failure Is Not An Error) can be used, the is expressions can test a type directly, so it isn't even necessary to use a template to ask questions about a type:

    void test()
    {
        alias int fp(int);

        assert(is(fp == function));
    }

## Template Metaprogramming With Floats

Let's move on to things that are impractical with templates in C++. For example, this template returns the square root of real number x using the Babylonian method:

    import std.stdio;

    template sqrt(real x, real root = x/2, int ntries = 0)
    {
        static if (ntries == 5)
            // precision doubles with each iteration,
            // 5 should be enough
            const sqrt = root;
        else static if (root * root - x == 0)
            const sqrt = root;  // exact match
        else
            // iterate again
            const sqrt = sqrt!(x, (root+x/root)/2, ntries+1);
    }

    void main()
    {
        real x = sqrt!(2);
        writefln("%.20g", x); // 1.4142135623730950487
    }

Literal square roots are often needed for speed reasons in other runtime floating point computations, such as computing the gamma function. These template floating point algorithms need not be efficient as they are computed at compile time, they only need to be accurate.

Much more complex templates can be built, for example, Don Clugston has written a template to compute π at compile time. [2]

Again, we can just do this with a function that can be executed at compile time:

    real sqrt(real x)
    {
        real root = x / 2;
        for (int ntries = 0; ntries < 5; ntries++)
        {
            if (root * root - x == 0)
                break;
            root = (root + x / root) / 2;
        }
        return root;
    }
    static y = sqrt(10);   // y is statically initialized to 3.16228

## Template Metaprogramming With Strings

Even more interesting things can be done with strings. This example converts an integer to a string at compile time:

    template decimalDigit(int n)    // [3]
    {
        const string decimalDigit = "0123456789"[n..n+1];
    }

    template itoa(long n)
    {
        static if (n < 0)
            const string itoa = "-" ~ itoa!(-n);
        else static if (n < 10)
            const string itoa = decimalDigit!(n);
        else
            const string itoa = itoa!(n/10L) ~ decimalDigit!(n%10L);
    }

    string foo()
    {
        return itoa!(264);   // returns "264"
    }

This template will compute the hash of a string literal:

    template hash(char [] s, uint sofar=0)
    {
        static if (s.length == 0)
            const hash = sofar;
        else
            const hash = hash!(s[1 .. $], sofar * 11 + s[0]);
    }

    uint foo()
    {
        return hash!("hello world");
    }

## Regular Expression Compiler

How do D templates fare with something much more significant, like a regular expression compiler? Eric Niebler has written one for C++ that relies on expression templates. [4] The problem with using expression templates is that one is restricted to using only C++ operator syntax and precedence. Hence, regular expressions using expression templates don't look like regular expressions, they look like C++ expressions. Eric Anderton has written one for D that relies on the ability of templates to parse strings. [5] This means that, within the strings, one can use the expected regular expression grammar and operators.

The regex compiler templates parse the regex string argument, pulling off tokens one by one from the front, and instantiating custom template functions for each token predicate, eventually combining them all into one function that directly implements the regular expression. It even gives reasonable error messages for syntax errors in the regular expression.

Calling that function with an argument of a string to match returns an array of matching strings:

    import std.stdio;
    import regex;

    void main()
    {
        auto exp = &regexMatch!(r"[a-z]*\s*\w*");
        writefln("matches: %s", exp("hello    world"));
    }

What follows is a cut-down version of Eric Anderton's regex compiler. It is just enough to compile the regular expression above, serving to illustrate how it is done.

    module regex;

    const int testFail = -1;

    /**
     * Compile pattern[] and expand to a custom generated
     * function that will take a string str[] and apply the
     * regular expression to it, returning an array of matches.
     */

    template regexMatch(string pattern)
    {
        string[] regexMatch(string str)
        {
            string[] results;
            int n = regexCompile!(pattern).fn(str);
            if (n != testFail && n > 0)
                results ~= str[0..n];
            return results;
        }
    }

    /******************************
     * The testXxxx() functions are custom generated by templates
     * to match each predicate of the regular expression.
     *
     * Params:
     *      string str      the input string to match against
     *
     * Returns:
     *      testFail        failed to have a match
     *      n >= 0          matched n characters
     */

    /// Always match
    template testEmpty()
    {
        int testEmpty(string str) { return 0; }
    }

    /// Match if testFirst(str) and testSecond(str) match
    template testUnion(alias testFirst, alias testSecond)
    {
        int testUnion(string str)
        {
            int n1 = testFirst(str);
            if (n1 != testFail)
            {
                int n2 = testSecond(str[n1 .. $]);
                if (n2 != testFail)
                    return n1 + n2;
            }
            return testFail;
        }
    }

    /// Match if first part of str[] matches text[]
    template testText(string text)
    {
        int testText(string str)
        {
            if (str.length &&
                text.length <= str.length &&
                str[0..text.length] == text)
            {
                return text.length;
            }
            return testFail;
        }
    }

    /// Match if testPredicate(str) matches 0 or more times
    template testZeroOrMore(alias testPredicate)
    {
        int testZeroOrMore(string str)
        {
            if (str.length == 0)
                return 0;
            int n = testPredicate(str);
            if (n != testFail)
            {
                int n2 = testZeroOrMore!(testPredicate)(str[n .. $]);
                if (n2 != testFail)
                    return n + n2;
                return n;
            }
            return 0;
        }
    }

    /// Match if term1[0] <= str[0] <= term2[0]
    template testRange(string term1, string term2)
    {
        int testRange(string str)
        {
            if (str.length && str[0] >= term1[0]
                           && str[0] <= term2[0])
                return 1;
            return testFail;
        }
    }

    /// Match if ch[0]==str[0]
    template testChar(string ch)
    {
        int testChar(string str)
        {
            if (str.length && str[0] == ch[0])
                return 1;
            return testFail;
        }
    }

    /// Match if str[0] is a word character
    template testWordChar()
    {
        int testWordChar(string str)
        {
            if (str.length &&
                (
                 (str[0] >= 'a' && str[0] <= 'z') ||
                 (str[0] >= 'A' && str[0] <= 'Z') ||
                 (str[0] >= '0' && str[0] <= '9') ||
                 str[0] == '_'
                )
               )
            {
                return 1;
            }
            return testFail;
        }
    }

    /*****************************************************/

    /**
     * Returns the front of pattern[] up until
     * the end or a special character.
     */

    template parseTextToken(string pattern)
    {
        static if (pattern.length > 0)
        {
            static if (isSpecial!(pattern))
                const string parseTextToken = "";
            else
                const string parseTextToken =
                    pattern[0..1] ~ parseTextToken!(pattern[1..$]);
        }
        else
            const string parseTextToken="";
    }

    /**
     * Parses pattern[] up to and including terminator.
     * Returns:
     *      token[]         everything up to terminator.
     *      consumed        number of characters in pattern[] parsed
     */
    template parseUntil(string pattern,char terminator,bool fuzzy=false)
    {
        static if (pattern.length > 0)
        {
            static if (pattern[0] == '\\')
            {
                static if (pattern.length > 1)
                {
                    const string nextSlice = pattern[2 .. $];
                    alias next = parseUntil!(nextSlice,terminator,fuzzy);
                    const string token = pattern[0 .. 2] ~ next.token;
                    const uint consumed = next.consumed+2;
                }
                else
                {
                    pragma(msg,"Error: expected character to follow \\");
                    static assert(false);
                }
            }
            else static if (pattern[0] == terminator)
            {
                const string token="";
                const uint consumed = 1;
            }
            else
            {
                const string nextSlice = pattern[1 .. $];
                alias next = parseUntil!(nextSlice,terminator,fuzzy);
                const string token = pattern[0..1] ~ next.token;
                const uint consumed = next.consumed+1;
            }
        }
        else static if (fuzzy)
        {
            const string token = "";
            const uint consumed = 0;
        }
        else
        {
            pragma(msg, "Error: expected " ~
                        terminator ~
                        " to terminate group expression");
            static assert(false);
        }
    }

    /**
     * Parse contents of character class.
     * Params:
     *   pattern[] = rest of pattern to compile
     * Output:
     *   fn       = generated function
     *   consumed = number of characters in pattern[] parsed
     */

    template regexCompileCharClass2(string pattern)
    {
        static if (pattern.length > 0)
        {
            static if (pattern.length > 1)
            {
                static if (pattern[1] == '-')
                {
                    static if (pattern.length > 2)
                    {
                        alias termFn = testRange!(pattern[0..1], pattern[2..3]);
                        const uint thisConsumed = 3;
                        const string remaining = pattern[3 .. $];
                    }
                    else // length is 2
                    {
                        pragma(msg,
                          "Error: expected char following '-' in char class");
                        static assert(false);
                    }
                }
                else // not '-'
                {
                    alias termFn = testChar!(pattern[0..1]);
                    const uint thisConsumed = 1;
                    const string remaining = pattern[1 .. $];
                }
            }
            else
            {
                alias termFn = testChar!(pattern[0..1]);
                const uint thisConsumed = 1;
                const string remaining = pattern[1 .. $];
            }
            alias recurse = regexCompileCharClassRecurse!(termFn,remaining);
            alias fn = recurse.fn;
            const uint consumed = recurse.consumed + thisConsumed;
        }
        else
        {
            alias fn = testEmpty!();
            const uint consumed = 0;
        }
    }

    /**
     * Used to recursively parse character class.
     * Params:
     *  termFn = generated function up to this point
     *  pattern[] = rest of pattern to compile
     * Output:
     *  fn = generated function including termFn and
     *       parsed character class
     *  consumed = number of characters in pattern[] parsed
     */

    template regexCompileCharClassRecurse(alias termFn,string pattern)
    {
        static if (pattern.length > 0 && pattern[0] != ']')
        {
            alias next = regexCompileCharClass2!(pattern);
            alias fn = testOr!(termFn,next.fn,pattern);
            const uint consumed = next.consumed;
        }
        else
        {
            alias fn = termFn;
            const uint consumed = 0;
        }
    }

    /**
     * At start of character class. Compile it.
     * Params:
     *  pattern[] = rest of pattern to compile
     * Output:
     *  fn = generated function
     *  consumed = number of characters in pattern[] parsed
     */

    template regexCompileCharClass(string pattern)
    {
        static if (pattern.length > 0)
        {
            static if (pattern[0] == ']')
            {
                alias fn = testEmpty!();
                const uint consumed = 0;
            }
            else
            {
                alias charClass = regexCompileCharClass2!(pattern);
                alias fn = charClass.fn;
                const uint consumed = charClass.consumed;
            }
        }
        else
        {
            pragma(msg,"Error: expected closing ']' for character class");
            static assert(false);
        }
    }

    /**
     * Look for and parse '*' postfix.
     * Params:
     *  test = function compiling regex up to this point
     *  pattern[] = rest of pattern to compile
     * Output:
     *  fn = generated function
     *  consumed = number of characters in pattern[] parsed
     */

    template regexCompilePredicate(alias test, string pattern)
    {
        static if (pattern.length > 0 && pattern[0] == '*')
        {
            alias fn = testZeroOrMore!(test);
            const uint consumed = 1;
        }
        else
        {
            alias fn = test;
            const uint consumed = 0;
        }
    }

    /**
     * Parse escape sequence.
     * Params:
     *  pattern[] = rest of pattern to compile
     * Output:
     *  fn = generated function
     *  consumed = number of characters in pattern[] parsed
     */

    template regexCompileEscape(string pattern)
    {
        static if (pattern.length > 0)
        {
            static if (pattern[0] == 's')
            {
                // whitespace char
                alias fn = testRange!("\x00","\x20");
            }
            else static if (pattern[0] == 'w')
            {
                // word char
                alias fn = testWordChar!();
            }
            else
            {
                alias fn = testChar!(pattern[0 .. 1]);
            }
            const uint consumed = 1;
        }
        else
        {
            pragma(msg,"Error: expected char following '\\'");
            static assert(false);
        }
    }

    /**
     * Parse and compile regex represented by pattern[].
     * Params:
     *  pattern[] = rest of pattern to compile
     * Output:
     *  fn = generated function
     */

    template regexCompile(string pattern)
    {
        static if (pattern.length > 0)
        {
            static if (pattern[0] == '[')
            {
                const string charClassToken =
                    parseUntil!(pattern[1 .. $],']').token;
                alias charClass = regexCompileCharClass!(charClassToken);
                const string token = pattern[0 .. charClass.consumed+2];
                const string next = pattern[charClass.consumed+2 .. $];
                alias test = charClass.fn;
            }
            else static if (pattern[0] == '\\')
            {
                alias escapeSequence =
                    regexCompileEscape!(pattern[1 .. pattern.length]);
                const string token = pattern[0 .. escapeSequence.consumed+1];
                const string next =
                    pattern[escapeSequence.consumed+1 .. $];
                alias test = escapeSequence.fn;
            }
            else
            {
                const string token = parseTextToken!(pattern);
                static assert(token.length > 0);
                const string next = pattern[token.length .. $];
                alias test = testText!(token);
            }

            alias term = regexCompilePredicate!(test, next);
            const string remaining = next[term.consumed .. next.length];

            alias fn = regexCompileRecurse!(term,remaining).fn;
        }
        else
            alias fn = testEmpty!();
    }

    template regexCompileRecurse(alias term,string pattern)
    {
        static if (pattern.length > 0)
        {
            alias next = regexCompile!(pattern);
            alias fn = testUnion!(term.fn, next.fn);
        }
        else
            alias fn = term.fn;
    }

    /// Utility function for parsing
    template isSpecial(string pattern)
    {
        static if (
            pattern[0] == '*' ||
            pattern[0] == '+' ||
            pattern[0] == '?' ||
            pattern[0] == '.' ||
            pattern[0] == '[' ||
            pattern[0] == '{' ||
            pattern[0] == '(' ||
            pattern[0] == ')' ||
            pattern[0] == '$' ||
            pattern[0] == '^' ||
            pattern[0] == '\\'
        )
            const isSpecial = true;
        else
            const isSpecial = false;
    }

## More Template Metaprogramming

1. Tomasz Stachowiak's compile time raytracer.
2. Don Clugston's compile time 99 Bottles of Beer.

## References

[1] D programming language, see http://www.digitalmars.com/d/

[2] Don Clugston's π calculator, see http://trac.dsource.org/projects/ddl/browser/trunk/meta/demo/calcpi.d

[3] Don Clugston's decimaldigit and itoa, see http://trac.dsource.org/projects/ddl/browser/trunk/meta/conv.d

[4] Eric Niebler's Boost.Xpressive regular expression template library is at http://boost-sandbox.sourceforge.net/libs/xpressive/doc/html/index.html

[5] Eric Anderton's Regular Expression template library for D is at http://trac.dsource.org/projects/ddl/browser/trunk/meta/regex.d

## Acknowledgements

I gratefully acknowledge the inspiration and assistance of Don Clugston, Eric Anderton and Matthew Wilson.

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