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Last update Thu Jul 19 00:06:36 2007

# 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

## 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 Foo!(int,char) f;
    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 A.Foo!(int).bar 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 a class that
                    // implements interface I
      char[] string = "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, 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> 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; }

    typedef double A;

    class B(T)
    {
      typedef int A;
    }

    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()
    {
      writefln(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 if`'s 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

## SFINAE (Substitution Failure Is Not An Error)

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 char[] decimalDigit = "0123456789"[n..n+1];
    }

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

    char[] 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 .. length], 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(char[] pattern)
    {
      char[][] regexMatch(char[] str)
      {
        char[][] 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:
     *	char[] 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(char[] str) { return 0; }
    }

    /// Match if testFirst(str) and testSecond(str) match
    template testUnion(alias testFirst, alias testSecond)
    {
      int testUnion(char[] 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(char[] text)
    {
      int testText(char[] 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(char[] 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(char[] term1, char[] term2)
    {
      int testRange(char[] str)
      {
        if (str.length && str[0] >= term1[0]
                       && str[0] <= term2[0])
          return 1;
        return testFail;
      }
    }

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

    /// Match if str[0] is a word character
    template testWordChar()
    {
      int testWordChar(char[] 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(char[] pattern)
    {
      static if (pattern.length > 0)
      {
        static if (isSpecial!(pattern))
          const char[] parseTextToken = "";
        else
          const char[] parseTextToken =
               pattern[0..1] ~ parseTextToken!(pattern[1..$]);
      }
      else
        const char[] parseTextToken="";
    }

    /**
     * Parses pattern[] up to and including terminator.
     * Returns:
     *	token[]	 	everything up to terminator.
     *	consumed	number of characters in pattern[] parsed
     */
    template parseUntil(char[] pattern,char terminator,bool fuzzy=false)
    {
      static if (pattern.length > 0)
      {
        static if (pattern[0] == '\\')
        {
          static if (pattern.length > 1)
          {
            const char[] nextSlice = pattern[2 .. $];
            alias parseUntil!(nextSlice,terminator,fuzzy) next;
            const char[] 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 char[] token="";
          const uint consumed = 1;
        }
        else
        {
          const char[] nextSlice = pattern[1 .. $];
          alias parseUntil!(nextSlice,terminator,fuzzy) next;
          const char[] token = pattern[0..1] ~ next.token;
          const uint consumed = next.consumed+1;
        }
      }
      else static if (fuzzy)
      {
        const char[] 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(char[] pattern)
    {
      static if (pattern.length > 0)
      {
        static if (pattern.length > 1)
        {
          static if (pattern[1] == '-')
          {
            static if (pattern.length > 2)
            {
              alias testRange!(pattern[0..1], pattern[2..3]) termFn;
              const uint thisConsumed = 3;
              const char[] remaining = pattern[3 .. $];
            }
            else // length is 2
            {
              pragma(msg,
                "Error: expected char following '-' in char class");
              static assert(false);
            }
          }
          else // not '-'
          {
            alias testChar!(pattern[0..1]) termFn;
            const uint thisConsumed = 1;
            const char[] remaining = pattern[1 .. $];
          }
        }
        else
        {
          alias testChar!(pattern[0..1]) termFn;
          const uint thisConsumed = 1;
          const char[] remaining = pattern[1 .. $];
        }
        alias regexCompileCharClassRecurse!(termFn,remaining) recurse;
        alias recurse.fn fn;
        const uint consumed = recurse.consumed + thisConsumed;
      }
      else
      {
        alias testEmpty!() fn;
        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,char[] pattern)
    {
      static if (pattern.length > 0 && pattern[0] != ']')
      {
        alias regexCompileCharClass2!(pattern) next;
        alias testOr!(termFn,next.fn,pattern) fn;
        const uint consumed = next.consumed;
      }
      else
      {
        alias termFn fn;
        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(char[] pattern)
    {
      static if (pattern.length > 0)
      {
        static if (pattern[0] == ']')
        {
          alias testEmpty!() fn;
          const uint consumed = 0;
        }
        else
        {
          alias regexCompileCharClass2!(pattern) charClass;
          alias charClass.fn 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, char[] pattern)
    {
      static if (pattern.length > 0 && pattern[0] == '*')
      {
        alias testZeroOrMore!(test) fn;
        const uint consumed = 1;
      }
      else
      {
        alias test fn;
        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(char[] pattern)
    {
      static if (pattern.length > 0)
      {
        static if (pattern[0] == 's')
        {
          // whitespace char
          alias testRange!("\x00","\x20") fn;
        }
        else static if (pattern[0] == 'w')
        {
          //word char
          alias testWordChar!() fn;
        }
        else
        {
          alias testChar!(pattern[0 .. 1]) fn;
        }
        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(char[] pattern)
    {
      static if (pattern.length > 0)
      {
        static if (pattern[0] == '[')
        {
          const char[] charClassToken =
              parseUntil!(pattern[1 .. $],']').token;
          alias regexCompileCharClass!(charClassToken) charClass;
          const char[] token = pattern[0 .. charClass.consumed+2];
          const char[] next = pattern[charClass.consumed+2 .. $];
          alias charClass.fn test;
        }
        else static if (pattern[0] == '\\')
        {
          alias regexCompileEscape!(pattern[1..pattern.length]) escapeSequence;
          const char[] token = pattern[0 .. escapeSequence.consumed+1];
          const char[] next =
              pattern[escapeSequence.consumed+1 .. $];
          alias escapeSequence.fn test;
        }
        else
        {
          const char[] token = parseTextToken!(pattern);
          static assert(token.length > 0);
          const char[] next = pattern[token.length .. $];
          alias testText!(token) test;
        }

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

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

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

    /// Utility function for parsing
    template isSpecial(char[] 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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