5th MaCS Debrecen On the Turing-Completeness of Generative Metaprograms Zoltán Porkoláb, István Zólyomi Dept. of Programming Languages and Compilers Eotvos University, Budapest

25th MaCSDebrecen 2004 Agenda I always knew C++ templates were the work of the Devil, and now I'm sure... - Cliff Click cited by Todd Veldhuisen Generative program constructions Metaprograms Power of generative metaprograms Sample usages Open questions

35th MaCSDebrecen 2004 Generative constructions Widely used in modern programming languages: Smalltalk, Lisp, other functional langs. Eiffel ADA generics C++ templates Java generics: Pizza, GJ, Java 1.5 C#: soon

45th MaCSDebrecen 2004 Why generics? Conventional techniques are working only for complete types. int max( int a, int b) { if ( a > b ) return a; else return b; if ( a > b ) return a; else return b;} double max( double a, double b) { if ( a > b ) return a; else return b; if ( a > b ) return a; else return b;}Etc… class date { //… //… }; date d = max ( d1, d2);

55th MaCSDebrecen 2004 Preprocessor Macro? Ada generics : "a restricted form of context-sensitive macro facility" C++ templates: "a clever kind of macro that obeys the scope, naming, and type rules of C++" #define MAX(a,b) a > b ? a : b Works, because a macro is - typeless. Processed not by the compiler, therefore there are a number of "secondary effect": MAX( x, y)*2 x > y ? x : y*2 x > y ? x : y*2 MAX( ++x, y) ++x > y ? ++x : y

65th MaCSDebrecen 2004 Generative constructions void swap( int& x, int& y) void swap( int& x, int& y) { int temp = x; // !! how to detect type of x? int temp = x; // !! how to detect type of x? x = y; y = temp; x = y; y = temp; } Does not works: a macro is - typeless. We need a facility to use type parameters. template void swap( T& x, T& y) { T temp = x; x = y; y = temp; } Template depends only on the properties that is actually used Does not require different types used as arguments to be explicitly related. In particular, the argument types used as a template need not be from a single inheritance hierarchy.

75th MaCSDebrecen 2004 C++ Function Templates 1. Template is not a single function Rather a schema to instantiate functions on request template T max( T a, T b) { if ( a > b ) return a; if ( a > b ) return a; else return b; else return b;} int i = 3, j = 6, k; k = max(i,j); double x = 3.14, y = 4.15, z; z = max(x,y); Parameter deduction Template instantiation

85th MaCSDebrecen 2004 C++ Function Templates 2. Instantiation in compile-time Then strong type system rules are applied int i = 3; double y = 3.14, z; z = max(i,y); template T max( T a, S b) { if ( a > b ) return a; if ( a > b ) return a; else return b; else return b;} z == 3; No deduction on return type No runtime information could be used

95th MaCSDebrecen 2004 C++ Function Templates 3. Explicit specialization int i = 3; double y = 3.14, z; template template R max( T a, S b) { if ( a > b ) return a; if ( a > b ) return a; else return b; else return b;} z = max (i,y); Template overloading

105th MaCSDebrecen 2004 C++ Function Templates 4. User specialization const char *s1 = “Hello”; const char *s2 = “world”; template <> const char * max( const char *a, const char *b) { if ( strcmp(a,b) < 0 ) return a; if ( strcmp(a,b) < 0 ) return a; else return b; else return b;} The compiler selects the most specific matching type cout << max (4,5); cout (3.14,’6’); cout << max (“this”, “greater”);

115th MaCSDebrecen 2004 C++ Class Templates 1. Similar way template class matrix { public: matrix( int i, int j ); matrix( int i, int j ); matrix( const matrix &other) matrix( const matrix &other) ~matrix(); ~matrix(); matrix& operator=( const matrix &other); matrix& operator=( const matrix &other);private: vector v; vector v;}; Created always with explicit specialisation matrix m(4,5);

125th MaCSDebrecen 2004 C++ Class Templates 2. User specialization template <> class matrix template <> class matrix { public: matrix( int i, int j ); matrix( int i, int j ); matrix( const matrix &other) matrix( const matrix &other) ~matrix(); ~matrix(); matrix& operator=( const matrix &other); matrix& operator=( const matrix &other);private: a_better_representation v; a_better_representation v;}; Used the same way matrix m(4,5);

135th MaCSDebrecen 2004 C++ Class Templates 3. Partial specialization template class C { //... //... }; template class C template class C { //... //... }; The most specific matching will be applied C a; C b;

145th MaCSDebrecen 2004 C++ Templates The C++ templates were first implemented in the early ’90s Accepted as part of the ANSI/ISO in 1994 Erwin Unruh: 1994 unruh.cpp 30: conversion from enum to D requested

155th MaCSDebrecen 2004 Power of C++ templates The C++ templates are Turing-complete The Compiler “executes” template metaprograms The result is a non-templated program executed in “run-time” In 1966 Böhm and Jacopini proved: Turing machine implementation conditional and looping constructions Turing machine implementation conditional and looping constructions

165th MaCSDebrecen 2004 The Factorial example int factorial( int n) { return (n==0) ? 1 : n*factorial(n-1); return (n==0) ? 1 : n*factorial(n-1);} int main() { cout << factorial(15) << endl; cout << factorial(15) << endl; return 0; return 0;} template struct Factorial { enum { value = N * Factorial ::value }; enum { value = N * Factorial ::value };}; template <> struct Factorial { enum { value = 1 }; enum { value = 1 };}; int main() { const int fact5 = Factorial ::value; const int fact5 = Factorial ::value; std::cout << fact5 << endl; std::cout << fact5 << endl; return 0; return 0;}

175th MaCSDebrecen 2004 Conditional statement template template struct IF { typedef Then RET; typedef Then RET;}; template template struct IF struct IF { typedef Else RET; typedef Else RET;}; template template IF ::RET max(T t, S s) { if (t > s) return t; if (t > s) return t; else return s; else return s;}

185th MaCSDebrecen 2004 Higher order metaprograms accumulate(n,f) := f(0) + f(1) f(n) template class F> struct Accumulate { enum { RET = Accumulate ::RET + F ::RET }; enum { RET = Accumulate ::RET + F ::RET };}; template class F> struct Accumulate template class F> struct Accumulate { enum { RET = F ::RET }; enum { RET = F ::RET };}; template struct Square { enum { RET = n*n }; enum { RET = n*n };}; cout ::RET ::RET << endl;

195th MaCSDebrecen 2004 Programs vs. Metaprograms Function (runtime) Data VariableAssignmentConditionLoopClass Type and constant Symbolic names Const initialization enumerated values enumerated valuesRecursion

205th MaCSDebrecen 2004 Generative Metaprograms 1. metaprogramming: writing programs that represent and manipulate other programs or themselves (ie:reflection). Metaprograms are programs about programs. introspection: the ability of a program to observe its own state the ability of a program to observe its own state intercession: the ability to modify its own state the ability to modify its own state Open compilers: transformations on AST Hygenic macros Two level languages: Aspect J

215th MaCSDebrecen 2004 Generative Metaprograms 2. Dynamic languages (Smalltalk, Lisp, etc.) high level reflection Smalltalk: classes are objects of metaobjects methods, execution stack, etc. are represented by objects high level reflection Smalltalk: classes are objects of metaobjects methods, execution stack, etc. are represented by objectsJava provides lower level reflection C++ RTTI much lower level: (typeid)

225th MaCSDebrecen 2004 Main areas Expression templates Static interface checking Concept cheking Extend existing type system ???

235th MaCSDebrecen 2004 Expression templates Improve efficiency of programs Save space and / or time Keep the code correctly organized Supercomputing, numerical computing

245th MaCSDebrecen 2004 Expression templates Array a, b, c, d, e; // Object-oriented way of a = b + c + d + e double* _t1 = new double[N]; for ( int i=0; i<N; ++i) _t1[i] = b[i] + c[i]; double* _t2 = new double[N]; for ( int i=0; i<N; ++i) _t2[i] = _t1[i] + d[i]; double* _t3 = new double[N*M]; for ( int i=0; i<N; ++i) _t3[i] = _t2[i] + e[i]; for ( int i=0; i<N; ++i) a[i] = _t3[i]; delete [] _t3; delete [] _t2; delete [] _t1; // Fortran like solution: for ( int i=0; i<N; ++i) a[i] = b[i] + c[i] + d[i] + e[i];

255th MaCSDebrecen 2004 Concept checking interface Cloneable { T* T::Clone() const; T* T::Clone() const;} template class C { // T must provide T* T::Clone() const... // T must provide T* T::Clone() const...} template class C {public: void SomeFunc( const T* t) { t->Clone(); } void SomeFunc( const T* t) { t->Clone(); }};

265th MaCSDebrecen 2004 Extendig type system Family polymorphism Eric Ernst Eric Ernst Generic-Beta Generic-Beta Structural subtyping

275th MaCSDebrecen 2004 Structural subtyping Example from Harold Osher Example from Harold Osher OpEval PlusCheckPlusEval Operator Plus OpCheckOpDisplay PlusDisplay

285th MaCSDebrecen 2004 Open questions The real expressive power Standard tools but: Loki from Andrei Alexandrescu but: Loki from Andrei AlexandrescuGarantees How to design How to debug