Fonction d'ordre supérieur | EPFL Graph Search

En mathématiques et en informatique, les fonctions d'ordre supérieur sont des fonctions qui ont au moins une des propriétés suivantes :

elles prennent une ou plusieurs fonctions en entrée ;
elles renvoient une fonction. En mathématiques, on les appelle des opérateurs ou des fonctionnelles. L'opérateur de dérivation en calcul infinitésimal est un exemple classique, car elle associe une fonction (la dérivée) à une autre fonction (la fonction que l'on dérive).

Dans le lambda-calcul non typé, toutes les fonctions sont d'ordre supérieur. Dans le lambda-calcul typé, dont la plupart des langages de programmation fonctionnels sont issus, les fonctions d'ordre supérieur sont généralement celles dont le type contient plus d'une flèche (Flèches dans la programmation fonctionnelle). En programmation fonctionnelle, les fonctions d'ordre supérieur qui retournent d'autres fonctions sont dites curryfiées. La fonction map présente dans de nombreux langages de programmation fonctionnelle est un ex

Compiling Scala for Performance

Iulian Dragos

Scala is a new programming language bringing together object-oriented and functional programming. Its defining features are uniformity and extensibility. Scala offers great flexibility for programmers, allowing them to grow the language through libraries. Oftentimes what seems like a language feature is in fact implemented in a library, effectively giving programmers the power of language designers. The downside of this flexibility is that familiar looking code may hide unexpected performance costs. It is important for Scala compilers to bring down this cost as much as possible. We identify several areas of impact for Scala performance: higher-order functions and closures, and generic containers used with primitive types. We present two complementary approaches for improving performance in these areas: optimizations and specialization. Compiler optimization can bring down the cost through a combination of aggressive inlining of higher-order functions, an extended version of copy-propagation and dead-code elimination. Both anonymous functions and boxing can be eliminated by this approach. We show on a number of benchmarks that these language features can be up to 5 times faster when properly optimized, on current day JVMs. We propose a new approach to compiling parametric polymorphism for performance at primitive types. We mix a homogeneous translation scheme with user-directed specialization for primitive types. Type parameters may be annotated to require specialization of code depending on them. We propose definition-site specialization for primitive types, achieving separate compilation and no boxing when both the definition and call site are specialized. Specialized classes are compatible with unspecialized code, and specialization agnostic code can work with specialized instances, meaning that specialization is opportunistic. We present a formalism of a small subset of Scala with specialization and prove that specialization preserves types. We implemented this translation in the Scala compiler and report on improvements on a set of benchmarks, showing that specialization can make programs more than two times faster.

EPFL2010

Optimizing Higher-Order Functions in Scala

Iulian Dragos

Scala relies on libraries as the default mechanism for language extension. While this provides an elegant solution for growing the language, the performance penalty incurred by call-by-name parameters, boxing and anonymous functions is high. We show that inlining alone is not enough to remove this overhead, and present a solution based on decompilation of library code combined with inlining, dead code elimination, and copy propagation. We evaluate our approach on two language extensions, Java-like assert and C-like for-loops and show improvements of up to 45%.

2008

Fast And Space Efficient Trie Searches

Searching and traversing m-way trees using tries is a well known and broadly used technique. Three algorithms are presented, two have constant insert, search and delete cost, are faster than Hash Trees and can be searched twice as quickly cas Ternary Search Trees (TST). The third has a lg(N) byte compare cost like a TST, but is faster. All require 60% less memory space per node than TST and, unlike Hash Trees, are smoothly extensible and support sorted order functions. The new algorithms defining Array Compacted Trees (ACT), Array Mapped Trees (AMT), Unary Search Trees (UST) and their variants are discussed. These new search trees are applicable in many diverse areas such as high performance IP routers, symbol tables, lexicon scanners and FSA state tables.

2000

Compiling Scala for Performance

Iulian Dragos

EPFL2010