scholarly journals Beyond the elementary representations of program invariants over algebraic data types

2021 ◽  
Author(s):  
Yurii Kostyukov ◽  
Dmitry Mordvinov ◽  
Grigory Fedyukovich
Keyword(s):  
Data Types ◽  
Algebraic Data Types ◽  
Program Invariants

DERIVING AND SCHEDULING COMMUNICATION OPERATIONS FOR GENERIC SKELETON IMPLEMENTATIONS

2005 ◽  
Vol 15 (03) ◽  
pp. 337-352 ◽  
Author(s):  
THOMAS NITSCHE
Keyword(s):  
Iterative Solution ◽  
Synchronous Communication ◽  
Data Types ◽  
Communication Scheduling ◽  
Overlapping Data ◽  
Abstract Notion ◽  
Algebraic Data Types ◽  
Data Elements ◽  
Communication Operations

Data distributions are an abstract notion for describing parallel programs by means of overlapping data structures. A generic data distribution layer serves as a basis for implementing specific data distributions over arbitrary algebraic data types and arrays as well as generic skeletons. The necessary communication operations for exchanging overlapping data elements are derived automatically from the specification of the overlappings. This paper describes how the communication operations used internally by the generic skeletons are derived, especially for the asynchronous and synchronous communication scheduling. As a case study, we discuss the iterative solution of PDEs and compare a hand-coded MPI version with a skeletal one based on overlapping data distributions.

scholarly journals Stratified type inference for generalized algebraic data types

2006 ◽  
Vol 41 (1) ◽  
pp. 232-244 ◽  
Author(s):  
François Pottier ◽  
Yann Régis-Gianas
Keyword(s):  
Type Inference ◽  
Data Types ◽  
Algebraic Data Types

A fresh look at binary search trees

2002 ◽  
Vol 12 (6) ◽  
pp. 601-607 ◽  
Author(s):  
RALF HINZE
Keyword(s):  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Data Types ◽  
Code Size ◽  
Introductory Computer Science ◽  
Functional Formulation ◽  
Algebraic Data Types ◽  
Science Classes ◽  
Programming Courses

Binary search trees are old hat, aren't they? Search trees are routinely covered in introductory computer science classes and they are widely used in functional programming courses to illustrate the benefits of algebraic data types and pattern matching. And indeed, the operation of insertion enjoys a succinct and elegant functional formulation. Figure 1 contains the six-liner given in the language Haskell 98.Alas, both succinctness and elegance are lost when it comes to implementing the dual operation of deletion, also shown in figure 1. Two additional helper functions are required causing the code size to double in comparison with insertion.

scholarly journals The ins and outs of Clean I/O

1995 ◽  
Vol 5 (1) ◽  
pp. 81-110 ◽  
Author(s):  
Peter Achten ◽  
Rinus Plasmeijer
Keyword(s):  
Programming Languages ◽  
Programming Language ◽  
Functional Programming ◽  
Data Types ◽  
Spreadsheet Program ◽  
Functional Programming Languages ◽  
Hard Time ◽  
Functional Programming Language ◽  
Algebraic Data Types ◽  
High Level

AbstractFunctional programming languages have banned assignment because of its undesirable properties. The reward of this rigorous decision is that functional programming languages are side-effect free. There is another side to the coin: because assignment plays a crucial role in Input/Output (I/O), functional languages have a hard time dealing with I/O. Functional programming languages have therefore often been stigmatised as inferior to imperative programming languages because they cannot deal with I/O very well. In this paper, we show that I/O can be incorporated in a functional programming language without loss of any of the generally accepted advantages of functional programming languages. This discussion is supported by an extensive account of the I/O system offered by the lazy, purely functional programming language Clean. Two aspects that are paramount in its I/O system make the approach novel with respect to other approaches. These aspects are the technique of explicit multiple environment passing, and the Event I/O framework to program Graphical User I/O in a highly structured and high-level way. Clean file I/O is as powerful and flexible as it is in common imperative languages (one can read, write, and seek directly in a file). Clean Event I/O provides programmers with a high-level framework to specify complex Graphical User I/O. It has been used to write applications such as a window-based text editor, an object based drawing program, a relational database, and a spreadsheet program. These graphical interactive programs are completely machine independent, but still obey the look-and-feel of the concrete window environment being used. The specifications are completely functional and make extensive use of uniqueness typing, higher-order functions, and algebraic data types. Efficient implementations are present on the Macintosh, Sun (X Windows under Open Look) and PC (OS/2).

Generic top-down discrimination for sorting and partitioning in linear time

2012 ◽  
Vol 22 (3) ◽  
pp. 300-374 ◽  
Author(s):  
FRITZ HENGLEIN
Keyword(s):  
Linear Time ◽  
Source Code ◽  
Equivalence Relations ◽  
Asymptotic Performance ◽  
Data Types ◽  
Worst Case ◽  
First Order ◽  
Structural Recursion ◽  
Algebraic Data Types ◽  
Abstract Types

AbstractWe introduce the notion ofdiscriminationas a generalization of both sorting and partitioning, and show thatdiscriminators(discrimination functions) can be definedgenerically, by structural recursion on representations oforderingandequivalence relations. Discriminators improve the asymptotic performance of generic comparison-based sorting and partitioning, and can be implemented not to expose more information than the underlying ordering, respectively equivalence relation. For a large class of order and equivalence representations, including all standard orders for regular recursive first-order types, the discriminators execute in the worst-case linear time. The generic discriminators can be coded compactly using list comprehensions, with order and equivalence representations specified using Generalized Algebraic Data Types. We give some examples of the uses of discriminators, including the most-significant digit lexicographic sorting, type isomorphism with an associative-commutative operator, and database joins. Source code of discriminators and their applications in Haskell is included. We argue that built-in primitive types, notably pointers (references), should come with efficient discriminators, not just equality tests, since they facilitate the construction of discriminators for abstract types that are both highly efficient and representation-independent.

Sign in / Sign up

Export Citation Format

Share Document