A framework for working in a functional programming paradigm in R

Description

Provides dispatching implementations suitable for functional programming paradigms. The framework provides a mechanism for attaching guards to functions similar to Erlang, while also providing the safety of assertions reminiscent of Eiffel.

Details

In many ways R is a functional language. The futile.paradigm complements R's functional strengths to make it easier to develop software in this paradigm. This package implements a function dispatching method based on the guard concept (in lieu of direct pattern matching) for functional programming in R. In contrast to UseMethod, which is used for S3 object-oriented method dispatching, futile.paradigm introduces UseFunction for functional programming. Since UseMethod only detects the type of the first argument, dispatching can be tricky/cumbersome when multiple arguments and/or types are supported. Also, the direct manipulation of class attributes is dangerous in the S3 paradigm. In the futile.paradigm, access is restricted via encapsulation to reduce the fragility of such a mechanism. In lieu of the S4 style that requires significant up-front design, the futile.paradigm intends to ease the development process from initial experimentation to systems development. This package provides a richer syntax for defining functions including the constraints that must be satisfied in order to dispatch to the particular function. A happy consequence of this approach is that code becomes self-documenting and functions are more concise since there is a clean separation of concerns between the true logic of a function and the data management tasks within the function.

Concrete implementations of the abstract function, must be defined in a hierarchical naming scheme based on the name of the abstract function. Similar to UseMethod, the concrete function name is derived from the abstract function with a unique suffix separated by a dot. Unlike UseMethod, the suffix is arbitrary as the dispatching and association is controlled by the guard and the number of arguments in the concrete function. Guards are expressions using the same variables as the concrete function variant or explicit functions operating on the same number of arguments as the concrete function it is guarding. Either form of a guard must return a boolean value. Multiple guard functions can be defined in the guard call and in this situation all guards must resolve to TRUE for the function to execute. In addition to a function, a default function can be defined by setting the guard expression to TRUE.

To use the package, two key operators are introduced to implement guard statements and assertions. Guards are declared by using the '%when%' operator, which is reminiscent of the Erlang approach to guards. By convention the guard is declared before the function definition as this communicates immediately the criteria required to execute this particular implementation of the parent function. See the examples section for a trivial implementation.

In addition to guard statements, this package provides post-assertions reminiscent of Eiffel's design-by-contract approach. Using the '%must%' operator validates function outputs and fails if they aren't satisfied. The arguments to a generated assertion are ordered with the result object first (named 'result'), then all of the function arguments.

Conventions: . Types are named in PascalCase . Functions are named in lower case with words separated by underscore . Function namespaces are separated by dot . Declare guard statements before concrete implementations . Declare ensure statements after concrete implementations . Avoid explicit UseFunction definitions . Avoid default function implementations unless a package defines all possible variants

Note

Due to scoping rules with operators, logical expressions need to be wrapped in parentheses.

Author(s)

Brian Lee Yung Rowe

Maintainer: Brian Lee Yung Rowe <r@nurometic.com>

References

Some background on using guards and pattern matching: http://en.wikipedia.org/wiki/Guard_%28computing%29

See Also

UseFunction, %when%, %must%

Examples

# The guard must be defined before the concrete function variant
abs_max %when% is.numeric(a)
abs_max %also% (length(a) > 1)
# This adds a post-assertion to ensure the value is what you expect
abs_max %must% (result > 0)
abs_max %as% function(a) abs_max(a[1], abs_max(a[2:length(a)]))

abs_max %when% (is.numeric(a) && length(a) == 1)
abs_max %must% (result == a)
abs_max %as% function(a) a

abs_max %when% (a %isa% DataObject & a %hasa% data)
abs_max %as% function(a) abs_max(as.numeric(strsplit(a$data, ',')[[1]]))

abs_max %when% (is.numeric(a) & is.numeric(b))
abs_max %must% (result >= a | result >= b)
abs_max %as% function(a, b) max(abs(a), abs(b))

# Using a guard of TRUE acts as a default condition
abs_max %when% TRUE
abs_max %as% function(a,b) abs_max(as.numeric(a), as.numeric(b))

# Define constructor for DataObject
create.DataObject <- function(T, data, name=NA) list(name=name, data=data)

# Test some output
abs_max(2,-3) # Calls abs_max.twoArg

abs_max("3","-4") # Calls abs_max.twoArgDefault

abs_max(3,"-4") # Calls abs_max.twoArgDefault

a <- rnorm(10)
abs_max(a) # Calls abs_max.recursive1

b <- create(DataObject, c('12,-3,-5,8,-13,3,1,3'))
abs_max(b) # Calls abs_max.csv


## Newton-Raphson optimization
converged <- function(x1, x0, tolerance=1e-6) abs(x1 - x0) < tolerance
minimize <- function(x0, algo, max.steps=100)
{
  step <- 0
  old.x <- x0
  while (step < max.steps)
  {
    new.x <- iterate(old.x, algo)
    if (converged(new.x, old.x)) break
    old.x <- new.x
  }
  new.x
}

iterate %when% (algo %isa% NewtonRaphson)
iterate %as% function(x, algo) x - algo$f1(x) / algo$f2(x)

iterate %when% (algo %isa% GradientDescent)
iterate %as% function(x, algo) x - algo$step * algo$f1(x)

create.GradientDescent <- function(T, f1, step=0.01) list(f1=f1,step=step)


fx <- function(x) x^2 - 4
f1 <- function(x) 2*x
f2 <- function(x) 2

algo <- create(NewtonRaphson, f1=f1,f2=f2)
minimize(3, algo)

algo <- create(GradientDescent, f1=f1,step=0.1)
minimize(3, algo)

Results