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This brief tutorial illustrates how to combine S4 object oriented capabilities with function closures in order to develop classes with built in methods. Thanks to

Hadley Wickhamfor the great contribution of material and tutorials made available on the web and toBill VenablesandStefano Iacusfor their kind reviews.

## Regular polygons

As Wikipedia states:

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Square, pentagon, hexagon are regular polygons.

In order to define a regular polygon we need to state the number of sides the polygon is made of (n) and the dimension of its side (s).

## S4

We want to define a define a simple S4 based system to create and plot of regular polygons.

As a first step we define a very simple class for regular polygons, say rolygon, as:

^{?}View Code R

> setClass("rolygon", representation(n = "numeric", + s = "numeric")) |

In order to plot our rolygons we need a plot method for class rolygon. By mean of basic trigonometry we get:

^{?}View Code R

> setMethod(f = "plot", signature = "rolygon", + definition = function(x, y) { + object = x + s = [email protected] + n = [email protected] + rho = (2*pi)/n + h = .5*s*tan((pi/2)-(pi/n)) + r = sqrt(h^2+(s/2)^2) + sRho = ifelse(n %% 2 == 0, + (pi/2- rho/2), pi/2) + cumRho = cumsum(c(sRho, rep(rho, n))) + cumRho = ifelse(cumRho > 2*pi, + cumRho-2*pi, cumRho) + x = r*cos(cumRho) + y = r*sin(cumRho) + par(pty = "s") + plot(x, y, type = "n", xlab = "", ylab = "") + lines(x, y, col = "red", lwd = 2) + points(0, 0, pch = 16, col = "red") + grid() + invisible(NULL) + }) [1] "plot" |

And, as a result:

^{?}View Code R

> plot(new("rolygon", n = 5, s = 2)) |

## Function Closures

The *R Language Definition* manual states:

Functions … have three basic components: a formal argument list, a body and an environment. A function’s environment is the environment that was active at the time that the function was created. Any symbols bound in that environment are captured and available to the function. This combination of the code of the function and the bindings in its environment is called a ‘function closure’, a term from functional programming theory.

Moreover, any time a function is called, a new environment is created, whose enclosure is the environment where the function was defined. The computation, as expressed by the body of the function, occurs in the newly created environment. Thus, whenever we call a function we have at least two environments: the environment the function was defined in and the environment where the function evaluation takes place.

By using this idea, we can define a function `f()`

that returns a function `g()`

. As `g()`

is created within the evaluation environment of `f()`

, this last environment is the enclosure of `g()`

. Therefore, `g()`

remembers all symbols bound in that environment.

As a practical application of this idea consider this function:

^{?}View Code R

> f <- function(x) { + g = function(y){x+y} + g } |

As `g()`

is created within the evaluation environment of `f()`

, `g()`

“remembers” the value of x. Therefore we can define a simple function `f1()`

that adds one to the given `y`

argument as:

^{?}View Code R

> f1 <- f(x = 1) > f1(y = 3) |

Note that `f1()`

remembers the value of `x`

. As a result:

^{?}View Code R

> ls(env=environment(f1)) [1] "g" "x" > get("x", env=environment(f1)) [1] 1 |

The environment of `f1()`

can be directly accessed and manipulated:

^{?}View Code R

> environment(f1)$x <- 0 > f1(1) [1] 1 |

Clearly, the same exercise apply to any `fx()`

as:

^{?}View Code R

> f99 <- f(99) > f99(y = 1) [1] 100 |

Clearly this is a good way to avoid code duplication.

## Putting all together

Finally, the combination of the two previous ideas allows quite interesting coding techniques.

In this case we want to generate a set of functions each of them returning a regular polygon: square, pentagon, etc …, with a built in `plot`

method.

Thus, we first define a `rolygon()`

function that returns a generic `f()`

capable of generating specific regular polygons with plot method inherited from rolygon’s environment:

^{?}View Code R

> rolygon <- function(n) { + + # Define rolygon class + setClass("rolygon", representation( + n = "numeric", s = "numeric")) + + # Define a plot method for object of class rolygon + setMethod(f = "plot", signature = "rolygon", + definition = function(x, y){ + object <- x + s <- [email protected] + n <- [email protected] + pi <- base::pi + rho <- (2*pi)/n + h <- .5*s*tan((pi/2)-(pi/n)) + r <- sqrt(h^2+(s/2)^2) + sRho <- ifelse(n %% 2 == 0, + (pi/2- rho/2), pi/2) + cumRho <- cumsum(c(sRho, rep(rho, n))) + cumRho <- ifelse(cumRho > 2*pi, + cumRho-2*pi, cumRho) + x <- r*cos(cumRho) + y <- r*sin(cumRho) + par(pty = "s") + plot(x, y, type = "n", xlab = "", + ylab = "") + lines(x, y, col = "red", lwd = 2) + points(0, 0, pch = 16, col = "red") + grid() + invisible(NULL) + }) + + # Define a function that returns an object + # of class rolygon + f <- function(s){new("rolygon", n = n, + s = s)} + + # Return the newly created function + return(f) + } |

Note that class `rolygon`

, its `plot`

method and `f()`

are all defined within the evaluation environment of `rolygon()`

. When `rolygon()`

is evaluated, `f()`

is returned and `f()`

remembers about class `rolygon`

and its plotting method.

As a result, we can define an `heptagon()`

function as:

^{?}View Code R

> heptagon <- rolygon(n = 7) |

a specific heptagon of `side = 1`

becomes:

^{?}View Code R

> e1 <- heptagon(1) |

as `heptagon()`

has a `plot`

method built in, we only need:

^{?}View Code R

> plot(e1) |

Finally with a bit of imagination:

^{?}View Code R

> circumference <- rolygon(n = 10^4) > plot(circumference(s = base::pi/10^4)) |

View (and download) the full code:

^{?}Download closures.R

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### Function Closures and S4 Methods ### Andrea Spano', [email protected] ### www.milanor.net ### setClass setClass("rolygon", representation(n = "numeric", s = "numeric")) ### setMethod setMethod(f = "plot", signature = "rolygon", definition = function(x, y){ object = x s = [email protected] n = [email protected] rho = (2*pi)/n h = .5*s*tan((pi/2)-(pi/n)) r = sqrt(h^2+(s/2)^2) sRho = ifelse(n %% 2 == 0, (pi/2- rho/2), pi/2) cumRho = cumsum(c(sRho, rep(rho, n))) cumRho = ifelse(cumRho > 2*pi, cumRho-2*pi, cumRho) x = r*cos(cumRho) y = r*sin(cumRho) par(pty = "s") plot(x, y, type = "n", xlab = "", ylab = "") lines(x, y, col = "red", lwd = 2) points(0, 0, pch = 16, col = "red") grid() invisible(NULL) }) ### rolygon plot(new("rolygon", n = 5, s = 2)) ### f f <- function(x) { g = function(y){x+y} g } ### f1 f1 <- f(x = 1) f1(y = 3) ### ls ls(env=environment(f1)) get("x", env=environment(f1)) ### environment environment(f1)$x <- 0 f1(1) ### f99 f99 <- f(99) f99(y = 1) ### rolygon rolygon <- function(n) { # Define rolygon class setClass("rolygon", representation( n = "numeric", s = "numeric")) # Define a plot method for object of class rolygon setMethod(f = "plot", signature = "rolygon", definition = function(x, y){ object <- x s <- [email protected] n <- [email protected] pi <- base::pi rho <- (2*pi)/n h <- .5*s*tan((pi/2)-(pi/n)) r <- sqrt(h^2+(s/2)^2) sRho <- ifelse(n %% 2 == 0, (pi/2- rho/2), pi/2) cumRho <- cumsum(c(sRho, rep(rho, n))) cumRho <- ifelse(cumRho > 2*pi, cumRho-2*pi, cumRho) x <- r*cos(cumRho) y <- r*sin(cumRho) par(pty = "s") plot(x, y, type = "n", xlab = "", ylab = "") lines(x, y, col = "red", lwd = 2) points(0, 0, pch = 16, col = "red") grid() invisible(NULL) }) # Define a function that returns an object # of class rolygon f <- function(s){new("rolygon", n = n, s = s)} # Return the newly created function return(f) } ### heptagon heptagon <- rolygon(n = 7) e1 <- heptagon(1) plot(e1) ### circumference circumference <- rolygon(n = 10^4) plot(circumference(s = base::pi/10^4)) |

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