03.org

construir

construir <- function(l, v)
{
    if (length(l) == 0) return(c())
    cabeca <- head(l, n=1)[[1]];
    resto <- tail(l, n=length(l)-1)
    return(c(cabeca(v), construir(resto, v)))
}

f <- function (x) x*x
g <- function (x) x*x*x
h <- function (x) x*x*x*x

l <- c(f, g, h);

construir(l, 2)

[1]  4  8 16

construirdois

construirdois <- function(l, ...)
{
    if (length(l) == 0) return(c())
    cabeca <- head(l, n=1)[[1]];
    resto <- tail(l, n=length(l)-1)
    return(c(cabeca(...), construirdois(resto, ...)))
}

construirdois(l, c(2,3))

[1]  4  9  8 27 16 81

duplica

duplica <- function (l)
{
    unlist(lapply(l, function(x) x*2));
}
duplica (c(1,2,3))

[1] 2 4 6

soma

soma <- function(l)
{
    accum = 0;

    somainterna <- function(l, accum)
    {
        if (length(l) == 0) return(accum);
        cabeca <- head(l, n=1)[[1]];
        accum <- accum + cabeca;
        resto <- tail(l, n=length(l)-1)
        return(somainterna(resto, accum))
    }


    return(somainterna(l, accum));
}
soma(c(1,2,3));

[1] 6

positivos

positivos <- function (l)
{
    if (length(l) == 0) return(c());
    cabeca <- head(l, n=1)[[1]];
    resto <- tail(l, n=length(l)-1)
    if(cabeca > 0){
        return(c(TRUE, positivos(resto)));
    }else{
        return(c(FALSE, positivos(resto)));
    }
}

positivos <- function(l)
{
    unlist(lapply(l, function(x) ifelse(x < 0, FALSE, TRUE)))
}

positivos(c(-1, 2, -4))

[1] FALSE  TRUE FALSE

norma

A solução abaixo usa:

• a função expoente, do CATP anterior, e
• a soma deste CATP.

norma <- function(l)
{
    expoente <- function (lista, expo)
    {
        len = length(lista);
        if (len == 0) return(list());

        h <- head(lista, n = 1);
        t <- tail(lista, n = len-1)

        l <- c(unlist(h) ^ expo, expoente(t, expo))
        return(unlist(l));
    }

    soma <- function(l)
    {
        accum = 0;

        somainterna <- function(l, accum)
        {
            if (length(l) == 0) return(accum);
            cabeca <- head(l, n=1)[[1]];
            accum <- accum + cabeca;
            resto <- tail(l, n=length(l)-1)
            return(somainterna(resto, accum))
        }


        return(somainterna(l, accum));
    }
    l1 <- expoente (l, 2);
    return(sqrt(soma(l1)))
}

norma(c(0.1, 0.2, 0.3, 0.4));

[1] 0.5477226