algorithm,swift,recursion , Understanding a recursive function involving generators

## Question:

Tag: algorithm,swift,recursion

I've come across the following recursive algorithm, written here in Swift, that given an array, produces a generator that generates sub-arrays that are one element shorter than the original array. The sub arrays are created by removing one element at every index.

ie input `[1,2,3]` would return a generator that generated `[1,2] [2,3] [1,3]`.

The algorithm works, but I'm having real trouble understanding how. Could someone explain what's happening, or offer advice on how to analyze or understand it? Thanks in advance

``````// Main algorithm
func smaller1<T>(xs:[T]) -> GeneratorOf<[T]> {
if let (head, tail) = xs.decompose {

var gen1:GeneratorOf<[T]> = one(tail)

var gen2:GeneratorOf<[T]> = map(smaller1(tail)) {
smallerTail in
}
return gen1 + gen2
}

return one(nil)
}

// Auxillary functions used
func map<A, B>(var generator:GeneratorOf<A>, f:A -> B) -> GeneratorOf<B> {
return GeneratorOf {
return generator.next().map(f)
}
}

func one<X>(x:X?) -> GeneratorOf<X> {
return GeneratorOf(GeneratorOfOne(x))
}
``````

The code is taken from the book 'Functional Programming in Swift' by Chris Eidhof, Florian Kugler, and Wouter Swierstra

Given an array [a_1,…,a_n], the code:

• Generates the sub-array [a_2,…,a_n];
• For each sub-array B of [a_2,…,a_n] (generated recursively), generates [a_1] + B.

For example, given the array [1,2,3], we:

• Generate [2,3];
• For each sub-array B of [2,3] (namely, [3] and [2]), generate [1] + B (this generates [1,3] and [1,2]).

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