I'm trying to define primitive recursion in term of foldr
, as explained in A tutorial on the universality and expressiveness on fold chapter 4.1.
Here is first attempt at it
simpleRecursive f v xs = fst $ foldr g (v,[]) xs
where
g x (acc, xs) = (f x xs acc,x:xs)
However, above definition does not halt for head $ simpleRecursive (\x xs acc -> x:xs) [] [1..]
Below is definition that halt
simpleRecursive f v xs = fst $ foldr g (v,[]) xs
where
g x r = let (acc,xs) = r
in (f x xs acc,x:xs)
Given almost similar definition but different result, why does it differ? Does it have to do with how Haskell pattern match?
The crucial difference between the two functions is that in
g x r = let (acc, xs) = r
in (f x xs acc, x:xs)
The pattern match on the tuple constructor is irrefutable, whereas in
g x (acc, xs) = (f x xs acc, x:xs)
it is not. In other words, the first definition of g
is equivalent to
g x ~(acc, xs) = (f x xs acc, x:xs)