# Re: [isabelle-dev] Of lazy lists and friendly corecs

```Hi Manuel,

```
I've played around a bit with lmerge. It magically works if you replace the selectors with case statements (in Isabelle/5c2c559f01eb):

```
friend_of_corec lmerge :: "int llist ⇒ int llist ⇒ int llist" where
"lmerge xs ys =
(case xs of LNil ⇒ (case ys of LNil ⇒ LNil | LCons y ys' ⇒ LCons y ys')
| LCons x xs' ⇒ (case ys of LNil ⇒ LCons x xs' | LCons y ys' ⇒
if x ≤ y then LCons x (lmerge xs' ys)
else LCons y (lmerge xs ys')))"
subgoal by(subst lmerge.code)(simp split: llist.split)
subgoal by transfer_prover
done

Hope this helps,
Andreas

On 07/10/16 14:22, Manuel Eberl wrote:
```
```Hallo,

I've been playing around with corec and friends in combination with the lazy
lists from
"\$AFP/Coinductive/Coinductive_List" and encountered the following problem:

Suppose I want a function that takes two (implicitly sorted) lazy lists and
merges them in
the following fashion:

primcorec lmerge :: "int llist ⇒ int llist ⇒ int llist" where
"lmerge xs ys = (if lnull xs then ys
else if lnull ys then xs
else if lhd xs ≤ lhd ys then LCons (lhd xs) (lmerge (ltl xs)
ys)
else LCons (lhd ys) (lmerge xs (ltl ys)))"

I've still not fully understood what ‘friendly’ means, but I should be very
surprised if
this function were not friendly. So I tried this:

friend_of_corec lmerge where
"lmerge xs ys = (if lnull xs ∧ lnull ys then LNil
else if lnull xs then LCons (lhd ys) (ltl ys)
else if lnull ys then LCons (lhd xs) (ltl xs)
else if lhd xs ≤ lhd ys then LCons (lhd xs) (lmerge (ltl xs)
ys)
else LCons (lhd ys) (lmerge xs (ltl ys)))"

Unfortunately, I get the following error:

exception TYPE raised (line 168 of "consts.ML"): Illegal type for constant
"Coinductive_List.llist.LNil" :: 'b

I now have the following questions:
1. Something like "if lnull xs then ys" works in primcorec, but in corec and
friend_of_corec I have to do odd things like "LCons (lhd ys) (ltl ys)". Is that
a known
limitation?
2. What is the relationship between primcorec and friendliness? If I have a
function
defined by primcorec, is the additional step with friend_of_corec fundamentally
necessary
or is that just a technical issue? (I would have naïvely assumed that
primitively-corecursive functions are always friendly or something like that)
3. What causes the above error and how do I get around it?

Cheers,

Manuel

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