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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