[Agda] difficult "unsolved metas"
Serge D. Mechveliani
mechvel at botik.ru
Thu Feb 7 17:45:41 CET 2013
People,
I am stuck with a program that forms sub-DSet -- something similar to
sub-DecSetoid, defined by a membership predicate.
Agda-2.3.2 MAlonzo (lib-0.7)
reports of "unsolved metas" for the last line of the code.
So far, I do not find, how to fix the code.
The program uses the type constructor ->c for congruent maps,
imported from Function.Equality (and renamed to ->c).
"unsolved metas" is reported exactly for the line of "cong = eCong"
in the final fragment of
...
eTo : sub-Setoid ->c baseSetoid
eTo = record{ _($)_ = fromSub -- : subCarrier -> baseCarrier
; cong = eCong }
where
eCong : _=s_ =[ fromSub ]=> _\equiv_
eCong {x} {y} x-=s-y = ...
This record is required by Function.Equality._->_,
and eCong needs to express that fromSub preserves the equivalence
with respect to _=s_ on subCarrier and _\equiv_ on baseCarrier
-- which part must be most trivial in this case.
The report preserves independently on whether the implementation for
eCong is given or it is postulated as
postulate eCong : _=s_ =[ fromSub ]=> _\equiv_
The code is still simplified as contrived, and does not exactly serve
the initial need of sub-DSet (`Injection' is skipped, and other parts),
because I needed to reduce the example.
This precise code (about 170 lines) is
attached to this letter as Main.agda.zip
-- 2 Kb archive.
(Is a 2 Kb attachement large to send to this list?,
for I could alternatively put it to a public domain).
Can you, please, help with solving these "unsolved metas" ?
Thanks,
------
Sergei
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