This commit adds full universe polymorphism and fast projections to Coq.

Add [Polymorphic] and [Monomorphic] local flag for definitions as well as
[Set Universe Polymorphism] global flag to make all following definitions
polymorphic. Mainly syntax for now.

First part of the big changes to the kernel:
- Const, Ind, Construct now come with a universe level instance
- It is used for type inference in the kernel, which now also takes
a graph as input: actually a set of local universe variables and their
constraints. Type inference just checks that the constraints are enough
to satisfy its own rules.
- Remove polymorphic_arity and _knowing_parameters everywhere: we
don't need full applications for polymorphism to apply anymore, as
we generate fresh variables at each constant/inductive/constructor
application. However knowing_parameters variants might be reinstated
later for optimization.
- New structures exported in univ.mli:
  - universe_list for universe level instances
  - universe_context(_set) for the local universe constraints, also
recording which variables will be local and hence generalized after
inference if defining a polymorphic ind/constant.
- this patch makes coq stop compiling at indtypes.ml

Adapt kernel, library, pretyping, tactics and toplevel to universe polymorphism.
Various degrees of integration, places where I was not sure what to do or
just postponed bigger reorganizations of the code are marked with FIXMEs.
Main changes:
- Kernel now checks constraints and does not infer them anymore.
- The inference functions produce a context of constraints that were checked
during inference, useful to do double-checking of the univ. poly. code
but might be removed later.
- Constant, Inductive entries now have a universe context (local variables
and constraints) associated to them.
- Printing, debugging functions for the new structures are also implemented.
- Now stopping at Logic.v
- Lots of new code in kernel/univ.ml that should be reviewed.
- kernel/indtypes probably does not do what's right when inferring inductive
type constraints.
- Adapted evd to use the new universe context structure.
- Did not deal with unification/evar_conv.

- Add externalisation code for universe level instances.
- Support for polymorphism in pretyping/command and proofs/proofview etc.
  Needed wrapping of [fresh_.._instance] through the evar_map, which
  contains the local state of universes during type-checking.
- Correct the inductive scheme generation to support polymorphism as well.
- Have to review kernel code for correctness, and especially rework the
  computation of universe constraints for inductives.
Stops somewhat later in Logic.v

- Fix naming of local/toplevel universes to be correctly done at typechecking time:
  local variables have no dirpath.
- Add code to do substitution of universes in modules, not finished yet.
- Move fresh_* functions out of kernel, it won't ever build a universe level again!
- Adapt a lot of new_Type to use the correct dirpath and declare the new types in the evar_map
so we keep track of them.
- A bit of code factorization (evd_comb moved, pretype_global).

- Refactor more code
- Adapt plugins code (sometimes wrong, marked with FIXME)
- Fix cases generating unneeded universe (not sure it's ok though)
- Fix scheme generation for good, might have opportunity to cleanup
the terms later.

Init compiles now (which means rewrite, inversion, elim etc.. work as well).
- Unsolved issue of pretyping to lower sorts properly (to Prop for example).
  This has to do with the (Retyping.get_type_of) giving algebraic universes that
  would appear on the right of constraints.
  This makes checking for dangling universes at the end of pretyping fail,
  hence the check in kernel/univ was removed. It should come back when we have
  a fix for this.
- Correctly (?) compute the levels of inductive types.
  Removed old code pertaining to universe polymorphism. Note that we generate
  constraint variables for the conclusion of inductive types invariably.
- Shrink constraints before going to the kernel, combine substitution of the
  smaller universe set with normalization of evars (maybe not done everywhere,
  only ordinary inductives, definitions and proofs)
- More API reworks overall. tclPUSHCONTEXT can be used to add fresh universes
  to the proof goal (used in a few places to get the right instance.
- Quick fix for auto that won't work in the long run. It should always have been
  restricted to take constant references as input, without any loss of generality
  over constrs.

Fix some plugins and insertion of non-polymorphic constants in a module.
Now stops in relation classes.

Cleanup and move code from kernel to library and from pretyping to library too.
Now there is a unique universe counter declared in library/universes.ml along
with all the functions to generate new universes and get fresh constant/inductive
terms.
- Various function renamings
- One important change in kernel/univ.ml: now [sup] can be applied to Prop.
- Adapt records/classes to universe polymorphism
- Now stops in EqDepFacts due to imprecise universe polymorphism.

Forgot to git add those files.

interp_constr returns the universe context

The context is then pushed through the environment (or proof goal
sigma).
- Fix insertion of constants/inductives in env, pushing constraints to
the global env for non-polymorphic ones.
- Add Prop as a universe level to do proper type inference with sorts.
It is allowed to take [sup] of [Prop] now.
- New nf_evar based on new Evd.map(_undefined)
- In proofs/logic.ml: conv_leq_goal might create some constraints that
are now recorded.
- Adapt Program code to universes.

Merge with latest trunk + fixes

-Use new constr_of_global from universes
- fix eqschemes to use polymorphic universes
- begin fixing cctac but f_equal still fails
- fix [simpl] and rest of tacred
- all the eq_constr with mkConst foo should be fixed as well, only
partially done

- Fix term hashing function to recognize equal terms up to universe instances.
- Fix congruence closure to equate terms that differ only in universe instances,
these will be resolved by constraints.

Add a set of undefined universe variables to unification.
Universe variables can now be declared rigid or flexible (unifiable).
Flexible variables are resolved at the end of typechecking by instantiating
them to their glb, adding upper bound constraints associated to them.
Also:
- Add polymorphic flag for inductives.
- Fix cooking partially
- Fix kernel/univ.ml to do normalization of universe expressions at
the end of substitution.

Correct classes/structures universe inference

- Required a bit of extension in Univ to handle Max properly (sup u
(u+1)) was returning (max(u,u+1)) for example.
- Try a version where substitution of universe expressions for universe
levels is allowed at the end of unification. By an invariant this
should only instantiate with max() types that are morally "on the
right" only.
This is controlled using a rigidity attribute of universe variables,
also allowing to properly do unification w.r.t. universes during
typechecking/inference.
- Currently fails in Vectors/Fin.v because case compilation generates
"flexible" universes that actually appear in the term...

Fix unification of universe variables.

- Fix choice of canonical universe in presence of universe constraints,
and do so by relying on a trichotomy for universe variables: rigid
(won't be substituted), flexible (might be if not substituted by an
algebraic) and flexible_alg (always substituted).
- Fix romega code and a few more plugins, most of the standard library
goes through now.
- Had to define some inductives as Polymorphic explicitly to make
proofs go through, more to come, and definitions should be polymorphic
too, otherwise inconsistencies appear quickly (two uses of the same
polymorphic ind through monomorphic functions (like nth on lists of
Props and nats) will fix the monomorphic function's universe with eq
constraints that are incompatible).
- Correct universe polymorphism handling for fixpoint/cofixpoint
definitions.

- Fix romega to use the right universes for list constructors.
- Fix internalization/externalization to deal properly with the
implicit parsing of params.
- Fix fourier tactic w.r.t. GRefs

- Fix substitution saturation of universes.
- Fix number syntax plugin.
- Fix setoid_ring to take its coefficients in a Set rather
than a Type, avoiding a large number of useless universe constraints.

- Fix minor checker decl
- Fix btauto w.r.t. GRef
- Fix proofview to normalize universes in the original types as well.
- Fix definitions of projections to not take two universes at the same level,
but at different levels instead, avoiding unnecessary constraints that could
lower the level of one component depending on the use of the other component.

Fix simpl fst, snd to use @fst @snd as they have maximal implicits now.

- More simpl snd, fst fixes.
- Try to make the nth theory of lists polymorphic.

Check with Enrico if this change is ok. Case appearing in RingMicromega's call
to congruence l417, through a call to refine -> the_conv_x_leq.

Compile everything.
- "Fix" checker by deactivating code related to polymorphism, should
be updated.
- Make most of List.v polymorphic to help with following definitions.
- When starting a lemma, normalize w.r.t. universes, so that the types
get a fixed universe, not refinable later.
- In record, don't assign a fully flexible universe variable to the record
type if it is a definitional typeclass, as translate_constant doesn't expect
an algebraic universe in the type of a constant. It certainly should though.
- Fix micromega code.

Fix after rebase.

Update printing functions to print the polymorphic status of definitions
and their universe context.

Refine printing of universe contexts

- Fix printer for universe constraints
- Rework normalization of constraints to separate the Union-Find result
  from computation of lubs/glbs.

Keep universe contexts of inductives/constants in entries for correct
substitution inside modules. Abstract interface to get an instantiation
of an inductive with its universe substitution in the kernel (no
substitution if the inductive is not polymorphic, even if mind_universes
is non-empty).

Make fst and snd polymorphic, fix instances in RelationPairs to use
different universes for the two elements of a pair.

- Fix bug in nf_constraints: was removing Set <= constraints, but should
remove Prop <= constraints only.
- Make proj1_sig, projT1... polymorphic to avoid weird universe unifications,
giving rise to universe inconsistenties.

Adapt auto hints to polymorphic references.

Really produce polymorphic hints... second try

- Remove algebraic universes that can't appear in the goal when taking the
  type of a lemma to start.

Proper handling of universe contexts in clenv and auto so that
polymorphic hints are really refreshed at each application.

Fix erroneous shadowing of sigma variable.

- Make apparent the universe context used in pretyping, including information
about flexibility of universe variables.
- Fix induction to generate a fresh constant instance with flexible universe variables.

Add function to do conversion w.r.t. an evar map and its local universes.

- Fix define_evar_as_sort to not forget constraints coming from the refinement.
- Do not nf_constraints while we don't have the whole term at hand to substitute in.

- Move substitution of full universes to Universes
- Normalize universes inside an evar_map when doing nf_evar_map_universes.
- Normalize universes at each call to interp_ltac (potentially expensive)

Do not normalize all evars at each call to interp_gen in tactics: rather
incrementally normalize the terms at hand, supposing the normalization of universes
will concern only those appearing in it (dangerous but much more efficient).

Do not needlessly generate new universes constraints for projections of records.

Correct polymorphic discharge of section variables.

Fix autorewrite w.r.t. universes: polymorphic rewrite hints get fresh universe
instances at each application.

Fix r2l rewrite scheme to support universe polymorphism

Fix a bug in l2r_forward scheme and fix congruence scheme to handle polymorphism correctly.

Second try at fixing autorewrite, cannot do without pushing the constraints and the set of fresh
universe variables into the proof context.

- tclPUSHCONTEXT allow to set the ctx universe variables as flexible or rigid
- Fix bug in elimschemes, not taking the right sigma

Wrong sigma used in leibniz_rewrite

Avoid recomputation of bounds for equal universes in normalization of constraints,
only the canonical one need to be computed.

Make coercions work with universe polymorphic projections.

Fix eronneous bound in universes constraint solving.

Make kernel reduction and term comparison strictly aware of universe instances,
with variants for relaxed comparison that output constraints.
Otherwise some constraints that should appear during pretyping don't and we generate
unnecessary constraints/universe variables.
Have to adapt a few tactics to this new behavior by making them universe aware.

- Fix elimschemes to minimize universe variables
- Fix coercions to not forget the universe constraints generated by an application
- Change universe substitutions to maps instead of assoc lists.
- Fix absurd tactic to handle univs properly
- Make length and app polymorphic in List, unification sets their levels otherwise.

Move to modules for namespace management instead of long names in universe code.

More putting things into modules.

Change evar_map structure to support an incremental substitution of universes
(populated from Eq constraints), allowing safe and fast inference of precise levels,
without computing lubs.
- Add many printers and reorganize code
- Extend nf_evar to normalize universe variables according to the substitution.
- Fix ChoiceFacts.v in Logic, no universe inconsistencies anymore. But Diaconescu
still has one (something fixes a universe to Set).
- Adapt omega, functional induction to the changes.

Fix congruence, eq_constr implem, discharge of polymorphic inductives.

Fix merge in auto.

The [-parameters-matter] option (formerly relevant_equality).

Add -parameters-matter to coqc

Do compute the param levels at elaboration time if parameters_matter.

- Fix generalize tactic
- add ppuniverse_subst
- Start fixing normalize_universe_context w.r.t. normalize_univ_variables.

- Fix HUGE bug in Ltac interpretation not folding the sigma correctly if interpreting a tactic application
to multiple arguments.
- Fix bug in union of universe substitution.

- rename parameters-matter to indices-matter
- Fix computation of levels from indices not parameters.

- Fixing parsing so that [Polymorphic] can be applied to gallina extensions.
- When elaborating definitions, make the universes from the type rigid when
checking the term: they should stay abstracted.
- Fix typeclasses eauto's handling of universes for exact hints.

Rework all the code for infering the levels of inductives and checking their
allowed eliminations sorts.

This is based on the computation of a natural level for an inductive type I.
The natural level [nat] of [I : args -> sort := c1 : A1 -> I t1 .. cn : An -> I tn] is
computed by taking the max of the levels of the args (if indices matter) and the
levels of the constructor arguments.
The declared level [decl] of I is [sort], which might be Prop, Set or some Type u (u fresh
or not).
If [decl >= nat && not (decl = Prop && n >= 2)], the level of the inductive is [decl],
otherwise, _smashing_ occured.
If [decl] is impredicative (Prop or Set when Set is impredicative), we accept the
declared level, otherwise it's an error.

To compute the allowed elimination sorts, we have the following situations:
- No smashing occured: all sorts are allowed. (Recall props that are not
smashed are Empty/Unitary props)
- Some smashing occured:
 - if [decl] is Type, we allow all eliminations (above or below [decl],
   not sure why this is justified in general).
 - if [decl] is Set, we used smashing for impredicativity, so only
   small sorts are allowed (Prop, Set).
 - if [decl] is Prop, only logical sorts are allowed: I has either
   large universes inside it or more than 1 constructor.
   This does not treat the case where only a Set appeared in I which
   was previously accepted it seems.

All the standard library works with these changes. Still have to cleanup
kernel/indtypes.ml. It is a good time to have a whiskey with OJ.

Thanks to Peter Lumsdaine for bug reporting:
- fix externalisation of universe instances (still appearing when no Printing Universes)
- add [convert] and [convert_leq] tactics that keep track of evars and universe constraints.
- use them in [exact_check].

Fix odd behavior in inductive type declarations allowing to silently lower a Type i parameter
to Set for squashing a naturally Type i inductive to Set. Reinstate the LargeNonPropInductiveNotInType
exception.

Fix the is_small function not dealing properly with aliases of Prop/Set in Type.

Add check_leq in Evd and use it to decide if we're trying to squash an
inductive naturally in some Type to Set.

- Fix handling of universe polymorphism in typeclasses Class/Instance declarations.
- Don't allow lowering a rigid Type universe to Set silently.

- Move Ring/Field back to Type. It was silently putting R in Set due to the definition of ring_morph.
- Rework inference of universe levels for inductive definitions.
- Make fold_left/right polymorphic on both levels A and B (the list's type). They don't have to be
at the same level.

Handle selective Polymorphic/Monomorphic flag right for records.

Remove leftover command

Fix after update with latest trunk.

Backport patches on HoTT/coq to rebased version of universe polymorphism.

- Fix autorewrite wrong handling of universe-polymorphic rewrite rules. Fixes part of issue #7.
- Fix the [eq_constr_univs] and add an [leq_constr_univs] to avoid eager equation of universe
 levels that could just be inequal. Use it during kernel conversion. Fixes issue #6.
- Fix a bug in unification that was failing too early if a choice in unification of universes
 raised an inconsistency.
- While normalizing universes, remove Prop in the le part of Max expressions.
- Stop rigidifying the universes on the right hand side of a : in definitions.
- Now Hints can be declared polymorphic or not. In the first case they
 must be "refreshed" (undefined universes are renamed) at each application.
- Have to refresh the set of universe variables associated to a hint
 when it can be used multiple times in a single proof to avoid fixing
 a level... A better & less expensive solution should exist.
- Do not include the levels of let-ins as part of records levels.
- Fix a NotConvertible uncaught exception to raise a more informative
 error message.
- Better substitution of algebraics in algebraics (for universe variables that
 can be algebraics).
- Fix issue #2, Context was not properly normalizing the universe context.
- Fix issue with typeclasses that were not catching UniverseInconsistencies
  raised by unification, resulting in early failure of proof-search.
- Let the result type of definitional classes be an algebraic.
- Adapt coercions to universe polymorphic flag (Identity Coercion etc..)
- Move away a dangerous call in autoinstance that added constraints for every
polymorphic definitions once in the environment for no use.

Forgot one part of the last patch on coercions.

- Adapt auto/eauto to polymorphic hints as well.
- Factor out the function to refresh a clenv w.r.t. undefined universes.

Use leq_univ_poly in evarconv to avoid fixing universes.

Disallow polymorphic hints based on a constr as it is not possible to infer their universe
context. Only global references can be made polymorphic. Fixes issue #8.

Fix SearchAbout bug (issue #10).

Fix program w.r.t. universes: the universe context of a definition changes
according to the successive refinements due to typechecking obligations.
This requires the Proof modules to return the generated universe substitution
when finishing a proof, and this information is passed in the closing hook.
The interface is not very clean, will certainly change in the future.

- Better treatment of polymorphic hints in auto: terms can be polymorphic now, we refresh their
context as well.
- Needs a little change in test-pattern that seems breaks multiary uses of destruct in NZDiv.v, l495.
FIX to do.

Fix [make_pattern_test] to keep the universe information around and still
allow tactics to take multiple patterns at once.

- Fix printing of universe instances that should not be factorized blindly
- Fix handling of the universe context in program definitions by allowing the
hook at the end of an interactive proof to give back the refined universe context,
before it is transformed in the kernel.
- Fix a bug in evarconv where solve_evar_evar was not checking types of instances,
resulting in a loss of constraints in unification of universes and a growing number
of useless parametric universes.

- Move from universe_level_subst to universe_subst everywhere.

- Changed representation of universes for a canonical one
- Adapt the code so that universe variables might be substituted by
arbitrary universes (including algebraics). Not used yet except for
polymorphic universe variables instances.

- Adapt code to new constraint structure.
- Fix setoid rewrite handling of evars that was forgetting the initial
universe substitution !
- Fix code that was just testing conversion instead of keeping the
resulting universe constraints around in the proof engine.
- Make a version of reduction/fconv that deals with the more general
set of universe constraints.

- [auto using] should use polymorphic versions of the constants.
- When starting a proof, don't forget about the algebraic universes in
the universe context.

Rationalize substitution and normalization functions for universes.
Also change back the structure of universes to avoid considering levels
n+k as pure levels: they are universe expressions like max.
Everything is factored out in the Universes and Univ modules now and
the normalization functions can be efficient in the sense that they
can cache the normalized universes incrementally.

- Adapt normalize_context code to new normalization/substitution functions.
- Set more things to be polymorphic, e.g. in Ring or SetoidList for the rest
of the code to work properly while the constraint generation code is not adapted.
And temporarily extend the universe constraint code in univ to solve max(is) = max(js)
by first-order unification (these constraints should actually be implied not enforced).
- Fix romega plugin to use the right universes for polymorphic lists.
- Fix auto not refreshing the poly hints correctly.

- Proper postponing of universe constraints during unification, avoid making
arbitrary choices.
- Fix nf_evars_and* to keep the substitution around for later normalizations.
- Do add simplified universe constraints coming from unification during typechecking.
- Fix solve_by_tac in obligations to handle universes right, and the corresponding
substitution function.

Test global universe equality early during simplication of constraints.

Better hashconsing, but still not good on universe lists.

- Add postponing of "lub" constraints that should not be checked early,
they are implied by the others.
- Fix constructor tactic to use a fresh constructor instance avoiding
fixing universes.
- Use [eq_constr_universes] instead of [eq_constr_univs] everywhere,
this is the comparison function that doesn't care about the universe
instances.
- Almost all the library compiles in this new setting, but some more tactics
need to be adapted.

- Reinstate hconsing.
- Keep Prop <= u constraints that can be used to set the level of a universe
metavariable.

Add better hashconsing and unionfind in normalisation of constraints.
Fix a few problems in choose_canonical, normalization and substitution functions.

Fix after merge

Fixes after rebase with latest Coq trunk, everything compiles again,
albeit slowly in some cases.
- Fix module substitution and comparison of table keys in conversion
using the wrong order (should always be UserOrd now)
- Cleanup in universes, removing commented code.
- Fix normalization of universe context which was assigning global
levels to local ones. Should always be the other way!
- Fix universe implementation to implement sorted cons of universes
preserving order. Makes Univ.sup correct again, keeping universe in
normalized form.
- In evarconv.ml, allow again a Fix to appear as head of a weak-head normal
form (due to partially applied fixpoints).
- Catch anomalies of conversion as errors in reductionops.ml, sad but
necessary as eta-expansion might build ill-typed stacks like FProd,
[shift;app Rel 1], as it expands not only if the other side is rigid.
- Fix module substitution bug in auto.ml

- Fix case compilation: impossible cases compilation was generating useless universe
levels. Use an IDProp constant instead of the polymorphic identity to not influence
the level of the original type when building the case construct for the return type.
- Simplify normalization of universe constraints.
- Compute constructor levels of records correctly.

Fall back to levels for universe instances, avoiding issues of unification.
Add more to the test-suite for universe polymorphism.

Fix after rebase with trunk

Fix substitution of universes inside fields/params of records to be made
after all normalization is done and the level of the record has been
computed.

Proper sharing of lower bounds with fixed universes.

Conflicts:
	library/universes.ml
	library/universes.mli

Constraints were not enforced in compilation of cases

Fix after rebase with trunk

- Canonical projections up to universes
- Fix computation of class/record universe levels to allow
squashing to Prop/Set in impredicative set mode.

- Fix descend_in_conjunctions to properly instantiate projections with universes
- Avoid Context-bound variables taking extra universes in their associated universe context.

- Fix evar_define using the wrong direction when refreshing a universe under cumulativity
- Do not instantiate a local universe with some lower bound to a global one just because
they have the same local glb (they might not have the same one globally).

- Was loosing some global constraints during normalization (brought again by the kernel), fixed now.
- Proper [abstract] with polymorphic lemmas (polymorphic if the current proof is).
- Fix silly bug in autorewrite: any hint after the first one was always monomorphic.

- Fix fourier after rebase
- Refresh universes when checking types of metas in unification (avoid (sup (sup univ))).
- Speedup a script in FSetPositive.v

Rework definitions in RelationClasses and Morphisms to share universe
levels as much as possible. This factorizes many useless x <=
RelationClasses.foo constraints in code that uses setoid rewriting.
Slight incompatible change in the implicits for Reflexivity and
Irreflexivity as well.

- Share even more universes in Morphisms using a let.
- Use splay_prod instead of splay_prod_assum which doesn't reduce let's
to find a relation in setoid_rewrite
- Fix [Declare Instance] not properly dealing with let's in typeclass contexts.

Fixes in inductiveops, evarutil.

Patch by Yves Bertot to allow naming universes in inductive definitions.

Fixes in tacinterp not propagating evars correctly.

Fix for issue #27: lowering a Type to Prop is allowed during
inference (resulting in a Type (* Set *)) but kernel reduction
was wrongly refusing the equation [Type (*Set*) = Set].

Fix in interface of canonical structures: an instantiated polymorphic
projection is not needed to lookup a structure, just the projection name
is enough (reported by C. Cohen).

Move from universe inference to universe checking in the kernel.

All tactics have to be adapted so that they carry around their generated
constraints (living in their sigma), which is mostly straightforward.
The more important changes are when refering to Coq constants, the
tactics code is adapted so that primitive eq, pairing and sigma types might
be polymorphic.
Fix another few places in tacinterp and evarconv/evarsolve where the sigma
was not folded correctly.

- Fix discharge adding spurious global constraints on polymorphic universe variables
appearing in assumptions.
- Fixes in inductiveops not taking into account universe polymorphic inductives.

WIP on checked universe polymorphism, it is clearly incompatible
with the previous usage of polymorphic inductives + non-polymorphic
definitions on them as universe levels now appear in the inductive type,
and add equality constraints between universes that were otherwise just
in a cumulativity relation (not sure that was actually correct).

Refined version of unification of universe instances for first-order unification,
prefering unfolding to arbitrary identification of universes.

Moved kernel to universe checking only.

Adapt the code to properly infer constraints during typechecking and
refinement (tactics) and only check constraints when adding
constants/inductives to the environment. Exception made of module
subtyping that needs inference of constraints...  The kernel conversion
(fconv) has two modes: checking only and inference, the later being used
by modules only. Evarconv/unification make use of a different strategy for
conversion of constants that prefer unfolding to blind unification of
rigid universes. Likewise, conversion checking backtracks on different universe
instances (modulo the constraints).

- adapt congruence/funind/ring plugins to this new mode, forcing them to
declare their constraints.
- To avoid big performance penalty with reification, make ring/field non-polymorphic
(non-linear explosion in run time to be investigated further).
- pattern and change tactics need special treatment: as they are not _reduction_
but conversion functions, their operation requires to update an evar_map with
new universe constraints.
- Fix vm_compute to work better with universes. If the normal
form is made only of constructors then the readback is correct. However a deeper change will
be needed to treat substitution of universe instances when unfolding constants.

Remove libtypes.ml

Fix after merge.

Fix after rebase with trunk.

**** Add projections to the kernel, as optimized implementations of constants.

- New constructor Proj expects a projection constant applied to its principal
inductive argument.
- Reduction machines shortcut the expansion to a case and directly project the
right argument.
- No need to keep parameters as part of the projection's arguments as they
are inferable from the type of the principal argument.
- ML code now compiles, debugging needed.

Start debugging the implementation of projections. Externalisation should
keep the information about projections.

Internalization, pattern-matching, unification and reduction
of projections.

Fix some code that used to have _ for parameters that are no longer
present in projections.

Fixes in unification, reduction, term indexing, auto hints based on projections,
add debug printers.

Fix byte-compilation of projections, unification, congruence with projections.
Adapt .v files using "@proj _ _ record" syntax, should come back on this later.
Fix coercion insertion code to properly deal with projection coercions.
Fix [simpl proj]... TODO [unfold proj], proj is not considered evaluable.

- Fix whnf of projections, now respecting opacity information.
- Fix conversion of projections to try first-order first and then
incrementally unfold them.
- Fix computation of implicit args for projections, simply dropping
the information for parameters.
- Fix a few scripts that relied on projections carrying their parameters (few at's,
rewrites).
- Fix unify_with_subterm to properly match under projections.
- Fix bug in cooking of projections.
- Add pattern PProj for projections.
- A very strange bug appeared in BigZ.v, making coqtop segfault on the export
of BigN... tofix

Fixes after rebase with trunk. Everything compiles now, with efficient
projections.

Fixes after rebase with trunk (esp. reductionops).

Remove warnings, backport patch from old univs+projs branch.

Proper expansion of projections during unification.

They are considered as maybe flexible keys in evarconv/unification. We
try firstorder unification and otherwise expand them as necessary,
completely mimicking the original behavior, when they were
constants.  Fix head_constr_bound interface, the arguments are never
needed (they're outside their environment actually).  [simpl] and
[red]/[intro] should behave just like before now.

Fix evarconv that was giving up on proj x = ?e problems too early.

- Port patch by Maxime Denes implementing fast projections in the native conversion.
- Backport patch to add eta-expansion for records.

Do not raise an exception but simply fails if trying to do eta on an inductive that is not a record.

Fix projections detyping/matching and unification.ml not always
recovering on first-order universe inequalities.

Correct eta-expansion for records, and change strategy for conversion
with projections to favor reduction over first-order unification a
little more. Fix a bug in Ltac pattern matching on projections.

Fix evars_reset_evd to not recheck existing constraints in case it is just an update
(performance improvement for typeclass resolution).

- Respect Global/Transparent oracle during unification. Opaque means
_never_ unfolded there.
- Add empty universes as well as the initial universes (having Prop < Set).
- Better display of universe inconsistencies.

- Add Beta Ziliani's patch to go fast avoiding imitation when possible.
- Allow instantiation by lower bound even if there are universes above
- (tentative) In refinement, avoid incremental refinement of terms
  containing no holes and do it in one step (much faster on big terms).
  Turned on only if not a checked command.

Remove dead code in univ/universes.ml and cleanup setup of hashconsing,
for a small speed and memory footprint improvement.

- Fix bug in unification using cumulativity when conversion should have been used.
- Fix unification of evars having type Type, no longer forcing them to be equal
(potentially more constraints): algorithm is now complete w.r.t. cumulativity.
- In clenvtac, use refine_nocheck as we are guaranteed to get well-typed terms
from unification now, including sufficient universe constraints. Small general
speedup.

- Fix inference of universe levels of inductive types to avoid smashing
  inadvertently from Set to Prop.
- Fix computation of discharged hypotheses forgetting the arity in inductives.

- Fix wrong order in printing of universe inconsistency explanation
- Allow coercions between two polymorphic instances of the same inductive/constant.
- Do evar normalization and saturation by classes before trying to use program coercion
  during pretyping.
- In unification, force equalities of universes when unifying the same rigid head constants.

- Fix omission of projections in constr_leq
- Fix [admit] tactic's handling of normalized universes.

Fix typing of projections not properly normalizing w.r.t. evars, resulting in anomaly sometimes.

Adapt rewrite to work with computational relations (in Type), while
maintaining backward compatibility with Propositional rewriting.

Introduce a [diff] function on evar maps and universe contexts to
properly deal with clause environments. Local hints in auto now store
just the extension of the evar map they rely on, so merging them becomes
efficient. This fixes an important performance issue in auto and typeclass
resolution in presence of a large number of universe constraints.

Change FSetPositive and MSetPositive to put their [elt] and [t] universes in
Type to avoid restricting global universes to [Set]. This is due to [flip]s
polymorphic type being fixed in monomorphic instances of Morphisms.v,
and rewriting hence forcing unification of levels that could be left unrelated.

- Try a fast_typeops implementation of kernel type inference that
  allocates less by not rebuilding the term, shows a little performance
  improvement, and less allocation.
- Build universe inconsistency explanations lazily, avoiding huge blowup
  (x5) in check_constraints/merge_constraints in time and space (these
  are stressed in universe polymorphic mode).
- Hashcons universe instances.

Add interface file for fast_typeops

Use monomorphic comparisons, little optimizations of hashconsing and
comparison in univ.ml.

Fix huge slowdown due to building huge error messages. Lazy is not
enough to tame this completely.

Fix last performance issue, due to abstracts building huge terms abstracting on parts of the section
context. Was due to wrong handling of Let... Qed.s in abstract. Performance is a tiny bit better than the
trunk now.

First step at compatibility layer for projections.

Compatibility mode for projections. c.(p), p c use primitive projs,
while @p refers to an expansion [λ params c, c.(p)]. Recovers almost
entire source compatibility with trunk scripts, except when mixing
@p and p and doing syntactic matching (they're unifiable though).

Add a [Set Primitive Projections] flag to set/unset the use of primitive
projections, selectively for each record. Adapt code to handle both the
legacy encoding and the primitive projections. Library is almost
source-to-source compatible, except for syntactic operations relying
on the presence of parameters. In primitive projections mode, @p refers
to an expansion [λ params r. p.(r)]. More information in CHANGES (to be
reformated/moved to reference manual).

Backport changes from HoTT/coq:

- Fix anomaly on uncatched NotASort in retyping.
- Better recognition of evars that are subject to typeclass resolution.
  Fixes bug reported by J. Gross on coq-club.
- Print universe polymorphism information for parameters as well.

Fix interface for unsatisfiable constraints error, now a type error.
Try making ring polymorphic again, with a big slowdown, to be investigated.
Fix evar/universe leak in setoid rewrite.

- Add profiling flag
- Move setoid_ring back to non-polymorphic mode to compare perfs with trunk
- Change unification to allow using infer_conv more often (big perf culprit),
  but semantics of backtracking on unification of constants is not properly
  implemented there.
- Fix is_empty/union_evar_universe_context forgetting about some assignments.
- Performance is now very close to the trunk from june,
  with projections deactivated.

1 files changed, 242 insertions, 89 deletions

diff --git a/toplevel/command.ml b/toplevel/command.ml
index f41acaba27..d2111f0fb2 100644
--- a/toplevel/command.ml
+++ b/toplevel/command.ml
@@ -56,8 +56,8 @@ let rec complete_conclusion a cs = function
 	user_err_loc (loc,"",
 	  strbrk"Cannot infer the non constant arguments of the conclusion of "
 	  ++ pr_id cs ++ str ".");
-      let args = List.map (fun id -> CRef(Ident(loc,id))) params in
-      CAppExpl (loc,(None,Ident(loc,name)),List.rev args)
+      let args = List.map (fun id -> CRef(Ident(loc,id),None)) params in
+      CAppExpl (loc,(None,Ident(loc,name),None),List.rev args)
   | c -> c
 
 (* Commands of the interface *)
@@ -74,29 +74,34 @@ let red_constant_entry n ce = function
            under_binders env
              (fst (reduction_of_red_expr env red)) n body,eff) }
 
-let interp_definition bl red_option c ctypopt =
+let interp_definition bl p red_option c ctypopt =
   let env = Global.env() in
-  let evdref = ref Evd.empty in
+  let evdref = ref (Evd.from_env env) in
   let impls, ((env_bl, ctx), imps1) = interp_context_evars evdref env bl in
   let nb_args = List.length ctx in
   let imps,ce =
     match ctypopt with
       None ->
+        let subst = evd_comb0 Evd.nf_univ_variables evdref in
+	let ctx = map_rel_context (Vars.subst_univs_constr subst) ctx in
+	let env_bl = push_rel_context ctx env in
 	let c, imps2 = interp_constr_evars_impls ~impls evdref env_bl c in
-	let body = nf_evar !evdref (it_mkLambda_or_LetIn c ctx) in
-	imps1@(Impargs.lift_implicits nb_args imps2),
-	{ const_entry_body = Future.from_val (body,Declareops.no_seff);
-          const_entry_secctx = None;
-	  const_entry_type = None;
-          const_entry_opaque = false;
-          const_entry_inline_code = false;
-          const_entry_feedback = None;
-	}
+        let nf,subst = Evarutil.e_nf_evars_and_universes evdref in
+        let body = nf (it_mkLambda_or_LetIn c ctx) in
+	let vars = Universes.universes_of_constr body in
+	let ctx = Universes.restrict_universe_context
+	  (Evd.get_universe_context_set !evdref) vars in
+ 	imps1@(Impargs.lift_implicits nb_args imps2),
+	  definition_entry ~univs:(Univ.ContextSet.to_context ctx) ~poly:p body
     | Some ctyp ->
 	let ty, impsty = interp_type_evars_impls ~impls evdref env_bl ctyp in
+	let subst = evd_comb0 Evd.nf_univ_variables evdref in
+	let ctx = map_rel_context (Vars.subst_univs_constr subst) ctx in
+	let env_bl = push_rel_context ctx env in
 	let c, imps2 = interp_casted_constr_evars_impls ~impls evdref env_bl c ty in
-	let body = nf_evar !evdref (it_mkLambda_or_LetIn c ctx) in
-	let typ = nf_evar !evdref (it_mkProd_or_LetIn ty ctx) in
+	let nf, subst = Evarutil.e_nf_evars_and_universes evdref in
+	let body = nf (it_mkLambda_or_LetIn c ctx) in
+	let typ = nf (it_mkProd_or_LetIn ty ctx) in
         let beq b1 b2 = if b1 then b2 else not b2 in
         let impl_eq (x,y,z) (x',y',z') = beq x x' && beq y y' && beq z z' in
 	(* Check that all implicit arguments inferable from the term
@@ -108,14 +113,13 @@ let interp_definition bl red_option c ctypopt =
 	then msg_warning
           (strbrk "Implicit arguments declaration relies on type." ++ spc () ++
 	   strbrk "The term declares more implicits than the type here.");
+        let vars = Univ.LSet.union (Universes.universes_of_constr body) 
+          (Universes.universes_of_constr typ) in
+        let ctx = Universes.restrict_universe_context
+          (Evd.get_universe_context_set !evdref) vars in
 	imps1@(Impargs.lift_implicits nb_args impsty),
-        { const_entry_body = Future.from_val(body,Declareops.no_seff);
-          const_entry_secctx = None;
-	  const_entry_type = Some typ;
-          const_entry_opaque = false;
-          const_entry_inline_code = false;
-          const_entry_feedback = None;
-	}
+	  definition_entry ~types:typ ~poly:p 
+	    ~univs:(Univ.ContextSet.to_context ctx) body
   in
   red_constant_entry (rel_context_length ctx) ce red_option, !evdref, imps
 
@@ -144,7 +148,7 @@ let declare_definition_hook = ref ignore
 let set_declare_definition_hook = (:=) declare_definition_hook
 let get_declare_definition_hook () = !declare_definition_hook
 
-let declare_definition ident (local,k) ce imps hook =
+let declare_definition ident (local, p, k) ce imps hook =
   let () = !declare_definition_hook ce in
   let r = match local with
   | Discharge when Lib.sections_are_opened () ->
@@ -164,7 +168,7 @@ let declare_definition ident (local,k) ce imps hook =
 let _ = Obligations.declare_definition_ref := declare_definition
 
 let do_definition ident k bl red_option c ctypopt hook =
-  let (ce, evd, imps as def) = interp_definition bl red_option c ctypopt in
+  let (ce, evd, imps as def) = interp_definition bl (pi2 k) red_option c ctypopt in
     if Flags.is_program_mode () then
       let env = Global.env () in
       let c,sideff = Future.force ce.const_entry_body in
@@ -177,16 +181,17 @@ let do_definition ident k bl red_option c ctypopt hook =
       let obls, _, c, cty = 
 	Obligations.eterm_obligations env ident evd 0 c typ
       in
-      ignore(Obligations.add_definition ident ~term:c cty ~implicits:imps ~kind:k ~hook obls)
+      let ctx = Evd.get_universe_context_set evd in
+	ignore(Obligations.add_definition ident ~term:c cty ctx ~implicits:imps ~kind:k ~hook obls)
     else let ce = check_definition def in
       ignore(declare_definition ident k ce imps
         (fun l r -> hook l r;r))
 
 (* 2| Variable/Hypothesis/Parameter/Axiom declarations *)
 
-let declare_assumption is_coe (local, kind) c imps impl nl (_,ident) = match local with
+let declare_assumption is_coe (local,p,kind) (c,ctx) imps impl nl (_,ident) = match local with
 | Discharge when Lib.sections_are_opened () ->
-  let decl = (Lib.cwd(), SectionLocalAssum (c,impl), IsAssumption kind) in
+  let decl = (Lib.cwd(), SectionLocalAssum ((c,ctx),p,impl), IsAssumption kind) in
   let _ = declare_variable ident decl in
   let () = assumption_message ident in
   let () =
@@ -196,8 +201,9 @@ let declare_assumption is_coe (local, kind) c imps impl nl (_,ident) = match loc
   in
   let r = VarRef ident in
   let () = Typeclasses.declare_instance None true r in
-  let () = if is_coe then Class.try_add_new_coercion r ~local:true in
+  let () = if is_coe then Class.try_add_new_coercion r ~local:true false in
   (r,true)
+
 | Global | Local | Discharge ->
   let local = get_locality ident local in
   let inl = match nl with
@@ -205,18 +211,25 @@ let declare_assumption is_coe (local, kind) c imps impl nl (_,ident) = match loc
     | DefaultInline -> Some (Flags.get_inline_level())
     | InlineAt i -> Some i
   in
-  let decl = (ParameterEntry (None,c,inl), IsAssumption kind) in
+  let ctx = Univ.ContextSet.to_context ctx in
+  let decl = (ParameterEntry (None,p,(c,ctx),inl), IsAssumption kind) in
   let kn = declare_constant ident ~local decl in
   let gr = ConstRef kn in
   let () = maybe_declare_manual_implicits false gr imps in
   let () = assumption_message ident in
   let () = Typeclasses.declare_instance None false gr in
-  let () = if is_coe then Class.try_add_new_coercion gr local in
+  let () = if is_coe then Class.try_add_new_coercion gr local p in
   (gr,Lib.is_modtype_strict ())
 
+let declare_assumptions_hook = ref ignore
+let set_declare_assumptions_hook = (:=) declare_assumptions_hook
+
 let interp_assumption evdref env bl c =
   let c = prod_constr_expr c bl in
-  interp_type_evars_impls evdref env c
+  let ty, impls = interp_type_evars_impls evdref env c in
+  let evd, nf = nf_evars_and_universes !evdref in
+  let ctx = Evd.get_universe_context_set evd in
+    ((nf ty, ctx), impls)
 
 let declare_assumptions idl is_coe k c imps impl_is_on nl =
   let refs, status =
@@ -229,16 +242,16 @@ let do_assumptions kind nl l =
   let env = Global.env () in
   let evdref = ref Evd.empty in
   let _,l = List.fold_map (fun env (is_coe,(idl,c)) ->
-    let t,imps = interp_assumption evdref env [] c in
+    let (t,ctx),imps = interp_assumption evdref env [] c in
     let env =
       push_named_context (List.map (fun (_,id) -> (id,None,t)) idl) env in
-    (env,((is_coe,idl),t,imps))) env l in
+    (env,((is_coe,idl),t,(ctx,imps)))) env l in
   let evd = solve_remaining_evars all_and_fail_flags env Evd.empty !evdref in
   let l = List.map (on_pi2 (nf_evar evd)) l in
-  snd (List.fold_left (fun (subst,status) ((is_coe,idl),t,imps) ->
+  snd (List.fold_left (fun (subst,status) ((is_coe,idl),t,(ctx,imps)) ->
     let t = replace_vars subst t in
-    let (refs,status') = declare_assumptions idl is_coe kind t imps false nl in
-    let subst' = List.map2 (fun (_,id) c -> (id,constr_of_global c)) idl refs in
+    let (refs,status') = declare_assumptions idl is_coe kind (t,ctx) imps false nl in
+    let subst' = List.map2 (fun (_,id) c -> (id,Universes.constr_of_global c)) idl refs in
     (subst'@subst, status' && status)) ([],true) l)
 
 (* 3a| Elimination schemes for mutual inductive definitions *)
@@ -290,6 +303,23 @@ let prepare_param = function
   | (na,None,t) -> out_name na, LocalAssum t
   | (na,Some b,_) -> out_name na, LocalDef b
 
+
+let make_conclusion_flexible evdref ty = 
+  if isArity ty then
+    let _, concl = destArity ty in
+      match concl with
+      | Type u -> 
+        (match Univ.universe_level u with
+        | Some u -> evdref := Evd.make_flexible_variable !evdref true u
+	| None -> ())
+      | _ -> ()
+  else () 
+	
+let is_impredicative env u = 
+  u = Prop Null || 
+  (engagement env = Some Declarations.ImpredicativeSet && u = Prop Pos)
+
+(** Make the arity conclusion flexible to avoid generating an upper bound universe now. *)
 let interp_ind_arity evdref env ind =
   interp_type_evars_impls evdref env ind.ind_arity
 
@@ -301,10 +331,88 @@ let interp_cstrs evdref env impls mldata arity ind =
   let ctyps'', cimpls = List.split (List.map (interp_type_evars_impls evdref env ~impls) ctyps') in
     (cnames, ctyps'', cimpls)
 
-let interp_mutual_inductive (paramsl,indl) notations finite =
+let sign_level env evd sign =
+  fst (List.fold_right
+    (fun (_,_,t as d) (lev,env) ->
+      let s = destSort (Reduction.whd_betadeltaiota env 
+			  (nf_evar evd (Retyping.get_type_of env evd t)))
+      in
+      let u = univ_of_sort s in
+	(Univ.sup u lev, push_rel d env))
+    sign (Univ.type0m_univ,env))
+
+let sup_list = List.fold_left Univ.sup Univ.type0m_univ
+
+let extract_level env evd tys = 
+  let sorts = List.map (fun ty -> 
+    let ctx, concl = Reduction.dest_prod_assum env ty in
+      sign_level env evd ctx) tys 
+  in sup_list sorts
+
+let inductive_levels env evdref arities inds =
+  let destarities = List.map (Reduction.dest_arity env) arities in
+  let levels = List.map (fun (ctx,a) -> 
+    if a = Prop Null then None
+    else Some (univ_of_sort a)) destarities
+  in
+  let cstrs_levels, min_levels, sizes = 
+    CList.split3
+      (List.map2 (fun (_,tys,_) (ctx,du) -> 
+	let len = List.length tys in
+	let clev = extract_level env !evdref tys in
+	let minlev =
+	  if len > 1 && not (is_impredicative env du) then
+	    Univ.type0_univ
+	  else Univ.type0m_univ
+	in
+	  (clev, minlev, len)) inds destarities)
+  in
+  (* Take the transitive closure of the system of constructors *)
+  (* level constraints and remove the recursive dependencies *)
+  let levels' = Univ.solve_constraints_system (Array.of_list levels)
+    (Array.of_list cstrs_levels) (Array.of_list min_levels)
+  in
+  let evd =
+    CList.fold_left3 (fun evd cu (ctx,du) len ->
+      if is_impredicative env du then
+	(** Any product is allowed here. *)
+	evd
+      else (** If in a predicative sort, or asked to infer the type,
+	       we take the max of:
+	       - indices (if in indices-matter mode)
+	       - constructors
+	       - Type(1) if there is more than 1 constructor
+	   *)
+	let evd = 
+	  (** Indices contribute. *)
+	  if Indtypes.is_indices_matter () then (
+	    let ilev = sign_level env !evdref ctx in
+	      Evd.set_leq_sort evd (Type ilev) du)
+	  else evd
+	in
+        (** Constructors contribute. *)
+	let evd = 
+	  if Sorts.is_set du then
+	    if not (Evd.check_leq evd cu Univ.type0_univ) then 
+	      raise (Indtypes.InductiveError Indtypes.LargeNonPropInductiveNotInType)
+	    else evd
+	  else Evd.set_leq_sort evd (Type cu) du 
+	in
+	let evd = 
+	  if len >= 2 && Univ.is_type0m_univ cu then 
+	   (** "Polymorphic" type constraint and more than one constructor, 
+	       should not land in Prop. Add constraint only if it would
+	       land in Prop directly (no informative arguments as well). *)
+	    Evd.set_leq_sort evd (Prop Pos) du
+	  else evd
+	in evd)
+    !evdref (Array.to_list levels') destarities sizes
+  in evdref := evd; arities
+
+let interp_mutual_inductive (paramsl,indl) notations poly finite =
   check_all_names_different indl;
   let env0 = Global.env() in
-  let evdref = ref Evd.empty in
+  let evdref = ref Evd.(from_env env0) in
   let _, ((env_params, ctx_params), userimpls) =
     interp_context_evars evdref env0 paramsl
   in
@@ -316,12 +424,14 @@ let interp_mutual_inductive (paramsl,indl) notations finite =
 
   (* Interpret the arities *)
   let arities = List.map (interp_ind_arity evdref env_params) indl in
+
   let fullarities = List.map (fun (c, _) -> it_mkProd_or_LetIn c ctx_params) arities in
   let env_ar = push_types env0 indnames fullarities in
   let env_ar_params = push_rel_context ctx_params env_ar in
 
   (* Compute interpretation metadatas *)
-  let indimpls = List.map (fun (_, impls) -> userimpls @ lift_implicits (rel_context_nhyps ctx_params) impls) arities in
+  let indimpls = List.map (fun (_, impls) -> userimpls @ 
+    lift_implicits (rel_context_nhyps ctx_params) impls) arities in
   let arities = List.map fst arities in
   let impls = compute_internalization_env env0 (Inductive params) indnames fullarities indimpls in
   let mldatas = List.map2 (mk_mltype_data evdref env_params params) arities indnames in
@@ -336,9 +446,24 @@ let interp_mutual_inductive (paramsl,indl) notations finite =
 
   (* Try further to solve evars, and instantiate them *)
   let sigma = solve_remaining_evars all_and_fail_flags env_params Evd.empty !evdref in
-  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map (nf_evar sigma) cl,impsl)) constructors in
-  let ctx_params = Context.map_rel_context (nf_evar sigma) ctx_params in
-  let arities = List.map (nf_evar sigma) arities in
+  evdref := sigma;
+  (* Compute renewed arities *)
+  let nf,_ = e_nf_evars_and_universes evdref in
+  let arities = List.map nf arities in
+  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf cl,impsl)) constructors in
+  let _ = List.iter (fun ty -> make_conclusion_flexible evdref ty) arities in
+  let arities = inductive_levels env_ar_params evdref arities constructors in
+  let nf',_ = e_nf_evars_and_universes evdref in
+  let nf x = nf' (nf x) in
+  let arities = List.map nf' arities in
+  let constructors = List.map (fun (idl,cl,impsl) -> (idl,List.map nf' cl,impsl)) constructors in
+  let ctx_params = map_rel_context nf ctx_params in
+  let evd = !evdref in
+  List.iter (check_evars env_params Evd.empty evd) arities;
+  iter_rel_context (check_evars env0 Evd.empty evd) ctx_params;
+  List.iter (fun (_,ctyps,_) ->
+    List.iter (check_evars env_ar_params Evd.empty evd) ctyps)
+    constructors;
 
   (* Build the inductive entries *)
   let entries = List.map3 (fun ind arity (cnames,ctypes,cimpls) -> {
@@ -357,7 +482,9 @@ let interp_mutual_inductive (paramsl,indl) notations finite =
   { mind_entry_params = List.map prepare_param ctx_params;
     mind_entry_record = false;
     mind_entry_finite = finite;
-    mind_entry_inds = entries },
+    mind_entry_inds = entries;
+    mind_entry_polymorphic = poly;
+    mind_entry_universes = Evd.universe_context evd },
     impls
 
 (* Very syntactical equality *)
@@ -412,16 +539,19 @@ type one_inductive_impls =
   Impargs.manual_explicitation list (* for inds *)*
   Impargs.manual_explicitation list list (* for constrs *)
 
-let do_mutual_inductive indl finite =
+type one_inductive_expr =
+  lident * local_binder list * constr_expr option * constructor_expr list
+
+let do_mutual_inductive indl poly finite =
   let indl,coes,ntns = extract_mutual_inductive_declaration_components indl in
   (* Interpret the types *)
-  let mie,impls = interp_mutual_inductive indl ntns finite in
+  let mie,impls = interp_mutual_inductive indl ntns poly finite in
   (* Declare the mutual inductive block with its associated schemes *)
   ignore (declare_mutual_inductive_with_eliminations UserVerbose mie impls);
   (* Declare the possible notations of inductive types *)
   List.iter Metasyntax.add_notation_interpretation ntns;
   (* Declare the coercions *)
-  List.iter (fun qid -> Class.try_add_new_coercion (locate qid) false) coes
+  List.iter (fun qid -> Class.try_add_new_coercion (locate qid) false poly) coes
 
 (* 3c| Fixpoints and co-fixpoints *)
 
@@ -525,11 +655,14 @@ let interp_fix_body evdref env_rec impls (_,ctx) fix ccl =
 
 let build_fix_type (_,ctx) ccl = it_mkProd_or_LetIn ccl ctx
 
-let declare_fix kind f def t imps =
+let declare_fix (_,poly,_ as kind) ctx f def t imps =
   let ce = {
     const_entry_body = Future.from_val def;
     const_entry_secctx = None;
     const_entry_type = Some t;
+    const_entry_polymorphic = poly;
+    const_entry_universes = ctx;
+    const_entry_proj = None;
     const_entry_opaque = false;
     const_entry_inline_code = false;
     const_entry_feedback = None;
@@ -576,7 +709,7 @@ let fix_sub_ref = make_ref fixsub_module "Fix_sub"
 let measure_on_R_ref = make_ref fixsub_module "MR"
 let well_founded = init_constant ["Init"; "Wf"] "well_founded"
 let mkSubset name typ prop =
-  mkApp ((delayed_force build_sigma).typ,
+  mkApp (Universes.constr_of_global (delayed_force build_sigma).typ,
 	 [| typ; mkLambda (name, typ, prop) |])
 let sigT = Lazy.lazy_from_fun build_sigma_type
 
@@ -591,15 +724,19 @@ let rec telescope = function
 	List.fold_left
 	  (fun (ty, tys, (k, constr)) (n, b, t) ->
 	    let pred = mkLambda (n, t, ty) in
-	    let sigty = mkApp ((Lazy.force sigT).typ, [|t; pred|]) in
-	    let intro = mkApp ((Lazy.force sigT).intro, [|lift k t; lift k pred; mkRel k; constr|]) in
+	    let ty = Universes.constr_of_global (Lazy.force sigT).typ in
+	    let intro = Universes.constr_of_global (Lazy.force sigT).intro in
+	    let sigty = mkApp (ty, [|t; pred|]) in
+	    let intro = mkApp (intro, [|lift k t; lift k pred; mkRel k; constr|]) in
 	      (sigty, pred :: tys, (succ k, intro)))
 	  (t, [], (2, mkRel 1)) tl
       in
       let (last, subst) = List.fold_right2
 	(fun pred (n, b, t) (prev, subst) ->
-	  let proj1 = applistc (Lazy.force sigT).proj1 [t; pred; prev] in
-	  let proj2 = applistc (Lazy.force sigT).proj2 [t; pred; prev] in
+	  let p1 = Universes.constr_of_global (Lazy.force sigT).proj1 in
+	  let p2 = Universes.constr_of_global (Lazy.force sigT).proj2 in
+	  let proj1 = applistc p1 [t; pred; prev] in
+	  let proj2 = applistc p2 [t; pred; prev] in
 	    (lift 1 proj2, (n, Some proj1, t) :: subst))
 	(List.rev tys) tl (mkRel 1, [])
       in ty, ((n, Some last, t) :: subst), constr
@@ -648,7 +785,7 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
       it_mkLambda_or_LetIn measure letbinders,
       it_mkLambda_or_LetIn measure binders
     in
-    let comb = constr_of_global (delayed_force measure_on_R_ref) in
+    let comb = Universes.constr_of_global (delayed_force measure_on_R_ref) in
     let wf_rel = mkApp (comb, [| argtyp; relargty; rel; measure |]) in
     let wf_rel_fun x y =
       mkApp (rel, [| subst1 x measure_body;
@@ -663,7 +800,7 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
   in
   let intern_bl = wfarg 1 :: [arg] in
   let _intern_env = push_rel_context intern_bl env in
-  let proj = (delayed_force build_sigma).Coqlib.proj1 in
+  let proj = (*FIXME*)Universes.constr_of_global (delayed_force build_sigma).Coqlib.proj1 in
   let wfargpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel 3)) in
   let projection = (* in wfarg :: arg :: before *)
     mkApp (proj, [| argtyp ; wfargpred ; mkRel 1 |])
@@ -676,7 +813,8 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
   let intern_fun_binder = (Name (add_suffix recname "'"), None, intern_fun_arity_prod) in
   let curry_fun =
     let wfpred = mkLambda (Name argid', argtyp, wf_rel_fun (mkRel 1) (mkRel (2 * len + 4))) in
-    let arg = mkApp ((delayed_force build_sigma).intro, [| argtyp; wfpred; lift 1 make; mkRel 1 |]) in
+    let intro = (*FIXME*)Universes.constr_of_global (delayed_force build_sigma).Coqlib.intro in
+    let arg = mkApp (intro, [| argtyp; wfpred; lift 1 make; mkRel 1 |]) in
     let app = mkApp (mkRel (2 * len + 2 (* recproof + orig binders + current binders *)), [| arg |]) in
     let rcurry = mkApp (rel, [| measure; lift len measure |]) in
     let lam = (Name (Id.of_string "recproof"), None, rcurry) in
@@ -701,7 +839,7 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
   let intern_body_lam = it_mkLambda_or_LetIn intern_body (curry_fun :: lift_lets @ fun_bl) in
   let prop = mkLambda (Name argname, argtyp, top_arity_let) in
   let def =
-    mkApp (constr_of_global (delayed_force fix_sub_ref),
+    mkApp (Universes.constr_of_global (delayed_force fix_sub_ref),
 	  [| argtyp ; wf_rel ;
 	     Evarutil.e_new_evar evdref env 
 	       ~src:(Loc.ghost, Evar_kinds.QuestionMark (Evar_kinds.Define false)) wf_proof;
@@ -715,16 +853,20 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
     if List.length binders_rel > 1 then
       let name = add_suffix recname "_func" in
       let hook l gr = 
-	let body = it_mkLambda_or_LetIn (mkApp (constr_of_global gr, [|make|])) binders_rel in
+	let body = it_mkLambda_or_LetIn (mkApp (Universes.constr_of_global gr, [|make|])) binders_rel in
 	let ty = it_mkProd_or_LetIn top_arity binders_rel in
 	let ce =
           { const_entry_body = Future.from_val (Evarutil.nf_evar !evdref body,Declareops.no_seff);
             const_entry_secctx = None;
 	    const_entry_type = Some ty;
-            const_entry_opaque = false;
-            const_entry_inline_code = false;
+	    (* FIXME *)
+	    const_entry_proj = None;
+	    const_entry_polymorphic = false;
+	    const_entry_universes = Evd.universe_context !evdref;
             const_entry_feedback = None;
-        } in 
+        const_entry_opaque = false;
+        const_entry_inline_code = false}
+	in 
 	(** FIXME: include locality *)
 	let c = Declare.declare_constant recname (DefinitionEntry ce, IsDefinition Definition) in
 	let gr = ConstRef c in
@@ -746,9 +888,9 @@ let build_wellfounded (recname,n,bl,arityc,body) r measure notation =
   let evars, _, evars_def, evars_typ = 
     Obligations.eterm_obligations env recname !evdref 0 fullcoqc fullctyp 
   in
-    ignore(Obligations.add_definition
-      recname ~term:evars_def evars_typ evars ~hook)
-
+  let ctx = Evd.get_universe_context_set !evdref in
+    ignore(Obligations.add_definition recname ~term:evars_def 
+	     evars_typ ctx evars ~hook)
 
 let interp_recursive isfix fixl notations =
   let env = Global.env() in
@@ -794,8 +936,9 @@ let interp_recursive isfix fixl notations =
 
   (* Instantiate evars and check all are resolved *)
   let evd = consider_remaining_unif_problems env_rec !evdref in
-  let fixdefs = List.map (Option.map (nf_evar evd)) fixdefs in
-  let fixtypes = List.map (nf_evar evd) fixtypes in
+  let evd, nf = nf_evars_and_universes evd in
+  let fixdefs = List.map (Option.map nf) fixdefs in
+  let fixtypes = List.map nf fixtypes in
   let fixctxnames = List.map (fun (_,ctx) -> List.map pi1 ctx) fixctxs in
 
   (* Build the fix declaration block *)
@@ -811,25 +954,25 @@ let check_recursive isfix env evd (fixnames,fixdefs,_) =
 let interp_fixpoint l ntns =
   let (env,_,evd),fix,info = interp_recursive true l ntns in
   check_recursive true env evd fix;
-  fix,info
+  (fix,Evd.get_universe_context_set evd,info)
 
 let interp_cofixpoint l ntns =
   let (env,_,evd),fix,info = interp_recursive false l ntns in
   check_recursive false  env evd fix;
-  fix,info
+  fix,Evd.get_universe_context_set evd,info
     
-let declare_fixpoint local ((fixnames,fixdefs,fixtypes),fiximps) indexes ntns =
+let declare_fixpoint local poly ((fixnames,fixdefs,fixtypes),ctx,fiximps) indexes ntns =
   if List.exists Option.is_empty fixdefs then
     (* Some bodies to define by proof *)
     let thms =
-      List.map3 (fun id t (len,imps,_) -> (id,(t,(len,imps)))) fixnames fixtypes fiximps in
+      List.map3 (fun id t (len,imps,_) -> (id,((t,ctx),(len,imps)))) fixnames fixtypes fiximps in
     let init_tac =
       Some (List.map (Option.cata Tacmach.refine_no_check Tacticals.tclIDTAC)
         fixdefs) in
     let init_tac =
       Option.map (List.map Proofview.V82.tactic) init_tac
     in
-    Lemmas.start_proof_with_initialization (Global,DefinitionBody Fixpoint)
+    Lemmas.start_proof_with_initialization (Global,poly,DefinitionBody Fixpoint)
       (Some(false,indexes,init_tac)) thms None (fun _ _ -> ())
   else begin
     (* We shortcut the proof process *)
@@ -841,25 +984,27 @@ let declare_fixpoint local ((fixnames,fixdefs,fixtypes),fiximps) indexes ntns =
     let fixdecls =
       List.map_i (fun i _ -> mkFix ((indexes,i),fixdecls)) 0 fixnames in
     let fixdecls = List.map (fun c -> c, Declareops.no_seff) fixdecls in
-    ignore (List.map4 (declare_fix (local, Fixpoint)) fixnames fixdecls fixtypes fiximps);
+    let ctx = Univ.ContextSet.to_context ctx in
+    ignore (List.map4 (declare_fix (local, poly, Fixpoint) ctx)
+	      fixnames fixdecls fixtypes fiximps);
     (* Declare the recursive definitions *)
     fixpoint_message (Some indexes) fixnames;
   end;
   (* Declare notations *)
   List.iter Metasyntax.add_notation_interpretation ntns
 
-let declare_cofixpoint local ((fixnames,fixdefs,fixtypes),fiximps) ntns =
+let declare_cofixpoint local poly ((fixnames,fixdefs,fixtypes),ctx,fiximps) ntns =
   if List.exists Option.is_empty fixdefs then
     (* Some bodies to define by proof *)
     let thms =
-      List.map3 (fun id t (len,imps,_) -> (id,(t,(len,imps)))) fixnames fixtypes fiximps in
+      List.map3 (fun id t (len,imps,_) -> (id,((t,ctx),(len,imps)))) fixnames fixtypes fiximps in
     let init_tac =
       Some (List.map (Option.cata Tacmach.refine_no_check Tacticals.tclIDTAC)
         fixdefs) in
     let init_tac =
       Option.map (List.map Proofview.V82.tactic) init_tac
     in
-    Lemmas.start_proof_with_initialization (Global,DefinitionBody CoFixpoint)
+    Lemmas.start_proof_with_initialization (Global,poly, DefinitionBody CoFixpoint)
       (Some(true,[],init_tac)) thms None (fun _ _ -> ())
   else begin
     (* We shortcut the proof process *)
@@ -868,7 +1013,9 @@ let declare_cofixpoint local ((fixnames,fixdefs,fixtypes),fiximps) ntns =
     let fixdecls = List.map_i (fun i _ -> mkCoFix (i,fixdecls)) 0 fixnames in
     let fixdecls = List.map (fun c-> c,Declareops.no_seff) fixdecls in
     let fiximps = List.map (fun (len,imps,idx) -> imps) fiximps in
-    ignore (List.map4 (declare_fix (local, CoFixpoint)) fixnames fixdecls fixtypes fiximps);
+    let ctx = Univ.ContextSet.to_context ctx in
+    ignore (List.map4 (declare_fix (local, poly, CoFixpoint) ctx) 
+	      fixnames fixdecls fixtypes fiximps);
     (* Declare the recursive definitions *)
     cofixpoint_message fixnames
   end;
@@ -898,7 +1045,12 @@ let out_def = function
   | Some def -> def
   | None -> error "Program Fixpoint needs defined bodies."
 
-let do_program_recursive local fixkind fixl ntns =
+let collect_evars_of_term evd c ty =
+  let evars = Evar.Set.union (evars_of_term c) (evars_of_term ty) in
+    Evar.Set.fold (fun ev acc -> Evd.add acc ev (Evd.find_undefined evd ev))
+      evars Evd.empty
+      
+let do_program_recursive local p fixkind fixl ntns =
   let isfix = fixkind != Obligations.IsCoFixpoint in
   let (env, rec_sign, evd), fix, info = 
     interp_recursive isfix fixl ntns 
@@ -934,13 +1086,14 @@ let do_program_recursive local fixkind fixl ntns =
 	Pretyping.search_guard Loc.ghost (Global.env ()) possible_indexes fixdecls in
 	List.iteri (fun i _ -> Inductive.check_fix env ((indexes,i),fixdecls)) fixl
   end in
+  let ctx = Evd.get_universe_context_set evd in
   let kind = match fixkind with
-  | Obligations.IsFixpoint _ -> (local, Fixpoint)
-  | Obligations.IsCoFixpoint -> (local, CoFixpoint)
+  | Obligations.IsFixpoint _ -> (local, p, Fixpoint)
+  | Obligations.IsCoFixpoint -> (local, p, CoFixpoint)
   in
-  Obligations.add_mutual_definitions defs ~kind ntns fixkind
+  Obligations.add_mutual_definitions defs ~kind ctx ntns fixkind
 
-let do_program_fixpoint local l =
+let do_program_fixpoint local poly l =
   let g = List.map (fun ((_,wf,_,_,_),_) -> wf) l in
     match g, l with
     | [(n, CWfRec r)], [(((_,id),_,bl,typ,def),ntn)] ->
@@ -954,30 +1107,30 @@ let do_program_fixpoint local l =
 	     
     | [(n, CMeasureRec (m, r))], [(((_,id),_,bl,typ,def),ntn)] ->
 	build_wellfounded (id, n, bl, typ, out_def def)
-	  (Option.default (CRef lt_ref) r) m ntn
+	  (Option.default (CRef (lt_ref,None)) r) m ntn
 	  
     | _, _ when List.for_all (fun (n, ro) -> ro == CStructRec) g ->
 	let fixl,ntns = extract_fixpoint_components true l in
 	let fixkind = Obligations.IsFixpoint g in
-	  do_program_recursive local fixkind fixl ntns
+	  do_program_recursive local poly fixkind fixl ntns
 
     | _, _ ->
 	errorlabstrm "do_program_fixpoint"
 	  (str "Well-founded fixpoints not allowed in mutually recursive blocks")
 
-let do_fixpoint local l =
-  if Flags.is_program_mode () then do_program_fixpoint local l
+let do_fixpoint local poly l =
+  if Flags.is_program_mode () then do_program_fixpoint local poly l
   else
     let fixl, ntns = extract_fixpoint_components true l in
     let fix = interp_fixpoint fixl ntns in
     let possible_indexes =
-      List.map compute_possible_guardness_evidences (snd fix) in
-    declare_fixpoint local fix possible_indexes ntns
+      List.map compute_possible_guardness_evidences (pi3 fix) in
+    declare_fixpoint local poly fix possible_indexes ntns
 
-let do_cofixpoint local l =
+let do_cofixpoint local poly l =
   let fixl,ntns = extract_cofixpoint_components l in
     if Flags.is_program_mode () then
-      do_program_recursive local Obligations.IsCoFixpoint fixl ntns
+      do_program_recursive local poly Obligations.IsCoFixpoint fixl ntns
     else
       let cofix = interp_cofixpoint fixl ntns in
-	declare_cofixpoint local cofix ntns
+	declare_cofixpoint local poly cofix ntns