Please sign in to comment.
This commit adds full universe polymorphism 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].
- Loading branch information...
Oops, something went wrong.