|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open CErrors
open Util
open Names
open Constr
open Termops
open Environ
open EConstr
open Context
open Vars
open Reduction
open Reductionops
open Recordops
open Evarutil
open Evardefine
open Evarsolve
open Evd
open Pretype_errors
module RelDecl = Context.Rel.Declaration
module NamedDecl = Context.Named.Declaration
type unify_flags = Evarsolve.unify_flags
type unify_fun = unify_flags ->
env -> evar_map -> conv_pb -> EConstr.constr -> EConstr.constr -> Evarsolve.unification_result
let default_transparent_state env = TransparentState.full
(* Conv_oracle.get_transp_state (Environ.oracle env) *)
let default_flags_of ?(subterm_ts=TransparentState.empty) ts =
{ modulo_betaiota = true;
open_ts = ts; closed_ts = ts; subterm_ts;
frozen_evars = Evar.Set.empty; with_cs = true;
allow_K_at_toplevel = true }
let default_flags env =
let ts = default_transparent_state env in
default_flags_of ts
let debug_unification = ref (false)
let () = Goptions.(declare_bool_option {
optdepr = false;
optname =
"Print states sent to Evarconv unification";
optkey = ["Debug";"Unification"];
optread = (fun () -> !debug_unification);
optwrite = (fun a -> debug_unification:=a);
})
let debug_ho_unification = ref (false)
let () = Goptions.(declare_bool_option {
optdepr = false;
optname =
"Print higher-order unification debug information";
optkey = ["Debug";"HO";"Unification"];
optread = (fun () -> !debug_ho_unification);
optwrite = (fun a -> debug_ho_unification:=a);
})
(*******************************************)
(* Functions to deal with impossible cases *)
(*******************************************)
let impossible_default_case env =
let type_of_id = Coqlib.lib_ref "core.IDProp.type" in
let c, ctx = UnivGen.fresh_global_instance env (Coqlib.(lib_ref "core.IDProp.idProp")) in
let (_, u) = Constr.destRef c in
Some (c, Constr.mkRef (type_of_id, u), ctx)
let coq_unit_judge =
let open Environ in
let make_judge c t = make_judge (EConstr.of_constr c) (EConstr.of_constr t) in
let na1 = make_annot (Name (Id.of_string "A")) Sorts.Relevant in
let na2 = make_annot (Name (Id.of_string "H")) Sorts.Relevant in
fun env ->
match impossible_default_case env with
| Some (id, type_of_id, ctx) ->
make_judge id type_of_id, ctx
| None ->
(* In case the constants id/ID are not defined *)
Environ.make_judge (mkLambda (na1,mkProp,mkLambda(na2,mkRel 1,mkRel 1)))
(mkProd (na1,mkProp,mkArrow (mkRel 1) Sorts.Relevant (mkRel 2))),
Univ.ContextSet.empty
let unfold_projection env evd ts p c =
let cst = Projection.constant p in
if TransparentState.is_transparent_constant ts cst then
Some (mkProj (Projection.unfold p, c))
else None
let eval_flexible_term ts env evd c =
match EConstr.kind evd c with
| Const (c, u) ->
if TransparentState.is_transparent_constant ts c
then Option.map EConstr.of_constr (constant_opt_value_in env (c, EInstance.kind evd u))
else None
| Rel n ->
(try match lookup_rel n env with
| RelDecl.LocalAssum _ -> None
| RelDecl.LocalDef (_,v,_) -> Some (lift n v)
with Not_found -> None)
| Var id ->
(try
if TransparentState.is_transparent_variable ts id then
env |> lookup_named id |> NamedDecl.get_value
else None
with Not_found -> None)
| LetIn (_,b,_,c) -> Some (subst1 b c)
| Lambda _ -> Some c
| Proj (p, c) ->
if Projection.unfolded p then assert false
else unfold_projection env evd ts p c
| _ -> assert false
type flex_kind_of_term =
| Rigid
| MaybeFlexible of EConstr.t (* reducible but not necessarily reduced *)
| Flexible of EConstr.existential
let is_frozen flags (evk, _) = Evar.Set.mem evk flags.frozen_evars
let flex_kind_of_term flags env evd c sk =
match EConstr.kind evd c with
| LetIn _ | Rel _ | Const _ | Var _ | Proj _ ->
Option.cata (fun x -> MaybeFlexible x) Rigid (eval_flexible_term flags.open_ts env evd c)
| Lambda _ when not (Option.is_empty (Stack.decomp sk)) ->
if flags.modulo_betaiota then MaybeFlexible c
else Rigid
| Evar ev ->
if is_frozen flags ev then Rigid
else Flexible ev
| Lambda _ | Prod _ | Sort _ | Ind _ | Construct _ | CoFix _ | Int _ -> Rigid
| Meta _ -> Rigid
| Fix _ -> Rigid (* happens when the fixpoint is partially applied *)
| Cast _ | App _ | Case _ -> assert false
let apprec_nohdbeta flags env evd c =
let (t,sk as appr) = Reductionops.whd_nored_state evd (c, []) in
if flags.modulo_betaiota && Stack.not_purely_applicative sk
then Stack.zip evd (fst (whd_betaiota_deltazeta_for_iota_state
flags.open_ts env evd Cst_stack.empty appr))
else c
let position_problem l2r = function
| CONV -> None
| CUMUL -> Some l2r
(* [occur_rigidly ev evd t] tests if the evar ev occurs in a rigid
context in t. Precondition: t has a rigid head and is not reducible.
That function is an under approximation of occur-check, it can return
false even if the occur-check would succeed on the normal form. This
means we might postpone unsolvable constraints which will ultimately
result in an occur-check after reductions. If it returns true, we
know that the occur-check would also return true on the normal form.
[t] is assumed to have a rigid head, which can
appear under a elimination context (e.g. application, match or projection).
In the inner recursive function, the result indicates if the term is
rigid (irreducible), normal (succession of constructors) or
potentially reducible. For applications, this means than an
occurrence of the evar in arguments should be looked at to find an
occur-check if the head is rigid or normal. For inductive
eliminations, only an occurrence in a rigid context of the
discriminee counts as a rigid occurrence overall, not a normal
occurrence which might disappear after reduction. *)
type result = Rigid of bool | Normal of bool | Reducible
let rigid_normal_occ = function Rigid b -> b | Normal b -> b | _ -> false
let occur_rigidly flags env evd (evk,_) t =
let rec aux t =
match EConstr.kind evd t with
| App (f, c) ->
(match aux f with
| Rigid b -> Rigid (b || Array.exists (fun x -> rigid_normal_occ (aux x)) c)
| Normal b -> Normal (b || Array.exists (fun x -> rigid_normal_occ (aux x)) c)
| Reducible -> Reducible)
| Construct _ -> Normal false
| Ind _ | Sort _ -> Rigid false
| Proj (p, c) ->
let cst = Projection.constant p in
let rigid = not (TransparentState.is_transparent_constant flags.open_ts cst) in
if rigid then aux c
else (* if the evar appears rigidly in c then this elimination
cannot reduce and we have a rigid occurrence, otherwise
we don't know. *)
(match aux c with
| Rigid _ as res -> res
| Normal b -> Reducible
| Reducible -> Reducible)
| Evar (evk',l as ev) ->
if Evar.equal evk evk' then Rigid true
else if is_frozen flags ev then
Rigid (Array.exists (fun x -> rigid_normal_occ (aux x)) l)
else Reducible
| Cast (p, _, _) -> aux p
| Lambda (na, t, b) -> aux b
| LetIn (na, _, _, b) -> aux b
| Const (c,_) ->
if TransparentState.is_transparent_constant flags.open_ts c then Reducible
else Rigid false
| Prod (_, b, t) ->
let b' = aux b and t' = aux t in
if rigid_normal_occ b' || rigid_normal_occ t' then Rigid true
else Reducible
| Rel _ | Var _ -> Reducible
| Case (_,_,c,_) ->
(match aux c with
| Rigid b -> Rigid b
| _ -> Reducible)
| Meta _ | Fix _ | CoFix _ | Int _ -> Reducible
in
match aux t with
| Rigid b -> b
| Normal b -> b
| Reducible -> false
(* [check_conv_record env sigma (t1,stack1) (t2,stack2)] tries to decompose
the problem (t1 stack1) = (t2 stack2) into a problem
stack1 = params1@[c1]@extra_args1
stack2 = us2@extra_args2
t1 params1 c1 = proji params (c xs)
t2 us2 = head us
extra_args1 = extra_args2
by finding a record R and an object c := [xs:bs](Build_R params v1..vn)
with vi = (head us), for which we know that the i-th projection proji
satisfies
proji params (c xs) = head us
Rem: such objects, usable for conversion, are defined in the objdef
table; practically, it amounts to "canonically" equip t2 into a
object c in structure R (since, if c1 were not an evar, the
projection would have been reduced) *)
let check_conv_record env sigma (t1,sk1) (t2,sk2) =
let (proji, u), arg = Termops.global_app_of_constr sigma t1 in
let canon_s,sk2_effective =
try
match EConstr.kind sigma t2 with
Prod (_,a,b) -> (* assert (l2=[]); *)
let _, a, b = destProd sigma t2 in
if noccurn sigma 1 b then
lookup_canonical_conversion (proji, Prod_cs),
(Stack.append_app [|a;pop b|] Stack.empty)
else raise Not_found
| Sort s ->
let s = ESorts.kind sigma s in
lookup_canonical_conversion
(proji, Sort_cs (Sorts.family s)),[]
| Proj (p, c) ->
let c2 = Globnames.ConstRef (Projection.constant p) in
let c = Retyping.expand_projection env sigma p c [] in
let _, args = destApp sigma c in
let sk2 = Stack.append_app args sk2 in
lookup_canonical_conversion (proji, Const_cs c2), sk2
| _ ->
let (c2, _) = Termops.global_of_constr sigma t2 in
lookup_canonical_conversion (proji, Const_cs c2),sk2
with Not_found ->
let (c, cs) = lookup_canonical_conversion (proji,Default_cs) in
(c,cs),[]
in
let t', { o_DEF = c; o_CTX = ctx; o_INJ=n; o_TABS = bs;
o_TPARAMS = params; o_NPARAMS = nparams; o_TCOMPS = us } = canon_s in
let us = List.map EConstr.of_constr us in
let params = List.map EConstr.of_constr params in
let params1, c1, extra_args1 =
match arg with
| Some c -> (* A primitive projection applied to c *)
let ty = Retyping.get_type_of ~lax:true env sigma c in
let (i,u), ind_args =
try Inductiveops.find_mrectype env sigma ty
with _ -> raise Not_found
in Stack.append_app_list ind_args Stack.empty, c, sk1
| None ->
match Stack.strip_n_app nparams sk1 with
| Some (params1, c1, extra_args1) -> params1, c1, extra_args1
| _ -> raise Not_found in
let us2,extra_args2 =
let l_us = List.length us in
if Int.equal l_us 0 then Stack.empty,sk2_effective
else match (Stack.strip_n_app (l_us-1) sk2_effective) with
| None -> raise Not_found
| Some (l',el,s') -> (l'@Stack.append_app [|el|] Stack.empty,s') in
let u, ctx' = UnivGen.fresh_instance_from ctx None in
let subst = Univ.make_inverse_instance_subst u in
let c = EConstr.of_constr c in
let c' = subst_univs_level_constr subst c in
let t' = EConstr.of_constr t' in
let t' = subst_univs_level_constr subst t' in
let bs' = List.map (EConstr.of_constr %> subst_univs_level_constr subst) bs in
let params = List.map (fun c -> subst_univs_level_constr subst c) params in
let us = List.map (fun c -> subst_univs_level_constr subst c) us in
let h, _ = decompose_app_vect sigma t' in
ctx',(h, t2),c',bs',(Stack.append_app_list params Stack.empty,params1),
(Stack.append_app_list us Stack.empty,us2),(extra_args1,extra_args2),c1,
(n, Stack.zip sigma (t2,sk2))
(* Precondition: one of the terms of the pb is an uninstantiated evar,
* possibly applied to arguments. *)
let join_failures evd1 evd2 e1 e2 =
match e1, e2 with
| _, CannotSolveConstraint (_,ProblemBeyondCapabilities) -> (evd1,e1)
| _ -> (evd2,e2)
let rec ise_try evd = function
[] -> assert false
| [f] -> f evd
| f1::l ->
match f1 evd with
| Success _ as x -> x
| UnifFailure (evd1,e1) ->
match ise_try evd l with
| Success _ as x -> x
| UnifFailure (evd2,e2) ->
let evd,e = join_failures evd1 evd2 e1 e2 in
UnifFailure (evd,e)
let ise_and evd l =
let rec ise_and i = function
[] -> assert false
| [f] -> f i
| f1::l ->
match f1 i with
| Success i' -> ise_and i' l
| UnifFailure _ as x -> x in
ise_and evd l
let ise_exact ise x1 x2 =
match ise x1 x2 with
| None, out -> out
| _, (UnifFailure _ as out) -> out
| Some _, Success i -> UnifFailure (i,NotSameArgSize)
let ise_array2 evd f v1 v2 =
let rec allrec i = function
| -1 -> Success i
| n ->
match f i v1.(n) v2.(n) with
| Success i' -> allrec i' (n-1)
| UnifFailure _ as x -> x in
let lv1 = Array.length v1 in
if Int.equal lv1 (Array.length v2) then allrec evd (pred lv1)
else UnifFailure (evd,NotSameArgSize)
(* Applicative node of stack are read from the outermost to the innermost
but are unified the other way. *)
let rec ise_app_stack2 env f evd sk1 sk2 =
match sk1,sk2 with
| Stack.App node1 :: q1, Stack.App node2 :: q2 ->
let (t1,l1) = Stack.decomp_node_last node1 q1 in
let (t2,l2) = Stack.decomp_node_last node2 q2 in
begin match ise_app_stack2 env f evd l1 l2 with
|(_,UnifFailure _) as x -> x
|x,Success i' -> x,f env i' CONV t1 t2
end
| _, _ -> (sk1,sk2), Success evd
(* This function tries to unify 2 stacks element by element. It works
from the end to the beginning. If it unifies a non empty suffix of
stacks but not the entire stacks, the first part of the answer is
Some(the remaining prefixes to tackle)) *)
let ise_stack2 no_app env evd f sk1 sk2 =
let rec ise_stack2 deep i sk1 sk2 =
let fail x = if deep then Some (List.rev sk1, List.rev sk2), Success i
else None, x in
match sk1, sk2 with
| [], [] -> None, Success i
| Stack.Case (_,t1,c1,_)::q1, Stack.Case (_,t2,c2,_)::q2 ->
(match f env i CONV t1 t2 with
| Success i' ->
(match ise_array2 i' (fun ii -> f env ii CONV) c1 c2 with
| Success i'' -> ise_stack2 true i'' q1 q2
| UnifFailure _ as x -> fail x)
| UnifFailure _ as x -> fail x)
| Stack.Proj (p1,_)::q1, Stack.Proj (p2,_)::q2 ->
if Projection.Repr.equal (Projection.repr p1) (Projection.repr p2)
then ise_stack2 true i q1 q2
else fail (UnifFailure (i, NotSameHead))
| Stack.Fix (((li1, i1),(_,tys1,bds1 as recdef1)),a1,_)::q1,
Stack.Fix (((li2, i2),(_,tys2,bds2)),a2,_)::q2 ->
if Int.equal i1 i2 && Array.equal Int.equal li1 li2 then
match ise_and i [
(fun i -> ise_array2 i (fun ii -> f env ii CONV) tys1 tys2);
(fun i -> ise_array2 i (fun ii -> f (push_rec_types recdef1 env) ii CONV) bds1 bds2);
(fun i -> ise_exact (ise_stack2 false i) a1 a2)] with
| Success i' -> ise_stack2 true i' q1 q2
| UnifFailure _ as x -> fail x
else fail (UnifFailure (i,NotSameHead))
| Stack.App _ :: _, Stack.App _ :: _ ->
if no_app && deep then fail ((*dummy*)UnifFailure(i,NotSameHead)) else
begin match ise_app_stack2 env f i sk1 sk2 with
|_,(UnifFailure _ as x) -> fail x
|(l1, l2), Success i' -> ise_stack2 true i' l1 l2
end
|_, _ -> fail (UnifFailure (i,(* Maybe improve: *) NotSameHead))
in ise_stack2 false evd (List.rev sk1) (List.rev sk2)
(* Make sure that the matching suffix is the all stack *)
let exact_ise_stack2 env evd f sk1 sk2 =
let rec ise_stack2 i sk1 sk2 =
match sk1, sk2 with
| [], [] -> Success i
| Stack.Case (_,t1,c1,_)::q1, Stack.Case (_,t2,c2,_)::q2 ->
ise_and i [
(fun i -> ise_stack2 i q1 q2);
(fun i -> ise_array2 i (fun ii -> f env ii CONV) c1 c2);
(fun i -> f env i CONV t1 t2)]
| Stack.Fix (((li1, i1),(_,tys1,bds1 as recdef1)),a1,_)::q1,
Stack.Fix (((li2, i2),(_,tys2,bds2)),a2,_)::q2 ->
if Int.equal i1 i2 && Array.equal Int.equal li1 li2 then
ise_and i [
(fun i -> ise_stack2 i q1 q2);
(fun i -> ise_array2 i (fun ii -> f env ii CONV) tys1 tys2);
(fun i -> ise_array2 i (fun ii -> f (push_rec_types recdef1 env) ii CONV) bds1 bds2);
(fun i -> ise_stack2 i a1 a2)]
else UnifFailure (i,NotSameHead)
| Stack.Proj (p1,_)::q1, Stack.Proj (p2,_)::q2 ->
if Projection.Repr.equal (Projection.repr p1) (Projection.repr p2)
then ise_stack2 i q1 q2
else (UnifFailure (i, NotSameHead))
| Stack.App _ :: _, Stack.App _ :: _ ->
begin match ise_app_stack2 env f i sk1 sk2 with
|_,(UnifFailure _ as x) -> x
|(l1, l2), Success i' -> ise_stack2 i' l1 l2
end
|_, _ -> UnifFailure (i,(* Maybe improve: *) NotSameHead)
in
if Reductionops.Stack.compare_shape sk1 sk2 then
ise_stack2 evd (List.rev sk1) (List.rev sk2)
else UnifFailure (evd, (* Dummy *) NotSameHead)
(* Add equality constraints for covariant/invariant positions. For
irrelevant positions, unify universes when flexible. *)
let compare_cumulative_instances evd variances u u' =
match Evarutil.compare_cumulative_instances CONV variances u u' evd with
| Inl evd ->
Success evd
| Inr p -> UnifFailure (evd, UnifUnivInconsistency p)
let conv_fun f flags on_types =
let typefn env evd pbty term1 term2 =
let flags = { (default_flags env) with
with_cs = flags.with_cs;
frozen_evars = flags.frozen_evars }
in f flags env evd pbty term1 term2
in
let termfn env evd pbty term1 term2 =
f flags env evd pbty term1 term2
in
match on_types with
| TypeUnification -> typefn
| TermUnification -> termfn
let rec evar_conv_x flags env evd pbty term1 term2 =
let term1 = whd_head_evar evd term1 in
let term2 = whd_head_evar evd term2 in
(* Maybe convertible but since reducing can erase evars which [evar_apprec]
could have found, we do it only if the terms are free of evar.
Note: incomplete heuristic... *)
let ground_test =
if is_ground_term evd term1 && is_ground_term evd term2 then (
let e =
match infer_conv ~catch_incon:false ~pb:pbty ~ts:flags.closed_ts env evd term1 term2 with
| Some evd -> Success evd
| None -> UnifFailure (evd, ConversionFailed (env,term1,term2))
| exception Univ.UniverseInconsistency e -> UnifFailure (evd, UnifUnivInconsistency e)
in
match e with
| UnifFailure (evd, e) when not (is_ground_env evd env) -> None
| _ -> Some e)
else None
in
match ground_test with
| Some result -> result
| None ->
(* Until pattern-unification is used consistently, use nohdbeta to not
destroy beta-redexes that can be used for 1st-order unification *)
let term1 = apprec_nohdbeta flags env evd term1 in
let term2 = apprec_nohdbeta flags env evd term2 in
let default () =
evar_eqappr_x flags env evd pbty
(whd_nored_state evd (term1,Stack.empty), Cst_stack.empty)
(whd_nored_state evd (term2,Stack.empty), Cst_stack.empty)
in
begin match EConstr.kind evd term1, EConstr.kind evd term2 with
| Evar ev, _ when Evd.is_undefined evd (fst ev) && not (is_frozen flags ev) ->
(match solve_simple_eqn (conv_fun evar_conv_x) flags env evd
(position_problem true pbty,ev,term2) with
| UnifFailure (_,(OccurCheck _ | NotClean _)) ->
(* Eta-expansion might apply *)
(* OccurCheck: eta-expansion could solve
?X = {| foo := ?X.(foo) |}
NotClean: pruning in solve_simple_eqn is incomplete wrt
Miller patterns *)
default ()
| x -> x)
| _, Evar ev when Evd.is_undefined evd (fst ev) && not (is_frozen flags ev) ->
(match solve_simple_eqn (conv_fun evar_conv_x) flags env evd
(position_problem false pbty,ev,term1) with
| UnifFailure (_, (OccurCheck _ | NotClean _)) ->
(* OccurCheck: eta-expansion could solve
?X = {| foo := ?X.(foo) |}
NotClean: pruning in solve_simple_eqn is incomplete wrt
Miller patterns *)
default ()
| x -> x)
| _ -> default ()
end
and evar_eqappr_x ?(rhs_is_already_stuck = false) flags env evd pbty
((term1,sk1 as appr1),csts1) ((term2,sk2 as appr2),csts2) =
let quick_fail i = (* not costly, loses info *)
UnifFailure (i, NotSameHead)
in
let miller_pfenning on_left fallback ev lF tM evd =
match is_unification_pattern_evar env evd ev lF tM with
| None -> fallback ()
| Some l1' -> (* Miller-Pfenning's patterns unification *)
let t2 = tM in
let t2 = solve_pattern_eqn env evd l1' t2 in
solve_simple_eqn (conv_fun evar_conv_x) flags env evd
(position_problem on_left pbty,ev,t2)
in
let consume_stack on_left (termF,skF) (termO,skO) evd =
let switch f a b = if on_left then f a b else f b a in
let not_only_app = Stack.not_purely_applicative skO in
match switch (ise_stack2 not_only_app env evd (evar_conv_x flags)) skF skO with
|Some (l,r), Success i' when on_left && (not_only_app || List.is_empty l) ->
switch (evar_conv_x flags env i' pbty) (Stack.zip evd (termF,l)) (Stack.zip evd (termO,r))
|Some (r,l), Success i' when not on_left && (not_only_app || List.is_empty l) ->
switch (evar_conv_x flags env i' pbty) (Stack.zip evd (termF,l)) (Stack.zip evd (termO,r))
|None, Success i' -> switch (evar_conv_x flags env i' pbty) termF termO
|_, (UnifFailure _ as x) -> x
|Some _, _ -> UnifFailure (evd,NotSameArgSize) in
let eta env evd onleft sk term sk' term' =
assert (match sk with [] -> true | _ -> false);
let (na,c1,c'1) = destLambda evd term in
let c = nf_evar evd c1 in
let env' = push_rel (RelDecl.LocalAssum (na,c)) env in
let out1 = whd_betaiota_deltazeta_for_iota_state
flags.open_ts env' evd Cst_stack.empty (c'1, Stack.empty) in
let out2 = whd_nored_state evd
(lift 1 (Stack.zip evd (term', sk')), Stack.append_app [|EConstr.mkRel 1|] Stack.empty),
Cst_stack.empty in
if onleft then evar_eqappr_x flags env' evd CONV out1 out2
else evar_eqappr_x flags env' evd CONV out2 out1
in
let rigids env evd sk term sk' term' =
let check_strict evd u u' =
let cstrs = Univ.enforce_eq_instances u u' Univ.Constraint.empty in
try Success (Evd.add_constraints evd cstrs)
with Univ.UniverseInconsistency p -> UnifFailure (evd, UnifUnivInconsistency p)
in
let compare_heads evd =
match EConstr.kind evd term, EConstr.kind evd term' with
| Const (c, u), Const (c', u') when Constant.equal c c' ->
let u = EInstance.kind evd u and u' = EInstance.kind evd u' in
check_strict evd u u'
| Const _, Const _ -> UnifFailure (evd, NotSameHead)
| Ind ((mi,i) as ind , u), Ind (ind', u') when Names.eq_ind ind ind' ->
if EInstance.is_empty u && EInstance.is_empty u' then Success evd
else
let u = EInstance.kind evd u and u' = EInstance.kind evd u' in
let mind = Environ.lookup_mind mi env in
let open Declarations in
begin match mind.mind_variance with
| None -> check_strict evd u u'
| Some variances ->
let nparamsaplied = Stack.args_size sk in
let nparamsaplied' = Stack.args_size sk' in
let needed = Reduction.inductive_cumulativity_arguments (mind,i) in
if not (Int.equal nparamsaplied needed && Int.equal nparamsaplied' needed)
then check_strict evd u u'
else
compare_cumulative_instances evd variances u u'
end
| Ind _, Ind _ -> UnifFailure (evd, NotSameHead)
| Construct (((mi,ind),ctor as cons), u), Construct (cons', u')
when Names.eq_constructor cons cons' ->
if EInstance.is_empty u && EInstance.is_empty u' then Success evd
else
let u = EInstance.kind evd u and u' = EInstance.kind evd u' in
let mind = Environ.lookup_mind mi env in
let open Declarations in
begin match mind.mind_variance with
| None -> check_strict evd u u'
| Some variances ->
let nparamsaplied = Stack.args_size sk in
let nparamsaplied' = Stack.args_size sk' in
let needed = Reduction.constructor_cumulativity_arguments (mind,ind,ctor) in
if not (Int.equal nparamsaplied needed && Int.equal nparamsaplied' needed)
then check_strict evd u u'
else
Success (compare_constructor_instances evd u u')
end
| Construct _, Construct _ -> UnifFailure (evd, NotSameHead)
| _, _ -> anomaly (Pp.str "")
in
ise_and evd [(fun i ->
try compare_heads i
with Univ.UniverseInconsistency p -> UnifFailure (i, UnifUnivInconsistency p));
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk sk')]
in
let consume on_left (_, skF as apprF) (_,skM as apprM) i =
if not (Stack.is_empty skF && Stack.is_empty skM) then
consume_stack on_left apprF apprM i
else quick_fail i
in
let miller on_left ev (termF,skF as apprF) (termM, skM as apprM) i =
let switch f a b = if on_left then f a b else f b a in
let not_only_app = Stack.not_purely_applicative skM in
match Stack.list_of_app_stack skF with
| None -> quick_fail evd
| Some lF ->
let tM = Stack.zip evd apprM in
miller_pfenning on_left
(fun () -> if not_only_app then (* Postpone the use of an heuristic *)
switch (fun x y -> Success (Evarutil.add_unification_pb (pbty,env,x,y) i)) (Stack.zip evd apprF) tM
else quick_fail i)
ev lF tM i
in
let flex_maybeflex on_left ev ((termF,skF as apprF),cstsF) ((termM, skM as apprM),cstsM) vM =
let switch f a b = if on_left then f a b else f b a in
let delta i =
switch (evar_eqappr_x flags env i pbty) (apprF,cstsF)
(whd_betaiota_deltazeta_for_iota_state flags.open_ts env i cstsM (vM,skM))
in
let default i = ise_try i [miller on_left ev apprF apprM;
consume on_left apprF apprM;
delta]
in
match EConstr.kind evd termM with
| Proj (p, c) when not (Stack.is_empty skF) ->
(* Might be ?X args = p.c args', and we have to eta-expand the
primitive projection if |args| >= |args'|+1. *)
let nargsF = Stack.args_size skF and nargsM = Stack.args_size skM in
begin
(* ?X argsF' ~= (p.c ..) argsM' -> ?X ~= (p.c ..), no need to expand *)
if nargsF <= nargsM then default evd
else
let f =
try
let termM' = Retyping.expand_projection env evd p c [] in
let apprM', cstsM' =
whd_betaiota_deltazeta_for_iota_state flags.open_ts env evd cstsM (termM',skM)
in
let delta' i =
switch (evar_eqappr_x flags env i pbty) (apprF,cstsF) (apprM',cstsM')
in
fun i -> ise_try i [miller on_left ev apprF apprM';
consume on_left apprF apprM'; delta']
with Retyping.RetypeError _ ->
(* Happens thanks to w_unify building ill-typed terms *)
default
in f evd
end
| _ -> default evd
in
let flex_rigid on_left ev (termF, skF as apprF) (termR, skR as apprR) =
let switch f a b = if on_left then f a b else f b a in
let eta evd =
match EConstr.kind evd termR with
| Lambda _ when (* if ever problem is ill-typed: *) List.is_empty skR ->
eta env evd false skR termR skF termF
| Construct u -> eta_constructor flags env evd skR u skF termF
| _ -> UnifFailure (evd,NotSameHead)
in
match Stack.list_of_app_stack skF with
| None ->
ise_try evd [consume_stack on_left apprF apprR; eta]
| Some lF ->
let tR = Stack.zip evd apprR in
miller_pfenning on_left
(fun () ->
ise_try evd
[eta;(* Postpone the use of an heuristic *)
(fun i ->
if not (occur_rigidly flags env i ev tR) then
let i,tF =
if isRel i tR || isVar i tR then
(* Optimization so as to generate candidates *)
let i,ev = evar_absorb_arguments env i ev lF in
i,mkEvar ev
else
i,Stack.zip evd apprF in
switch (fun x y -> Success (Evarutil.add_unification_pb (pbty,env,x,y) i))
tF tR
else
UnifFailure (evd,OccurCheck (fst ev,tR)))])
ev lF tR evd
in
let first_order env i t1 t2 sk1 sk2 =
(* Try first-order unification *)
match ise_stack2 false env i (evar_conv_x flags) sk1 sk2 with
| None, Success i' ->
(* We do have sk1[] = sk2[]: we now unify ?ev1 and ?ev2 *)
(* Note that ?ev1 and ?ev2, may have been instantiated in the meantime *)
let ev1' = whd_evar i' t1 in
if isEvar i' ev1' then
solve_simple_eqn (conv_fun evar_conv_x) flags env i'
(position_problem true pbty,destEvar i' ev1',term2)
else
evar_eqappr_x flags env evd pbty
((ev1', sk1), csts1) ((term2, sk2), csts2)
| Some (r,[]), Success i' ->
(* We have sk1'[] = sk2[] for some sk1' s.t. sk1[]=sk1'[r[]] *)
(* we now unify r[?ev1] and ?ev2 *)
let ev2' = whd_evar i' t2 in
if isEvar i' ev2' then
solve_simple_eqn (conv_fun evar_conv_x) flags env i'
(position_problem false pbty,destEvar i' ev2',Stack.zip i' (term1,r))
else
evar_eqappr_x flags env evd pbty
((ev2', sk1), csts1) ((term2, sk2), csts2)
| Some ([],r), Success i' ->
(* Symmetrically *)
(* We have sk1[] = sk2'[] for some sk2' s.t. sk2[]=sk2'[r[]] *)
(* we now unify ?ev1 and r[?ev2] *)
let ev1' = whd_evar i' t1 in
if isEvar i' ev1' then
solve_simple_eqn (conv_fun evar_conv_x) flags env i'
(position_problem true pbty,destEvar i' ev1',Stack.zip i' (term2,r))
else evar_eqappr_x flags env evd pbty
((ev1', sk1), csts1) ((term2, sk2), csts2)
| None, (UnifFailure _ as x) ->
(* sk1 and sk2 have no common outer part *)
if Stack.not_purely_applicative sk2 then
(* Ad hoc compatibility with 8.4 which treated non-app as rigid *)
flex_rigid true (destEvar evd t1) appr1 appr2
else
if Stack.not_purely_applicative sk1 then
(* Ad hoc compatibility with 8.4 which treated non-app as rigid *)
flex_rigid false (destEvar evd t2) appr2 appr1
else
(* We could instead try Miller unification, then
postpone to see if other equations help, as in:
[Check fun a b : unit => (eqᵣefl : _ a = _ a b)] *)
x
| Some _, Success _ ->
(* sk1 and sk2 have a common outer part *)
if Stack.not_purely_applicative sk2 then
(* Ad hoc compatibility with 8.4 which treated non-app as rigid *)
flex_rigid true (destEvar evd t1) appr1 appr2
else
if Stack.not_purely_applicative sk1 then
(* Ad hoc compatibility with 8.4 which treated non-app as rigid *)
flex_rigid false (destEvar evd t2) appr2 appr1
else
(* We could instead try Miller unification, then
postpone to see if other equations help, as in:
[Check fun a b c : unit => (eqᵣefl : _ a b = _ c a b)] *)
UnifFailure (i,NotSameArgSize)
| _, _ -> anomaly (Pp.str "Unexpected result from ise_stack2.")
in
let app_empty = match sk1, sk2 with [], [] -> true | _ -> false in
(* Evar must be undefined since we have flushed evars *)
let () = if !debug_unification then
let open Pp in
Feedback.msg_debug (v 0 (pr_state env evd appr1 ++ cut () ++ pr_state env evd appr2 ++ cut ())) in
match (flex_kind_of_term flags env evd term1 sk1,
flex_kind_of_term flags env evd term2 sk2) with
| Flexible (sp1,al1), Flexible (sp2,al2) ->
(* sk1[?ev1] =? sk2[?ev2] *)
let f1 i = first_order env i term1 term2 sk1 sk2
and f2 i =
if Evar.equal sp1 sp2 then
match ise_stack2 false env i (evar_conv_x flags) sk1 sk2 with
|None, Success i' ->
Success (solve_refl (fun flags p env i pbty a1 a2 ->
let flags =
match p with
| TypeUnification -> default_flags env
| TermUnification -> flags
in
is_success (evar_conv_x flags env i pbty a1 a2)) flags
env i' (position_problem true pbty) sp1 al1 al2)
|_, (UnifFailure _ as x) -> x
|Some _, _ -> UnifFailure (i,NotSameArgSize)
else UnifFailure (i,NotSameHead)
and f3 i = miller true (sp1,al1) appr1 appr2 i
and f4 i = miller false (sp2,al2) appr2 appr1 i
and f5 i =
(* We ensure failure of consuming the stacks does not
propagate an error about unification of the stacks while
the heads themselves cannot be unified, so we return
NotSameHead. *)
match consume true appr1 appr2 i with
| Success _ as x -> x
| UnifFailure _ -> quick_fail i
in
ise_try evd [f1; f2; f3; f4; f5]
| Flexible ev1, MaybeFlexible v2 ->
flex_maybeflex true ev1 (appr1,csts1) (appr2,csts2) v2
| MaybeFlexible v1, Flexible ev2 ->
flex_maybeflex false ev2 (appr2,csts2) (appr1,csts1) v1
| MaybeFlexible v1, MaybeFlexible v2 -> begin
match EConstr.kind evd term1, EConstr.kind evd term2 with
| LetIn (na1,b1,t1,c'1), LetIn (na2,b2,t2,c'2) ->
let f1 i = (* FO *)
ise_and i
[(fun i -> ise_try i
[(fun i -> evar_conv_x flags env i CUMUL t1 t2);
(fun i -> evar_conv_x flags env i CUMUL t2 t1)]);
(fun i -> evar_conv_x flags env i CONV b1 b2);
(fun i ->
let b = nf_evar i b1 in
let t = nf_evar i t1 in
let na = Nameops.Name.pick_annot na1 na2 in
evar_conv_x flags (push_rel (RelDecl.LocalDef (na,b,t)) env) i pbty c'1 c'2);
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2)]
and f2 i =
let out1 = whd_betaiota_deltazeta_for_iota_state flags.open_ts env i csts1 (v1,sk1)
and out2 = whd_betaiota_deltazeta_for_iota_state flags.open_ts env i csts2 (v2,sk2)
in evar_eqappr_x flags env i pbty out1 out2
in
ise_try evd [f1; f2]
| Proj (p, c), Proj (p', c') when Projection.repr_equal p p' ->
let f1 i =
ise_and i
[(fun i -> evar_conv_x flags env i CONV c c');
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2)]
and f2 i =
let out1 = whd_betaiota_deltazeta_for_iota_state flags.open_ts env i csts1 (v1,sk1)
and out2 = whd_betaiota_deltazeta_for_iota_state flags.open_ts env i csts2 (v2,sk2)
in evar_eqappr_x flags env i pbty out1 out2
in
ise_try evd [f1; f2]
(* Catch the p.c ~= p c' cases *)
| Proj (p,c), Const (p',u) when Constant.equal (Projection.constant p) p' ->
let res =
try Some (destApp evd (Retyping.expand_projection env evd p c []))
with Retyping.RetypeError _ -> None
in
(match res with
| Some (f1,args1) ->
evar_eqappr_x flags env evd pbty ((f1,Stack.append_app args1 sk1),csts1)
(appr2,csts2)
| None -> UnifFailure (evd,NotSameHead))
| Const (p,u), Proj (p',c') when Constant.equal p (Projection.constant p') ->
let res =
try Some (destApp evd (Retyping.expand_projection env evd p' c' []))
with Retyping.RetypeError _ -> None
in
(match res with
| Some (f2,args2) ->
evar_eqappr_x flags env evd pbty (appr1,csts1) ((f2,Stack.append_app args2 sk2),csts2)
| None -> UnifFailure (evd,NotSameHead))
| _, _ ->
let f1 i =
(* Gather the universe constraints that would make term1 and term2 equal.
If these only involve unifications of flexible universes to other universes,
allow this identification (first-order unification of universes). Otherwise
fallback to unfolding.
*)
let univs = EConstr.eq_constr_universes env evd term1 term2 in
match univs with
| Some univs ->
ise_and i [(fun i ->
try Success (Evd.add_universe_constraints i univs)
with UniversesDiffer -> UnifFailure (i,NotSameHead)
| Univ.UniverseInconsistency p -> UnifFailure (i, UnifUnivInconsistency p));
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2)]
| None ->
UnifFailure (i,NotSameHead)
and f2 i =
(try
if not flags.with_cs then raise Not_found
else conv_record flags env i
(try check_conv_record env i appr1 appr2
with Not_found -> check_conv_record env i appr2 appr1)
with Not_found -> UnifFailure (i,NoCanonicalStructure))
and f3 i =
(* heuristic: unfold second argument first, exception made
if the first argument is a beta-redex (expand a constant
only if necessary) or the second argument is potentially
usable as a canonical projection or canonical value *)
let rec is_unnamed (hd, args) = match EConstr.kind i hd with
| (Var _|Construct _|Ind _|Const _|Prod _|Sort _|Int _) ->
Stack.not_purely_applicative args
| (CoFix _|Meta _|Rel _)-> true
| Evar _ -> Stack.not_purely_applicative args
(* false (* immediate solution without Canon Struct *)*)
| Lambda _ -> assert (match args with [] -> true | _ -> false); true
| LetIn (_,b,_,c) -> is_unnamed
(fst (whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i Cst_stack.empty (subst1 b c, args)))
| Fix _ -> true (* Partially applied fix can be the result of a whd call *)
| Proj (p, _) -> Projection.unfolded p || Stack.not_purely_applicative args
| Case _ | App _| Cast _ -> assert false in
let rhs_is_stuck_and_unnamed () =
let applicative_stack = fst (Stack.strip_app sk2) in
is_unnamed
(fst (whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i Cst_stack.empty (v2, applicative_stack))) in
let rhs_is_already_stuck =
rhs_is_already_stuck || rhs_is_stuck_and_unnamed () in
if (EConstr.isLambda i term1 || rhs_is_already_stuck)
&& (not (Stack.not_purely_applicative sk1)) then
evar_eqappr_x ~rhs_is_already_stuck flags env i pbty
(whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i (Cst_stack.add_cst term1 csts1) (v1,sk1))
(appr2,csts2)
else
evar_eqappr_x flags env i pbty (appr1,csts1)
(whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i (Cst_stack.add_cst term2 csts2) (v2,sk2))
in
ise_try evd [f1; f2; f3]
end
| Rigid, Rigid when EConstr.isLambda evd term1 && EConstr.isLambda evd term2 ->
let (na1,c1,c'1) = EConstr.destLambda evd term1 in
let (na2,c2,c'2) = EConstr.destLambda evd term2 in
ise_and evd
[(fun i -> evar_conv_x flags env i CONV c1 c2);
(fun i ->
let c = nf_evar i c1 in
let na = Nameops.Name.pick_annot na1 na2 in
evar_conv_x flags (push_rel (RelDecl.LocalAssum (na,c)) env) i CONV c'1 c'2);
(* When in modulo_betaiota = false case, lambda's are not reduced *)
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2)]
| Flexible ev1, Rigid -> flex_rigid true ev1 appr1 appr2
| Rigid, Flexible ev2 -> flex_rigid false ev2 appr2 appr1
| MaybeFlexible v1, Rigid ->
let f3 i =
(try
if not flags.with_cs then raise Not_found
else conv_record flags env i (check_conv_record env i appr1 appr2)
with Not_found -> UnifFailure (i,NoCanonicalStructure))
and f4 i =
evar_eqappr_x flags env i pbty
(whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i (Cst_stack.add_cst term1 csts1) (v1,sk1))
(appr2,csts2)
in
ise_try evd [f3; f4]
| Rigid, MaybeFlexible v2 ->
let f3 i =
(try
if not flags.with_cs then raise Not_found
else conv_record flags env i (check_conv_record env i appr2 appr1)
with Not_found -> UnifFailure (i,NoCanonicalStructure))
and f4 i =
evar_eqappr_x flags env i pbty (appr1,csts1)
(whd_betaiota_deltazeta_for_iota_state
flags.open_ts env i (Cst_stack.add_cst term2 csts2) (v2,sk2))
in
ise_try evd [f3; f4]
(* Eta-expansion *)
| Rigid, _ when isLambda evd term1 && (* if ever ill-typed: *) List.is_empty sk1 ->
eta env evd true sk1 term1 sk2 term2
| _, Rigid when isLambda evd term2 && (* if ever ill-typed: *) List.is_empty sk2 ->
eta env evd false sk2 term2 sk1 term1
| Rigid, Rigid -> begin
match EConstr.kind evd term1, EConstr.kind evd term2 with
| Sort s1, Sort s2 when app_empty ->
(try
let s1 = ESorts.kind evd s1 in
let s2 = ESorts.kind evd s2 in
let evd' =
if pbty == CONV
then Evd.set_eq_sort env evd s1 s2
else Evd.set_leq_sort env evd s1 s2
in Success evd'
with Univ.UniverseInconsistency p ->
UnifFailure (evd,UnifUnivInconsistency p)
| e when CErrors.noncritical e -> UnifFailure (evd,NotSameHead))
| Prod (n1,c1,c'1), Prod (n2,c2,c'2) when app_empty ->
ise_and evd
[(fun i -> evar_conv_x flags env i CONV c1 c2);
(fun i ->
let c = nf_evar i c1 in
let na = Nameops.Name.pick_annot n1 n2 in
evar_conv_x flags (push_rel (RelDecl.LocalAssum (na,c)) env) i pbty c'1 c'2)]
| Rel x1, Rel x2 ->
if Int.equal x1 x2 then
exact_ise_stack2 env evd (evar_conv_x flags) sk1 sk2
else UnifFailure (evd,NotSameHead)
| Var var1, Var var2 ->
if Id.equal var1 var2 then
exact_ise_stack2 env evd (evar_conv_x flags) sk1 sk2
else UnifFailure (evd,NotSameHead)
| Const _, Const _
| Ind _, Ind _
| Construct _, Construct _
| Int _, Int _ ->
rigids env evd sk1 term1 sk2 term2
| Evar (sp1,al1), Evar (sp2,al2) -> (* Frozen evars *)
if Evar.equal sp1 sp2 then
match ise_stack2 false env evd (evar_conv_x flags) sk1 sk2 with
|None, Success i' ->
ise_array2 i' (fun i' -> evar_conv_x flags env i' CONV) al1 al2
|_, (UnifFailure _ as x) -> x
|Some _, _ -> UnifFailure (evd,NotSameArgSize)
else UnifFailure (evd,NotSameHead)
| Construct u, _ ->
eta_constructor flags env evd sk1 u sk2 term2
| _, Construct u ->
eta_constructor flags env evd sk2 u sk1 term1
| Fix ((li1, i1),(_,tys1,bds1 as recdef1)), Fix ((li2, i2),(_,tys2,bds2)) -> (* Partially applied fixs *)
if Int.equal i1 i2 && Array.equal Int.equal li1 li2 then
ise_and evd [
(fun i -> ise_array2 i (fun i' -> evar_conv_x flags env i' CONV) tys1 tys2);
(fun i -> ise_array2 i (fun i' -> evar_conv_x flags (push_rec_types recdef1 env) i' CONV) bds1 bds2);
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2)]
else UnifFailure (evd, NotSameHead)
| CoFix (i1,(_,tys1,bds1 as recdef1)), CoFix (i2,(_,tys2,bds2)) ->
if Int.equal i1 i2 then
ise_and evd
[(fun i -> ise_array2 i
(fun i -> evar_conv_x flags env i CONV) tys1 tys2);
(fun i -> ise_array2 i
(fun i -> evar_conv_x flags (push_rec_types recdef1 env) i CONV)
bds1 bds2);
(fun i -> exact_ise_stack2 env i
(evar_conv_x flags) sk1 sk2)]
else UnifFailure (evd,NotSameHead)
| (Meta _, _) | (_, Meta _) ->
begin match ise_stack2 true env evd (evar_conv_x flags) sk1 sk2 with
|_, (UnifFailure _ as x) -> x
|None, Success i' -> evar_conv_x flags env i' CONV term1 term2
|Some (sk1',sk2'), Success i' -> evar_conv_x flags env i' CONV (Stack.zip i' (term1,sk1')) (Stack.zip i' (term2,sk2'))
end
| (Ind _ | Sort _ | Prod _ | CoFix _ | Fix _ | Rel _ | Var _ | Const _ | Int _ | Evar _ | Lambda _), _ ->
UnifFailure (evd,NotSameHead)
| _, (Ind _ | Sort _ | Prod _ | CoFix _ | Fix _ | Rel _ | Var _ | Const _ | Int _ | Evar _ | Lambda _) ->
UnifFailure (evd,NotSameHead)
| Case _, _ -> UnifFailure (evd,NotSameHead)
| Proj _, _ -> UnifFailure (evd,NotSameHead)
| (App _ | Cast _), _ -> assert false
| LetIn _, _ -> assert false
end
and conv_record flags env evd (ctx,(h,h2),c,bs,(params,params1),(us,us2),(sk1,sk2),c1,(n,t2)) =
(* Tries to unify the states
(proji params1 c1 | sk1) = (proji params2 (c (?xs:bs)) | sk2)
and the terms
h us = h2 us2
where
c = the constant for the canonical structure (i.e. some term of the form
fun (xs:bs) => Build_R params v1 .. vi-1 (h us) vi+1 .. vn)
bs = the types of the parameters of the canonical structure
c1 = the main argument of the canonical projection
sk1, sk2 = the surrounding stacks of the conversion problem
params1, params2 = the params of the projection (empty if a primitive proj)
knowing that
(proji params1 c1 | sk1) = (h2 us2 | sk2)
had to be initially resolved
*)
let evd = Evd.merge_context_set Evd.univ_flexible evd ctx in
if Reductionops.Stack.compare_shape sk1 sk2 then
let (evd',ks,_,test) =
List.fold_left
(fun (i,ks,m,test) b ->
if match n with Some n -> Int.equal m n | None -> false then
let ty = Retyping.get_type_of env i t2 in
let test i = evar_conv_x flags env i CUMUL ty (substl ks b) in
(i,t2::ks, m-1, test)
else
let dloc = Loc.tag Evar_kinds.InternalHole in
let (i', ev) = Evarutil.new_evar env i ~src:dloc (substl ks b) in
(i', ev :: ks, m - 1,test))
(evd,[],List.length bs,fun i -> Success i) bs
in
let app = mkApp (c, Array.rev_of_list ks) in
ise_and evd'
[(fun i ->
exact_ise_stack2 env i
(fun env' i' cpb x1 x -> evar_conv_x flags env' i' cpb x1 (substl ks x))
params1 params);
(fun i ->
exact_ise_stack2 env i
(fun env' i' cpb u1 u -> evar_conv_x flags env' i' cpb u1 (substl ks u))
us2 us);
(fun i -> evar_conv_x flags env i CONV c1 app);
(fun i -> exact_ise_stack2 env i (evar_conv_x flags) sk1 sk2);
test;
(fun i -> evar_conv_x flags env i CONV h2
(fst (decompose_app_vect i (substl ks h))))]
else UnifFailure(evd,(*dummy*)NotSameHead)
and eta_constructor flags env evd sk1 ((ind, i), u) sk2 term2 =
let open Declarations in
let mib = lookup_mind (fst ind) env in
match get_projections env ind with
| Some projs when mib.mind_finite == BiFinite ->
let pars = mib.mind_nparams in
(try
let l1' = Stack.tail pars sk1 in
let l2' =
let term = Stack.zip evd (term2,sk2) in
List.map (fun p -> EConstr.mkProj (Projection.make p false, term)) (Array.to_list projs)
in
exact_ise_stack2 env evd (evar_conv_x { flags with with_cs = false}) l1'
(Stack.append_app_list l2' Stack.empty)
with
| Invalid_argument _ ->
(* Stack.tail: partially applied constructor *)
UnifFailure(evd,NotSameHead))
| _ -> UnifFailure (evd,NotSameHead)
let evar_conv_x flags = evar_conv_x flags
let evar_unify = conv_fun evar_conv_x
(* Profiling *)
let evar_conv_x =
if Flags.profile then
let evar_conv_xkey = CProfile.declare_profile "evar_conv_x" in
CProfile.profile6 evar_conv_xkey evar_conv_x
else evar_conv_x
let evar_conv_hook_get, evar_conv_hook_set = Hook.make ~default:evar_conv_x ()
let evar_conv_x flags = Hook.get evar_conv_hook_get flags
let set_evar_conv f = Hook.set evar_conv_hook_set f
(* We assume here |l1| <= |l2| *)
let first_order_unification flags env evd (ev1,l1) (term2,l2) =
let (deb2,rest2) = Array.chop (Array.length l2-Array.length l1) l2 in
ise_and evd
(* First compare extra args for better failure message *)
[(fun i -> ise_array2 i (fun i -> evar_conv_x flags env i CONV) rest2 l1);
(fun i ->
(* Then instantiate evar unless already done by unifying args *)
let t2 = mkApp(term2,deb2) in
if is_defined i (fst ev1) then
evar_conv_x flags env i CONV t2 (mkEvar ev1)
else
solve_simple_eqn ~choose:true ~imitate_defs:false
evar_unify flags env i (None,ev1,t2))]
let choose_less_dependent_instance evk evd term args =
let evi = Evd.find_undefined evd evk in
let subst = make_pure_subst evi args in
let subst' = List.filter (fun (id,c) -> EConstr.eq_constr evd c term) subst in
match subst' with
| [] -> None
| (id, _) :: _ -> Some (Evd.define evk (mkVar id) evd)
type occurrence_match_test =
env -> evar_map -> constr ->
env -> evar_map -> int -> constr -> constr -> bool * evar_map
type occurrence_selection =
| AtOccurrences of Locus.occurrences
| Unspecified of Abstraction.abstraction
type occurrences_selection =
occurrence_match_test * occurrence_selection list
let default_occurrence_selection = Unspecified Abstraction.Imitate
let default_occurrence_test ~frozen_evars ts _ origsigma _ env sigma _ c pat =
let flags = { (default_flags_of ~subterm_ts:ts ts) with frozen_evars } in
match evar_conv_x flags env sigma CONV c pat with
| Success sigma -> true, sigma
| UnifFailure _ -> false, sigma
let default_occurrences_selection ?(frozen_evars=Evar.Set.empty) ts n =
(default_occurrence_test ~frozen_evars ts,
List.init n (fun _ -> default_occurrence_selection))
let apply_on_subterm env evd fixedref f test c t =
let test = test env evd c in
let prc env evd = Termops.Internal.print_constr_env env evd in
let evdref = ref evd in
let rec applyrec (env,(k,c) as acc) t =
if Evar.Set.exists (fun fixed -> occur_evar !evdref fixed t) !fixedref then
match EConstr.kind !evdref t with
| Evar (ev, args) when Evar.Set.mem ev !fixedref -> t
| _ -> map_constr_with_binders_left_to_right !evdref
(fun d (env,(k,c)) -> (push_rel d env, (k+1,lift 1 c)))
applyrec acc t
else
(if !debug_ho_unification then
Feedback.msg_debug Pp.(str"Testing " ++ prc env !evdref c ++ str" against " ++ prc env !evdref t);
let b, evd =
try test env !evdref k c t
with e when CErrors.noncritical e -> assert false in
if b then (if !debug_ho_unification then Feedback.msg_debug (Pp.str "succeeded");
let evd', t' = f !evdref k t in
evdref := evd'; t')
else (
if !debug_ho_unification then Feedback.msg_debug (Pp.str "failed");
map_constr_with_binders_left_to_right !evdref
(fun d (env,(k,c)) -> (push_rel d env, (k+1,lift 1 c)))
applyrec acc t))
in
let t' = applyrec (env,(0,c)) t in
!evdref, t'
let filter_possible_projections evd c ty ctxt args =
(* Since args in the types will be replaced by holes, we count the
fv of args to have a well-typed filter; don't know how necessary
it is however to have a well-typed filter here *)
let fv1 = free_rels evd (mkApp (c,args)) (* Hack: locally untyped *) in
let fv2 = collect_vars evd (mkApp (c,args)) in
let len = Array.length args in
let tyvars = collect_vars evd ty in
List.map_i (fun i decl ->
let () = assert (i < len) in
let a = Array.unsafe_get args i in
(match decl with
| NamedDecl.LocalAssum _ -> false
| NamedDecl.LocalDef (_,c,_) -> not (isRel evd c || isVar evd c)) ||
a == c ||
(* Here we make an approximation, for instance, we could also be *)
(* interested in finding a term u convertible to c such that a occurs *)
(* in u *)
isRel evd a && Int.Set.mem (destRel evd a) fv1 ||
isVar evd a && Id.Set.mem (destVar evd a) fv2 ||
Id.Set.mem (NamedDecl.get_id decl) tyvars)
0 ctxt
let solve_evars = ref (fun _ -> failwith "solve_evars not installed")
let set_solve_evars f = solve_evars := f
(* We solve the problem env_rhs |- ?e[u1..un] = rhs knowing
* x1:T1 .. xn:Tn |- ev : ty
* by looking for a maximal well-typed abtraction over u1..un in rhs
*
* We first build C[e11..e1p1,..,en1..enpn] obtained from rhs by replacing
* all occurrences of u1..un by evars eij of type Ti' where itself Ti' has
* been obtained from the type of ui by also replacing all occurrences of
* u1..ui-1 by evars.
*
* Then, we use typing to infer the relations between the different
* occurrences. If some occurrence is still unconstrained after typing,
* we instantiate successively the unresolved occurrences of un by xn,
* of un-1 by xn-1, etc [the idea comes from Chung-Kil Hur, that he
* used for his Heq plugin; extensions to several arguments based on a
* proposition from Dan Grayson]
*)
let check_selected_occs env sigma c occ occs =
let notfound =
match occs with
| AtOccurrences occs ->
(match occs with
| Locus.AtLeastOneOccurrence -> occ == 1
| Locus.AllOccurrences -> false
| Locus.AllOccurrencesBut l -> List.last l > occ
| Locus.OnlyOccurrences l -> List.last l > occ
| Locus.NoOccurrences -> false)
| Unspecified abstract -> false
in if notfound then
raise (PretypeError (env,sigma,NoOccurrenceFound (c,None)))
else ()
exception TypingFailed of evar_map
let set_of_evctx l =
List.fold_left (fun s decl -> Id.Set.add (NamedDecl.get_id decl) s) Id.Set.empty l
(** Weaken the existentials so that they can be typed in sign and raise
an error if the term otherwise mentions variables not bound in sign. *)
let thin_evars env sigma sign c =
let sigma = ref sigma in
let ctx = set_of_evctx sign in
let rec applyrec (env,acc) t =
match kind !sigma t with
| Evar (ev, args) ->
let evi = Evd.find_undefined !sigma ev in
let filter = Array.map (fun c -> Id.Set.subset (collect_vars !sigma c) ctx) args in
let filter = Filter.make (Array.to_list filter) in
let candidates = Option.map (List.map EConstr.of_constr) (evar_candidates evi) in
let evd, ev = restrict_evar !sigma ev filter candidates in
sigma := evd; whd_evar !sigma t
| Var id ->
if not (Id.Set.mem id ctx) then raise (TypingFailed !sigma)
else t
| _ ->
map_constr_with_binders_left_to_right !sigma
(fun d (env,acc) -> (push_rel d env, acc+1))
applyrec (env,acc) t
in
let c' = applyrec (env,0) c in
(!sigma, c')
let second_order_matching flags env_rhs evd (evk,args) (test,argoccs) rhs =
try
let evi = Evd.find_undefined evd evk in
let evi = nf_evar_info evd evi in
let env_evar_unf = evar_env evi in
let env_evar = evar_filtered_env evi in
let sign = named_context_val env_evar in
let ctxt = evar_filtered_context evi in
if !debug_ho_unification then
(Feedback.msg_debug Pp.(str"env rhs: " ++ Termops.Internal.print_env env_rhs);
Feedback.msg_debug Pp.(str"env evars: " ++ Termops.Internal.print_env env_evar));
let args = Array.map (nf_evar evd) args in
let vars = List.map NamedDecl.get_id ctxt in
let argsubst = List.map2 (fun id c -> (id, c)) vars (Array.to_list args) in
let instance = List.map mkVar vars in
let rhs = nf_evar evd rhs in
if not (noccur_evar env_rhs evd evk rhs) then raise (TypingFailed evd);
(* Ensure that any progress made by Typing.e_solve_evars will not contradict
the solution we are trying to build here by adding the problem as a constraint. *)
let evd = Evarutil.add_unification_pb (CONV,env_rhs,mkEvar (evk,args),rhs) evd in
let prc env evd c = Termops.Internal.print_constr_env env evd c in
let rec make_subst = function
| decl'::ctxt', c::l, occs::occsl when isVarId evd (NamedDecl.get_id decl') c ->
begin match occs with
| AtOccurrences loc when not (Locusops.is_all_occurrences loc) ->
user_err Pp.(str "Cannot force abstraction on identity instance.")
| _ ->
make_subst (ctxt',l,occsl)
end
| decl'::ctxt', c::l, occs::occsl ->
let id = NamedDecl.get_annot decl' in
let t = NamedDecl.get_type decl' in
let evs = ref [] in
let c = nf_evar evd c in
(* ty is in env_rhs now *)
let ty = replace_vars argsubst t in
let filter' = filter_possible_projections evd c (nf_evar evd ty) ctxt args in
(id,t,c,ty,evs,Filter.make filter',occs) :: make_subst (ctxt',l,occsl)
| _, _, [] -> []
| _ -> anomaly (Pp.str "Signature or instance are shorter than the occurrences list.")
in
let fixed = ref Evar.Set.empty in
let rec set_holes env_rhs evd rhs = function
| (id,idty,c,cty,evsref,filter,occs)::subst ->
let c = nf_evar evd c in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"set holes for: " ++
prc env_rhs evd (mkVar id.binder_name) ++ spc () ++
prc env_rhs evd c ++ str" in " ++
prc env_rhs evd rhs);
let occ = ref 1 in
let set_var evd k inst =
let oc = !occ in
if !debug_ho_unification then
(Feedback.msg_debug Pp.(str"Found one occurrence");
Feedback.msg_debug Pp.(str"cty: " ++ prc env_rhs evd c));
incr occ;
match occs with
| AtOccurrences occs ->
if Locusops.is_selected oc occs then evd, mkVar id.binder_name
else evd, inst
| Unspecified prefer_abstraction ->
let evd, evty = set_holes env_rhs evd cty subst in
let evty = nf_evar evd evty in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"abstracting one occurrence " ++ prc env_rhs evd inst ++
str" of type: " ++ prc env_evar evd evty ++
str " for " ++ prc env_rhs evd c);
let instance = Filter.filter_list filter instance in
(* Allow any type lower than the variable's type as the
abstracted subterm might have a smaller type, which could be
crucial to make the surrounding context typecheck. *)
let evd, evty =
if isArity evd evty then
refresh_universes ~status:Evd.univ_flexible (Some true)
env_evar_unf evd evty
else evd, evty in
let (evd, ev) = new_evar_instance sign evd evty ~filter instance in
let evk = fst (destEvar evd ev) in
evsref := (evk,evty,inst,prefer_abstraction)::!evsref;
fixed := Evar.Set.add evk !fixed;
evd, ev
in
let evd, rhs' = apply_on_subterm env_rhs evd fixed set_var test c rhs in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"abstracted: " ++ prc env_rhs evd rhs');
let () = check_selected_occs env_rhs evd c !occ occs in
let env_rhs' = push_named (NamedDecl.LocalAssum (id,idty)) env_rhs in
set_holes env_rhs' evd rhs' subst
| [] -> evd, rhs in
let subst = make_subst (ctxt,Array.to_list args,argoccs) in
let evd, rhs' = set_holes env_rhs evd rhs subst in
let rhs' = nf_evar evd rhs' in
(* Thin evars making the term typable in env_evar *)
let evd, rhs' = thin_evars env_evar evd ctxt rhs' in
(* We instantiate the evars of which the value is forced by typing *)
if !debug_ho_unification then
(Feedback.msg_debug Pp.(str"solve_evars on: " ++ prc env_evar evd rhs');
Feedback.msg_debug Pp.(str"evars: " ++ pr_evar_map (Some 0) env_evar evd));
let evd,rhs' =
try !solve_evars env_evar evd rhs'
with e when Pretype_errors.precatchable_exception e ->
(* Could not revert all subterms *)
raise (TypingFailed evd) in
let rhs' = nf_evar evd rhs' in
(* We instantiate the evars of which the value is forced by typing *)
if !debug_ho_unification then
(Feedback.msg_debug Pp.(str"after solve_evars: " ++ prc env_evar evd rhs');
Feedback.msg_debug Pp.(str"evars: " ++ pr_evar_map (Some 0) env_evar evd));
let rec abstract_free_holes evd = function
| (id,idty,c,cty,evsref,_,_)::l ->
let id = id.binder_name in
let c = nf_evar evd c in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"abstracting: " ++
prc env_rhs evd (mkVar id) ++ spc () ++
prc env_rhs evd c);
let rec force_instantiation evd = function
| (evk,evty,inst,abstract)::evs ->
let evk = Option.default evk (Evarutil.advance evd evk) in
let evd =
if is_undefined evd evk then
(* We try abstraction or concretisation for *)
(* this unconstrained occurrence *)
(* and we use typing to propagate this instantiation *)
(* We avoid making an arbitrary choice by leaving candidates *)
(* if both can work *)
let evi = Evd.find_undefined evd evk in
let vid = mkVar id in
let candidates = [inst; vid] in
try
let evd, ev = Evarutil.restrict_evar evd evk (Evd.evar_filter evi) (Some candidates) in
let evi = Evd.find evd ev in
(match evar_candidates evi with
| Some [t] ->
if not (noccur_evar env_rhs evd ev (EConstr.of_constr t)) then
raise (TypingFailed evd);
instantiate_evar evar_unify flags evd ev (EConstr.of_constr t)
| Some l when abstract = Abstraction.Abstract &&
List.exists (fun c -> isVarId evd id (EConstr.of_constr c)) l ->
instantiate_evar evar_unify flags evd ev vid
| _ -> evd)
with e -> user_err (Pp.str "Cannot find an instance")
else
((if !debug_ho_unification then
let evi = Evd.find evd evk in
let env = Evd.evar_env evi in
Feedback.msg_debug Pp.(str"evar is defined: " ++
int (Evar.repr evk) ++ spc () ++
prc env evd (match evar_body evi with Evar_defined c -> c
| Evar_empty -> assert false)));
evd)
in force_instantiation evd evs
| [] -> abstract_free_holes evd l
in force_instantiation evd !evsref
| [] ->
if Evd.is_defined evd evk then
(* Can happen due to dependencies: instantiating evars in the arguments of evk might
instantiate evk itself. *)
(if !debug_ho_unification then
begin
let evi = Evd.find evd evk in
let evenv = evar_env evi in
let body = match evar_body evi with Evar_empty -> assert false | Evar_defined c -> c in
Feedback.msg_debug Pp.(str"evar was defined already as: " ++ prc evenv evd body)
end;
evd)
else
try
let evi = Evd.find_undefined evd evk in
let evenv = evar_env evi in
let rhs' = nf_evar evd rhs' in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"abstracted type before second solve_evars: " ++
prc evenv evd rhs');
(* solve_evars is not commuting with nf_evar, because restricting
an evar might provide a more specific type. *)
let evd, _ = !solve_evars evenv evd rhs' in
if !debug_ho_unification then
Feedback.msg_debug Pp.(str"abstracted type: " ++ prc evenv evd (nf_evar evd rhs'));
let flags = default_flags_of TransparentState.full in
Evarsolve.instantiate_evar evar_unify flags evd evk rhs'
with IllTypedInstance _ -> raise (TypingFailed evd)
in
let evd = abstract_free_holes evd subst in
evd, true
with TypingFailed evd -> evd, false
let default_evar_selection flags evd (ev,args) =
let evi = Evd.find_undefined evd ev in
let rec aux args abs =
match args, abs with
| _ :: args, a :: abs ->
let spec =
if not flags.allow_K_at_toplevel then
(* [evar_absorb_arguments] puts an Abstract flag for the
toplevel binders that were absorbed. *)
let occs =
if a == Abstraction.Abstract then Locus.AtLeastOneOccurrence
--> --------------------
--> maximum size reached
--> --------------------
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