Source file logic.ml
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open Pp
open CErrors
open Util
open Names
open Nameops
open Constr
open Vars
open Termops
open Environ
open Reductionops
open Inductiveops
open Typing
open Retyping
module NamedDecl = Context.Named.Declaration
type refiner_error =
| BadType of constr * constr * EConstr.t
| UnresolvedBindings of Name.t list
| CannotApply of constr * constr
| NonLinearProof of constr
| MetaInType of EConstr.constr
| IntroNeedsProduct
| NoSuchHyp of Id.t
exception RefinerError of Environ.env * Evd.evar_map * refiner_error
let error_no_such_hypothesis env sigma id = raise (RefinerError (env, sigma, NoSuchHyp id))
let check_typability ~check env sigma c =
if check then fst (type_of env sigma (EConstr.of_constr c)) else sigma
let mt_q = (Id.Map.empty,[])
let push_val y = function
(_,[] as q) -> q
| (m, (x,l)::q) -> (m, (x,Id.Set.add y l)::q)
let push_item x v (m,l) =
(Id.Map.add x v m, (x,Id.Set.empty)::l)
let mem_q x (m,_) = Id.Map.mem x m
let find_q x (m,q) =
let v = Id.Map.find x m in
let m' = Id.Map.remove x m in
let rec find accs acc = function
[] -> raise Not_found
| [(x',l)] ->
if Id.equal x x' then ((v,Id.Set.union accs l),(m',List.rev acc))
else raise Not_found
| (x',l as i)::((x'',l'')::q as itl) ->
if Id.equal x x' then
((v,Id.Set.union accs l),
(m',List.rev acc@(x'',Id.Set.add x (Id.Set.union l l''))::q))
else find (Id.Set.union l accs) (i::acc) itl in
find Id.Set.empty [] q
let occur_vars_in_decl env sigma hyps d =
if Id.Set.is_empty hyps then false else
let ohyps = global_vars_set_of_decl env sigma d in
Id.Set.exists (fun h -> Id.Set.mem h ohyps) hyps
let reorder_context env sigma sign ord =
let ords = List.fold_right Id.Set.add ord Id.Set.empty in
if not (Int.equal (List.length ord) (Id.Set.cardinal ords)) then
user_err Pp.(str "Order list has duplicates");
let rec step ord expected ctxt_head moved_hyps ctxt_tail =
match ord with
| [] -> List.rev ctxt_tail @ ctxt_head
| top::ord' when mem_q top moved_hyps ->
let ((d,h),mh) = find_q top moved_hyps in
if occur_vars_in_decl env sigma h d then
user_err ~hdr:"reorder_context"
(str "Cannot move declaration " ++ Id.print top ++ spc() ++
str "before " ++
pr_sequence Id.print
(Id.Set.elements (Id.Set.inter h
(global_vars_set_of_decl env sigma d))));
step ord' expected ctxt_head mh (d::ctxt_tail)
| _ ->
(match ctxt_head with
| [] -> error_no_such_hypothesis env sigma (List.hd ord)
| d :: ctxt ->
let x = NamedDecl.get_id d in
if Id.Set.mem x expected then
step ord (Id.Set.remove x expected)
ctxt (push_item x d moved_hyps) ctxt_tail
else
step ord expected
ctxt (push_val x moved_hyps) (d::ctxt_tail)) in
step ord ords sign mt_q []
let reorder_val_context env sigma sign ord =
match ord with
| [] | [_] ->
sign
| _ :: _ :: _ ->
let open EConstr in
val_of_named_context (reorder_context env sigma (named_context_of_val sign) ord)
let check_decl_position env sigma sign d =
let open EConstr in
let x = NamedDecl.get_id d in
let needed = global_vars_set_of_decl env sigma d in
let deps = dependency_closure env sigma (named_context_of_val sign) needed in
if Id.List.mem x deps then
user_err ~hdr:"Logic.check_decl_position"
(str "Cannot create self-referring hypothesis " ++ Id.print x);
x::deps
(** Move destination for hypothesis *)
type 'id move_location =
| MoveAfter of 'id
| MoveBefore of 'id
| MoveFirst
| MoveLast (** can be seen as "no move" when doing intro *)
(** Printing of [move_location] *)
let pr_move_location pr_id = function
| MoveAfter id -> brk(1,1) ++ str "after " ++ pr_id id
| MoveBefore id -> brk(1,1) ++ str "before " ++ pr_id id
| MoveFirst -> str " at top"
| MoveLast -> str " at bottom"
let move_location_eq m1 m2 = match m1, m2 with
| MoveAfter id1, MoveAfter id2 -> Id.equal id1 id2
| MoveBefore id1, MoveBefore id2 -> Id.equal id1 id2
| MoveLast, MoveLast -> true
| MoveFirst, MoveFirst -> true
| _ -> false
let mem_id_context id ctx = Id.Map.mem id ctx.Environ.env_named_map
let split_sign env sigma hfrom l =
let () = if not (mem_id_context hfrom l) then error_no_such_hypothesis env sigma hfrom in
let rec splitrec left sign = match EConstr.match_named_context_val sign with
| None -> assert false
| Some (d, _, right) ->
let hyp = NamedDecl.get_id d in
if Id.equal hyp hfrom then (left, right, d)
else splitrec (d :: left) right
in
splitrec [] l
let move_hyp env sigma toleft (left,declfrom,right) hto =
let open EConstr in
let push prefix sign = List.fold_right push_named_context_val prefix sign in
let push_rev prefix sign = List.fold_left (fun accu d -> push_named_context_val d accu) sign prefix in
let rec moverec_toleft ans first middle midvars = function
| [] -> push middle @@ push first ans
| d :: _ as right when move_location_eq hto (MoveBefore (NamedDecl.get_id d)) ->
push_rev right @@ push middle @@ push first ans
| d :: right ->
let hyp = NamedDecl.get_id d in
let (first', middle', midvars') =
if occur_vars_in_decl env sigma midvars d then
if not (move_location_eq hto (MoveAfter hyp)) then
(first, d :: middle, Id.Set.add hyp midvars)
else
user_err ~hdr:"move_hyp" (str "Cannot move " ++ Id.print (NamedDecl.get_id declfrom) ++
pr_move_location Id.print hto ++
str ": it occurs in the type of "
++ Id.print hyp ++ str ".")
else
(d::first, middle, midvars)
in
if move_location_eq hto (MoveAfter hyp) then
push_rev right @@ push middle' @@ push first' ans
else
moverec_toleft ans first' middle' midvars' right
in
let rec moverec_toright first middle depvars right = match EConstr.match_named_context_val right with
| None -> push_rev first @@ push_rev middle right
| Some (d, _, _) when move_location_eq hto (MoveBefore (NamedDecl.get_id d)) ->
push_rev first @@ push_rev middle @@ right
| Some (d, _, right) ->
let hyp = NamedDecl.get_id d in
let (first', middle', depvars') =
if Id.Set.mem hyp depvars then
if not (move_location_eq hto (MoveAfter hyp)) then
let vars = global_vars_set_of_decl env sigma d in
let depvars = Id.Set.union vars depvars in
(first, d::middle, depvars)
else
user_err ~hdr:"move_hyp" (str "Cannot move " ++ Id.print (NamedDecl.get_id declfrom) ++
pr_move_location Id.print hto ++
str ": it depends on "
++ Id.print hyp ++ str ".")
else
(d::first, middle, depvars)
in
if move_location_eq hto (MoveAfter hyp) then
push_rev first' @@ push_rev middle' @@ right
else
moverec_toright first' middle' depvars' right
in
if toleft then
let id = NamedDecl.get_id declfrom in
moverec_toleft right [] [declfrom] (Id.Set.singleton id) left
else
let depvars = global_vars_set_of_decl env sigma declfrom in
let right = moverec_toright [] [declfrom] depvars right in
push_rev left @@ right
let move_hyp_in_named_context env sigma hfrom hto sign =
let (left, right, declfrom) = split_sign env sigma hfrom sign in
let toleft = match hto with
| MoveLast -> true
| MoveAfter id | MoveBefore id ->
if mem_id_context id right then false
else if mem_id_context id sign then true
else error_no_such_hypothesis env sigma id
| MoveFirst -> false
in
move_hyp env sigma toleft (left,declfrom,right) hto
let insert_decl_in_named_context env sigma decl hto sign =
move_hyp env sigma false ([],decl,sign) hto
let error_unsupported_deep_meta c =
user_err (strbrk "Application of lemmas whose beta-iota normal " ++
strbrk "form contains metavariables deep inside the term is not " ++
strbrk "supported; try \"refine\" instead.")
let collect_meta_variables c =
let rec collrec deep acc c = match kind c with
| Meta mv -> if deep then error_unsupported_deep_meta () else mv::acc
| Cast(c,_,_) -> collrec deep acc c
| Case(ci,u,pms,p,iv,c,br) ->
let acc = Array.fold_left (collrec deep) acc pms in
let acc = Constr.fold (collrec deep) acc (snd p) in
let acc = Constr.fold_invert (collrec deep) acc iv in
let acc = Constr.fold (collrec deep) acc c in
Array.fold_left (fun accu (_, br) -> collrec deep accu br) acc br
| App _ -> Constr.fold (collrec deep) acc c
| Proj (_, c) -> collrec deep acc c
| _ -> Constr.fold (collrec true) acc c
in
List.rev (collrec false [] c)
let check_meta_variables env sigma c =
if not (List.distinct_f Int.compare (collect_meta_variables c)) then
raise (RefinerError (env, sigma, NonLinearProof c))
let check_conv_leq_goal ~check env sigma arg ty conclty =
if check then
let ans = Reductionops.infer_conv env sigma (EConstr.of_constr ty) conclty in
match ans with
| Some evm -> evm
| None -> raise (RefinerError (env, sigma, BadType (arg,ty,conclty)))
else sigma
exception Stop of EConstr.t list
let meta_free_prefix sigma a =
try
let a = Array.map EConstr.of_constr a in
let _ = Array.fold_left (fun acc a ->
if occur_meta sigma a then raise (Stop acc)
else a :: acc) [] a
in a
with Stop acc -> Array.rev_of_list acc
let goal_type_of ~check env sigma c =
if check then
let (sigma,t) = type_of env sigma (EConstr.of_constr c) in
(sigma, EConstr.Unsafe.to_constr t)
else (sigma, EConstr.Unsafe.to_constr (Retyping.get_type_of env sigma (EConstr.of_constr c)))
let rec mk_refgoals ~check env sigma goalacc conclty trm =
let hyps = Environ.named_context_val env in
let mk_goal hyps concl =
Goal.V82.mk_goal sigma hyps concl
in
if (not check) && not (occur_meta sigma (EConstr.of_constr trm)) then
let t'ty = Retyping.get_type_of env sigma (EConstr.of_constr trm) in
let t'ty = EConstr.Unsafe.to_constr t'ty in
let sigma = check_conv_leq_goal ~check env sigma trm t'ty conclty in
(goalacc,t'ty,sigma,trm)
else
match kind trm with
| Meta _ ->
let conclty = nf_betaiota env sigma conclty in
if check && occur_meta sigma conclty then
raise (RefinerError (env, sigma, MetaInType conclty));
let (gl,ev,sigma) = mk_goal hyps conclty in
let ev = EConstr.Unsafe.to_constr ev in
let conclty = EConstr.Unsafe.to_constr conclty in
gl::goalacc, conclty, sigma, ev
| Cast (t,k, ty) ->
let sigma = check_typability ~check env sigma ty in
let sigma = check_conv_leq_goal ~check env sigma trm ty conclty in
let res = mk_refgoals ~check env sigma goalacc (EConstr.of_constr ty) t in
if isMeta t then begin
assert (k != VMcast && k != NATIVEcast);
res
end else
let (gls,cty,sigma,ans) = res in
let ans = if ans == t then trm else mkCast(ans,k,ty) in
(gls,cty,sigma,ans)
| App (f,l) ->
let (acc',hdty,sigma,applicand) =
if Termops.is_template_polymorphic_ind env sigma (EConstr.of_constr f) then
let ty =
let firstmeta = Array.findi (fun i x -> occur_meta sigma (EConstr.of_constr x)) l in
let args, _ = Option.cata (fun i -> CArray.chop i l) (l, [||]) firstmeta in
type_of_global_reference_knowing_parameters env sigma (EConstr.of_constr f) (Array.map EConstr.of_constr args)
in
let ty = EConstr.Unsafe.to_constr ty in
goalacc, ty, sigma, f
else
mk_hdgoals ~check env sigma goalacc f
in
let ((acc'',conclty',sigma), args) = mk_arggoals ~check env sigma acc' hdty l in
let sigma = check_conv_leq_goal ~check env sigma trm conclty' conclty in
let ans = if applicand == f && args == l then trm else mkApp (applicand, args) in
(acc'',conclty',sigma, ans)
| Proj (p,c) ->
let (acc',cty,sigma,c') = mk_hdgoals ~check env sigma goalacc c in
let c = mkProj (p, c') in
let ty = get_type_of env sigma (EConstr.of_constr c) in
let ty = EConstr.Unsafe.to_constr ty in
(acc',ty,sigma,c)
| Case (ci, u, pms, p, iv, c, lf) ->
let (ci, p, iv, c, lf) = Inductive.expand_case env (ci, u, pms, p, iv, c, lf) in
let (acc',lbrty,conclty',sigma,p',c') = mk_casegoals ~check env sigma goalacc p c in
let sigma = check_conv_leq_goal ~check env sigma trm conclty' conclty in
let (acc'',sigma,rbranches) = treat_case ~check env sigma ci lbrty lf acc' in
let lf' = Array.rev_of_list rbranches in
let ans =
if p' == p && c' == c && Array.equal (==) lf' lf then trm
else mkCase (Inductive.contract_case env (ci,p',iv,c',lf'))
in
(acc'',conclty',sigma, ans)
| _ ->
if occur_meta sigma (EConstr.of_constr trm) then
anomaly (Pp.str "refiner called with a meta in non app/case subterm.");
let (sigma, t'ty) = goal_type_of ~check env sigma trm in
let sigma = check_conv_leq_goal ~check env sigma trm t'ty conclty in
(goalacc,t'ty,sigma, trm)
and mk_hdgoals ~check env sigma goalacc trm =
let hyps = Environ.named_context_val env in
let mk_goal hyps concl =
Goal.V82.mk_goal sigma hyps concl in
match kind trm with
| Cast (c,_, ty) when isMeta c ->
let sigma = check_typability ~check env sigma ty in
let (gl,ev,sigma) = mk_goal hyps (nf_betaiota env sigma (EConstr.of_constr ty)) in
let ev = EConstr.Unsafe.to_constr ev in
gl::goalacc,ty,sigma,ev
| Cast (t,_, ty) ->
let sigma = check_typability ~check env sigma ty in
mk_refgoals ~check env sigma goalacc (EConstr.of_constr ty) t
| App (f,l) ->
let (acc',hdty,sigma,applicand) =
if Termops.is_template_polymorphic_ind env sigma (EConstr.of_constr f)
then
let l' = meta_free_prefix sigma l in
(goalacc,EConstr.Unsafe.to_constr (type_of_global_reference_knowing_parameters env sigma (EConstr.of_constr f) l'),sigma,f)
else mk_hdgoals ~check env sigma goalacc f
in
let ((acc'',conclty',sigma), args) = mk_arggoals ~check env sigma acc' hdty l in
let ans = if applicand == f && args == l then trm else mkApp (applicand, args) in
(acc'',conclty',sigma, ans)
| Case (ci, u, pms, p, iv, c, lf) ->
let (ci, p, iv, c, lf) = Inductive.expand_case env (ci, u, pms, p, iv, c, lf) in
let (acc',lbrty,conclty',sigma,p',c') = mk_casegoals ~check env sigma goalacc p c in
let (acc'',sigma,rbranches) = treat_case ~check env sigma ci lbrty lf acc' in
let lf' = Array.rev_of_list rbranches in
let ans =
if p' == p && c' == c && Array.equal (==) lf' lf then trm
else mkCase (Inductive.contract_case env (ci,p',iv,c',lf'))
in
(acc'',conclty',sigma, ans)
| Proj (p,c) ->
let (acc',cty,sigma,c') = mk_hdgoals ~check env sigma goalacc c in
let c = mkProj (p, c') in
let ty = get_type_of env sigma (EConstr.of_constr c) in
let ty = EConstr.Unsafe.to_constr ty in
(acc',ty,sigma,c)
| _ ->
if check && occur_meta sigma (EConstr.of_constr trm) then
anomaly (Pp.str "refine called with a dependent meta.");
let (sigma, ty) = goal_type_of env ~check sigma trm in
goalacc, ty, sigma, trm
and mk_arggoals ~check env sigma goalacc funty allargs =
let foldmap (goalacc, funty, sigma) harg =
let t = whd_all env sigma (EConstr.of_constr funty) in
let t = EConstr.Unsafe.to_constr t in
let rec collapse t = match kind t with
| LetIn (_, c1, _, b) -> collapse (subst1 c1 b)
| _ -> t
in
let t = collapse t in
match kind t with
| Prod (_, c1, b) ->
let (acc, hargty, sigma, arg) = mk_refgoals ~check env sigma goalacc (EConstr.of_constr c1) harg in
(acc, subst1 harg b, sigma), arg
| _ ->
raise (RefinerError (env,sigma,CannotApply (t, harg)))
in
Array.Smart.fold_left_map foldmap (goalacc, funty, sigma) allargs
and mk_casegoals ~check env sigma goalacc p c =
let (acc',ct,sigma,c') = mk_hdgoals ~check env sigma goalacc c in
let ct = EConstr.of_constr ct in
let (acc'',pt,sigma,p') = mk_hdgoals ~check env sigma acc' p in
let ((ind, u), spec) =
try Tacred.find_hnf_rectype env sigma ct
with Not_found -> anomaly (Pp.str "mk_casegoals.") in
let indspec = ((ind, EConstr.EInstance.kind sigma u), spec) in
let (lbrty,conclty) = type_case_branches_with_names env sigma indspec p c in
(acc'',lbrty,conclty,sigma,p',c')
and treat_case ~check env sigma ci lbrty lf acc' =
let rec strip_outer_cast c = match kind c with
| Cast (c,_,_) -> strip_outer_cast c
| _ -> c in
let decompose_app_vect c = match kind c with
| App (f,cl) -> (f, cl)
| _ -> (c,[||]) in
Array.fold_left3
(fun (lacc,sigma,bacc) ty fi n ->
let ctx, body = Term.decompose_lam_n_decls n fi in
let head, args = decompose_app_vect body in
let head = strip_outer_cast head in
if isMeta head then begin
assert (args = Context.Rel.to_extended_vect mkRel 0 ctx);
let (r,_,s,head'') = mk_refgoals ~check env sigma lacc ty head in
let fi' = it_mkLambda_or_LetIn (mkApp (head'',args)) ctx in
(r,s,fi'::bacc)
end
else
let sigma, t'ty = goal_type_of ~check env sigma fi in
let sigma = check_conv_leq_goal ~check env sigma fi t'ty ty in
(lacc,sigma,fi::bacc))
(acc',sigma,[]) lbrty lf ci.ci_cstr_ndecls
let convert_hyp ~check ~reorder env sigma d =
let id = NamedDecl.get_id d in
let b = NamedDecl.get_value d in
let sign = Environ.named_context_val env in
match lookup_named_ctxt id sign with
| exception Not_found ->
if check then error_no_such_hypothesis env sigma id
else sign
| d' ->
let c = Option.map EConstr.of_constr (NamedDecl.get_value d') in
if check && not (is_conv env sigma (NamedDecl.get_type d) (EConstr.of_constr (NamedDecl.get_type d'))) then
user_err ~hdr:"Logic.convert_hyp"
(str "Incorrect change of the type of " ++ Id.print id ++ str ".");
if check && not (Option.equal (is_conv env sigma) b c) then
user_err ~hdr:"Logic.convert_hyp"
(str "Incorrect change of the body of "++ Id.print id ++ str ".");
let sign' = apply_to_hyp sign id (fun _ _ _ -> EConstr.Unsafe.to_named_decl d) in
if reorder then reorder_val_context env sigma sign' (check_decl_position env sigma sign d)
else sign'
let refiner ~check r =
let open Proofview.Notations in
Proofview.Goal.enter begin fun gl ->
let sigma = Proofview.Goal.sigma gl in
let env = Proofview.Goal.env gl in
let st = Proofview.Goal.state gl in
let cl = Proofview.Goal.concl gl in
check_meta_variables env sigma r;
let (sgl,cl',sigma,oterm) = mk_refgoals ~check env sigma [] cl r in
let map gl = Proofview.goal_with_state gl st in
let sgl = List.rev_map map sgl in
let sigma = Goal.V82.partial_solution env sigma (Proofview.Goal.goal gl) (EConstr.of_constr oterm) in
Proofview.Unsafe.tclEVARS sigma <*>
Proofview.Unsafe.tclSETGOALS sgl
end