Source file indrec.ml
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open Pp
open CErrors
open Util
open Names
open Libnames
open Nameops
open Term
open Constr
open Context
open Vars
open Namegen
open Declarations
open Declareops
open Inductive
open Inductiveops
open Environ
open Reductionops
open Context.Rel.Declaration
type dep_flag = bool
type recursion_scheme_error =
| NotAllowedCaseAnalysis of bool * Sorts.t * pinductive
| NotMutualInScheme of inductive * inductive
| NotAllowedDependentAnalysis of bool * inductive
exception RecursionSchemeError of env * recursion_scheme_error
let named_hd env t na = named_hd env (Evd.from_env env) (EConstr.of_constr t) na
let name_assumption env = function
| LocalAssum (na,t) -> LocalAssum (map_annot (named_hd env t) na, t)
| LocalDef (na,c,t) -> LocalDef (map_annot (named_hd env c) na, c, t)
let mkLambda_or_LetIn_name env d b = mkLambda_or_LetIn (name_assumption env d) b
let mkProd_or_LetIn_name env d b = mkProd_or_LetIn (name_assumption env d) b
let mkLambda_name env (n,a,b) = mkLambda_or_LetIn_name env (LocalAssum (n,a)) b
let mkProd_name env (n,a,b) = mkProd_or_LetIn_name env (LocalAssum (n,a)) b
let it_mkProd_or_LetIn_name env b l = List.fold_left (fun c d -> mkProd_or_LetIn_name env d c) b l
let it_mkLambda_or_LetIn_name env b l = List.fold_left (fun c d -> mkLambda_or_LetIn_name env d c) b l
let make_prod_dep dep env = if dep then mkProd_name env else mkProd
let mkLambda_string s r t c = mkLambda (make_annot (Name (Id.of_string s)) r, t, c)
let is_private mib =
match mib.mind_private with
| Some true -> true
| _ -> false
let check_privacy_block mib =
if is_private mib then
user_err (str"case analysis on a private inductive type")
let mis_make_case_com dep env sigma (ind, u as pind) (mib,mip as specif) kind =
let lnamespar = Vars.subst_instance_context u mib.mind_params_ctxt in
let indf = make_ind_family(pind, Context.Rel.to_extended_list mkRel 0 lnamespar) in
let constrs = get_constructors env indf in
let projs = get_projections env ind in
let relevance = Sorts.relevance_of_sort_family kind in
let () = if Option.is_empty projs then check_privacy_block mib in
let () =
if not (Sorts.family_leq kind (elim_sort specif)) then
raise
(RecursionSchemeError
(env, NotAllowedCaseAnalysis (false, fst (UnivGen.fresh_sort_in_family kind), pind)))
in
let ndepar = mip.mind_nrealdecls + 1 in
let env' = push_rel_context lnamespar env in
let rec add_branch env k =
if Int.equal k (Array.length mip.mind_consnames) then
let nbprod = k+1 in
let indf' = lift_inductive_family nbprod indf in
let arsign,sort = get_arity env indf' in
let r = Sorts.relevance_of_sort_family sort in
let depind = build_dependent_inductive env indf' in
let deparsign = LocalAssum (make_annot Anonymous r,depind)::arsign in
let rci = relevance in
let ci = make_case_info env (fst pind) rci RegularStyle in
let pbody =
appvect
(mkRel (ndepar + nbprod),
if dep then Context.Rel.to_extended_vect mkRel 0 deparsign
else Context.Rel.to_extended_vect mkRel 1 arsign) in
let p =
it_mkLambda_or_LetIn_name env'
((if dep then mkLambda_name env' else mkLambda)
(make_annot Anonymous r,depind,pbody))
arsign
in
let obj =
match projs with
| None ->
let iv = make_case_invert env (find_rectype env sigma (EConstr.of_constr (lift 1 depind))) ci in
let iv = EConstr.Unsafe.to_case_invert iv in
let ncons = Array.length mip.mind_consnames in
let mk_branch i =
let ft = get_type (lookup_rel (ncons - i) env) in
let (ctx, _) = decompose_prod_assum ft in
let n = mkRel (List.length ctx + 1) in
let args = Context.Rel.to_extended_vect mkRel 0 ctx in
let br = it_mkLambda_or_LetIn (mkApp (n, args)) ctx in
lift (ndepar + ncons - i - 1) br
in
let br = Array.init ncons mk_branch in
mkCase (Inductive.contract_case env (ci, lift ndepar p, iv, mkRel 1, br))
| Some ps ->
let term =
mkApp (mkRel 2,
Array.map
(fun p -> mkProj (Projection.make p true, mkRel 1)) ps) in
if dep then
let ty = mkApp (mkRel 3, [| mkRel 1 |]) in
mkCast (term, DEFAULTcast, ty)
else term
in
it_mkLambda_or_LetIn_name env' obj deparsign
else
let cs = lift_constructor (k+1) constrs.(k) in
let t = build_branch_type env sigma dep (mkRel (k+1)) cs in
mkLambda_string "f" relevance t
(add_branch (push_rel (LocalAssum (make_annot Anonymous relevance, t)) env) (k+1))
in
let (sigma, s) = Evd.fresh_sort_in_family ~rigid:Evd.univ_flexible_alg sigma kind in
let typP = make_arity env' sigma dep indf s in
let typP = EConstr.Unsafe.to_constr typP in
let c =
it_mkLambda_or_LetIn_name env
(mkLambda_string "P" Sorts.Relevant typP
(add_branch (push_rel (LocalAssum (make_annot Anonymous Sorts.Relevant,typP)) env') 0)) lnamespar
in
(sigma, c)
let type_rec_branch is_rec dep env sigma (vargs,depPvect,decP) tyi cs recargs =
let make_prod = make_prod_dep dep in
let nparams = List.length vargs in
let process_pos env depK pk =
let rec prec env i sign p =
let p',largs = whd_allnolet_stack env sigma (EConstr.of_constr p) in
let p' = EConstr.Unsafe.to_constr p' in
let largs = List.map EConstr.Unsafe.to_constr largs in
match kind p' with
| Prod (n,t,c) ->
let d = LocalAssum (n,t) in
make_prod env (n,t,prec (push_rel d env) (i+1) (d::sign) c)
| LetIn (n,b,t,c) when List.is_empty largs ->
let d = LocalDef (n,b,t) in
mkLetIn (n,b,t,prec (push_rel d env) (i+1) (d::sign) c)
| Ind (_,_) ->
let realargs = List.skipn nparams largs in
let base = applist (lift i pk,realargs) in
if depK then
Reduction.beta_appvect
base [|applist (mkRel (i+1), Context.Rel.to_extended_list mkRel 0 sign)|]
else
base
| _ ->
let t' = whd_all env sigma (EConstr.of_constr p) in
let t' = EConstr.Unsafe.to_constr t' in
if Constr.equal p' t' then assert false
else prec env i sign t'
in
prec env 0 []
in
let rec process_constr env i c recargs nhyps li =
if nhyps > 0 then match kind c with
| Prod (n,t,c_0) ->
let (optionpos,rest) =
match recargs with
| [] -> None,[]
| ra::rest ->
(match dest_recarg ra with
| Mrec (_,j) when is_rec -> (depPvect.(j),rest)
| Nested _ -> (None,rest)
| _ -> (None, rest))
in
(match optionpos with
| None ->
make_prod env
(n,t,
process_constr (push_rel (LocalAssum (n,t)) env) (i+1) c_0 rest
(nhyps-1) (i::li))
| Some(dep',p) ->
let nP = lift (i+1+decP) p in
let env' = push_rel (LocalAssum (n,t)) env in
let t_0 = process_pos env' dep' nP (lift 1 t) in
let r_0 = Retyping.relevance_of_type env' sigma (EConstr.of_constr t_0) in
make_prod_dep (dep || dep') env
(n,t,
mkArrow t_0 r_0
(process_constr
(push_rel (LocalAssum (make_annot Anonymous n.binder_relevance,t_0)) env')
(i+2) (lift 1 c_0) rest (nhyps-1) (i::li))))
| LetIn (n,b,t,c_0) ->
mkLetIn (n,b,t,
process_constr
(push_rel (LocalDef (n,b,t)) env)
(i+1) c_0 recargs (nhyps-1) li)
| _ -> assert false
else
if dep then
let realargs = List.rev_map (fun k -> mkRel (i-k)) li in
let params = List.map (lift i) vargs in
let co = applist (mkConstructU cs.cs_cstr,params@realargs) in
Reduction.beta_appvect c [|co|]
else c
in
let nhyps = List.length cs.cs_args in
let nP = match depPvect.(tyi) with
| Some(_,p) -> lift (nhyps+decP) p
| _ -> assert false in
let base = appvect (nP,cs.cs_concl_realargs) in
let c = it_mkProd_or_LetIn base cs.cs_args in
process_constr env 0 c recargs nhyps []
let make_rec_branch_arg env sigma (nparrec,fvect,decF) f cstr recargs =
let process_pos env fk =
let rec prec env i hyps p =
let p',largs = whd_allnolet_stack env sigma (EConstr.of_constr p) in
let p' = EConstr.Unsafe.to_constr p' in
let largs = List.map EConstr.Unsafe.to_constr largs in
match kind p' with
| Prod (n,t,c) ->
let d = LocalAssum (n,t) in
mkLambda_name env (n,t,prec (push_rel d env) (i+1) (d::hyps) c)
| LetIn (n,b,t,c) when List.is_empty largs ->
let d = LocalDef (n,b,t) in
mkLetIn (n,b,t,prec (push_rel d env) (i+1) (d::hyps) c)
| Ind _ ->
let realargs = List.skipn nparrec largs
and arg = appvect (mkRel (i+1), Context.Rel.to_extended_vect mkRel 0 hyps) in
applist(lift i fk,realargs@[arg])
| _ ->
let t' = whd_all env sigma (EConstr.of_constr p) in
let t' = EConstr.Unsafe.to_constr t' in
if Constr.equal t' p' then assert false
else prec env i hyps t'
in
prec env 0 []
in
let rec process_constr env i f = function
| (LocalAssum (n,t) as d)::cprest, recarg::rest ->
let optionpos =
match dest_recarg recarg with
| Norec -> None
| Nested _ -> None
| Mrec (_,i) -> fvect.(i)
in
(match optionpos with
| None ->
let env' = push_rel d env in
mkLambda_name env
(n,t,process_constr env' (i+1)
(EConstr.Unsafe.to_constr (whd_beta env' Evd.empty (EConstr.of_constr (applist (lift 1 f, [(mkRel 1)])))))
(cprest,rest))
| Some(_,f_0) ->
let nF = lift (i+1+decF) f_0 in
let env' = push_rel d env in
let arg = process_pos env' nF (lift 1 t) in
mkLambda_name env
(n,t,process_constr env' (i+1)
(EConstr.Unsafe.to_constr (whd_beta env' Evd.empty (EConstr.of_constr (applist (lift 1 f, [(mkRel 1); arg])))))
(cprest,rest)))
| (LocalDef (n,c,t) as d)::cprest, rest ->
mkLetIn
(n,c,t,
process_constr (push_rel d env) (i+1) (lift 1 f)
(cprest,rest))
| [],[] -> f
| _,[] | [],_ -> anomaly (Pp.str "process_constr.")
in
process_constr env 0 f (List.rev cstr.cs_args, recargs)
let mis_make_indrec env sigma ?(force_mutual=false) listdepkind mib u =
let nparams = mib.mind_nparams in
let nparrec = mib.mind_nparams_rec in
let evdref = ref sigma in
let lnonparrec,lnamesparrec =
Termops.context_chop (nparams-nparrec) (Vars.subst_instance_context u mib.mind_params_ctxt) in
let nrec = List.length listdepkind in
let depPvec =
Array.make mib.mind_ntypes (None : (bool * constr) option) in
let _ =
let rec
assign k = function
| [] -> ()
| ((indi,u),mibi,mipi,dep,_)::rest ->
(Array.set depPvec (snd indi) (Some(dep,mkRel k));
assign (k-1) rest)
in
assign nrec listdepkind in
let recargsvec =
Array.map (fun mip -> mip.mind_recargs) mib.mind_packets in
let rec recargparn l n =
if Int.equal n 0 then l else recargparn (mk_norec::l) (n-1) in
let recargpar = recargparn [] (nparams-nparrec) in
let make_one_rec p =
let makefix nbconstruct =
let rec mrec i ln lrelevance ltyp ldef = function
| ((indi,u),mibi,mipi,dep,target_sort)::rest ->
let tyi = snd indi in
let nctyi =
Array.length mipi.mind_consnames in
let args = Context.Rel.to_extended_list mkRel (nrec+nbconstruct) lnamesparrec in
let indf = make_ind_family((indi,u),args) in
let arsign,s = get_arity env indf in
let r = Sorts.relevance_of_sort_family s in
let depind = build_dependent_inductive env indf in
let deparsign = LocalAssum (make_annot Anonymous r,depind)::arsign in
let nonrecpar = Context.Rel.length lnonparrec in
let larsign = Context.Rel.length deparsign in
let ndepar = larsign - nonrecpar in
let dect = larsign+nrec+nbconstruct in
let args' = Context.Rel.to_extended_list mkRel (dect+nrec) lnamesparrec in
let args'' = Context.Rel.to_extended_list mkRel ndepar lnonparrec in
let indf' = make_ind_family((indi,u),args'@args'') in
let branches =
let constrs = get_constructors env indf' in
let fi = Termops.rel_vect (dect-i-nctyi) nctyi in
let vecfi = Array.map
(fun f -> appvect (f, Context.Rel.to_extended_vect mkRel ndepar lnonparrec))
fi
in
Array.map3
(make_rec_branch_arg env !evdref
(nparrec,depPvec,larsign))
vecfi constrs (dest_subterms recargsvec.(tyi))
in
let j = (match depPvec.(tyi) with
| Some (_,c) when isRel c -> destRel c
| _ -> assert false)
in
let depind' = build_dependent_inductive env indf' in
let arsign',s = get_arity env indf' in
let r = Sorts.relevance_of_sort_family s in
let deparsign' = LocalAssum (make_annot Anonymous r,depind')::arsign' in
let pargs =
let nrpar = Context.Rel.to_extended_list mkRel (2*ndepar) lnonparrec
and nrar = if dep then Context.Rel.to_extended_list mkRel 0 deparsign'
else Context.Rel.to_extended_list mkRel 1 arsign'
in nrpar@nrar
in
let target_relevance = Sorts.relevance_of_sort_family target_sort in
let deftyi =
let rci = target_relevance in
let ci = make_case_info env indi rci RegularStyle in
let concl = applist (mkRel (dect+j+ndepar),pargs) in
let pred =
it_mkLambda_or_LetIn_name env
((if dep then mkLambda_name env else mkLambda)
(make_annot Anonymous r,depind',concl))
arsign'
in
let obj =
let indty = find_rectype env sigma (EConstr.of_constr depind) in
Inductiveops.make_case_or_project env !evdref indty ci (EConstr.of_constr pred)
(EConstr.mkRel 1) (Array.map EConstr.of_constr branches)
in
let obj = EConstr.to_constr !evdref obj in
it_mkLambda_or_LetIn_name env obj
(Termops.lift_rel_context nrec deparsign)
in
let typtyi =
let concl =
let pargs = if dep then Context.Rel.to_extended_vect mkRel 0 deparsign
else Context.Rel.to_extended_vect mkRel 1 arsign
in appvect (mkRel (nbconstruct+ndepar+nonrecpar+j),pargs)
in it_mkProd_or_LetIn_name env
concl
deparsign
in
mrec (i+nctyi) (Context.Rel.nhyps arsign ::ln) (target_relevance::lrelevance) (typtyi::ltyp)
(deftyi::ldef) rest
| [] ->
let fixn = Array.of_list (List.rev ln) in
let fixtyi = Array.of_list (List.rev ltyp) in
let fixdef = Array.of_list (List.rev ldef) in
let lrelevance = CArray.rev_of_list lrelevance in
let names = Array.map (fun r -> make_annot (Name(Id.of_string "F")) r) lrelevance in
mkFix ((fixn,p),(names,fixtyi,fixdef))
in
mrec 0 [] [] [] []
in
let rec make_branch env i = function
| ((indi,u),mibi,mipi,dep,sfam)::rest ->
let tyi = snd indi in
let nconstr = Array.length mipi.mind_consnames in
let rec onerec env j =
if Int.equal j nconstr then
make_branch env (i+j) rest
else
let recarg = (dest_subterms recargsvec.(tyi)).(j) in
let recarg = recargpar@recarg in
let vargs = Context.Rel.to_extended_list mkRel (nrec+i+j) lnamesparrec in
let cs = get_constructor ((indi,u),mibi,mipi,vargs) (j+1) in
let p_0 =
type_rec_branch
true dep env !evdref (vargs,depPvec,i+j) tyi cs recarg
in
let r_0 = Sorts.relevance_of_sort_family sfam in
mkLambda_string "f" r_0 p_0
(onerec (push_rel (LocalAssum (make_annot Anonymous r_0,p_0)) env) (j+1))
in onerec env 0
| [] ->
makefix i listdepkind
in
let rec put_arity env i = function
| ((indi,u),_,_,dep,kinds)::rest ->
let indf = make_ind_family ((indi,u), Context.Rel.to_extended_list mkRel i lnamesparrec) in
let s =
let sigma, res = Evd.fresh_sort_in_family ~rigid:Evd.univ_flexible_alg !evdref kinds in
evdref := sigma; res
in
let typP = make_arity env !evdref dep indf s in
let typP = EConstr.Unsafe.to_constr typP in
mkLambda_string "P" Sorts.Relevant typP
(put_arity (push_rel (LocalAssum (anonR,typP)) env) (i+1) rest)
| [] ->
make_branch env 0 listdepkind
in
let ((indi,u),mibi,mipi,dep,kind) = List.nth listdepkind p in
if force_mutual || (mis_is_recursive_subset
(List.map (fun ((indi,u),_,_,_,_) -> snd indi) listdepkind)
mipi.mind_recargs)
then
let env' = push_rel_context lnamesparrec env in
it_mkLambda_or_LetIn_name env (put_arity env' 0 listdepkind)
lnamesparrec
else
let evd = !evdref in
let (evd, c) = mis_make_case_com dep env evd (indi,u) (mibi,mipi) kind in
evdref := evd; c
in
!evdref, List.init nrec make_one_rec
let build_case_analysis_scheme env sigma pity dep kind =
let (mib,mip) = lookup_mind_specif env (fst pity) in
if dep && not (Inductiveops.has_dependent_elim mib) then
raise (RecursionSchemeError (env, NotAllowedDependentAnalysis (false, fst pity)));
mis_make_case_com dep env sigma pity (mib,mip) kind
let is_in_prop mip =
match inductive_sort_family mip with
| InProp -> true
| _ -> false
let build_case_analysis_scheme_default env sigma pity kind =
let (mib,mip) = lookup_mind_specif env (fst pity) in
let dep = not (is_in_prop mip || not (Inductiveops.has_dependent_elim mib)) in
mis_make_case_com dep env sigma pity (mib,mip) kind
let change_sort_arity sort =
let rec drec a = match kind a with
| Cast (c,_,_) -> drec c
| Prod (n,t,c) -> let s, c' = drec c in s, mkProd (n, t, c')
| LetIn (n,b,t,c) -> let s, c' = drec c in s, mkLetIn (n,b,t,c')
| Sort s -> s, mkSort sort
| _ -> assert false
in
drec
let weaken_sort_scheme env evd set sort npars term ty =
let evdref = ref evd in
let rec drec ctx np elim =
match kind elim with
| Prod (n,t,c) ->
let ctx = LocalAssum (n, t) :: ctx in
if Int.equal np 0 then
let osort, t' = change_sort_arity sort t in
evdref := (if set then Evd.set_eq_sort else Evd.set_leq_sort) env !evdref sort osort;
mkProd (n, t', c),
mkLambda (n, t', mkApp(term, Context.Rel.to_extended_vect mkRel 0 ctx))
else
let c',term' = drec ctx (np-1) c in
mkProd (n, t, c'), mkLambda (n, t, term')
| LetIn (n,b,t,c) ->
let ctx = LocalDef (n, b, t) :: ctx in
let c',term' = drec ctx np c in
mkLetIn (n,b,t,c'), mkLetIn (n,b,t,term')
| _ -> anomaly ~label:"weaken_sort_scheme" (Pp.str "wrong elimination type.")
in
let ty, term = drec [] npars ty in
!evdref, ty, term
let check_arities env listdepkind =
let _ = List.fold_left
(fun ln (((_,ni as mind),u),mibi,mipi,dep,kind) ->
let kelim = elim_sort (mibi,mipi) in
if not (Sorts.family_leq kind kelim) then raise
(RecursionSchemeError
(env, NotAllowedCaseAnalysis (true, fst (UnivGen.fresh_sort_in_family kind),(mind,u))))
else if Int.List.mem ni ln then raise
(RecursionSchemeError (env, NotMutualInScheme (mind,mind)))
else ni::ln)
[] listdepkind
in true
let build_mutual_induction_scheme env sigma ?(force_mutual=false) = function
| ((mind,u),dep,s)::lrecspec ->
let (mib,mip) = lookup_mind_specif env mind in
if dep && not (Inductiveops.has_dependent_elim mib) then
raise (RecursionSchemeError (env, NotAllowedDependentAnalysis (true, mind)));
let (sp,tyi) = mind in
let listdepkind =
((mind,u),mib,mip,dep,s)::
(List.map
(function ((mind',u'),dep',s') ->
let (sp',_) = mind' in
if QMutInd.equal env sp sp' then
let (mibi',mipi') = lookup_mind_specif env mind' in
((mind',u'),mibi',mipi',dep',s')
else
raise (RecursionSchemeError (env, NotMutualInScheme (mind,mind'))))
lrecspec)
in
let _ = check_arities env listdepkind in
mis_make_indrec env sigma ~force_mutual listdepkind mib u
| _ -> anomaly (Pp.str "build_induction_scheme expects a non empty list of inductive types.")
let build_induction_scheme env sigma pind dep kind =
let (mib,mip) = lookup_mind_specif env (fst pind) in
if dep && not (Inductiveops.has_dependent_elim mib) then
raise (RecursionSchemeError (env, NotAllowedDependentAnalysis (true, fst pind)));
let sigma, l = mis_make_indrec env sigma [(pind,mib,mip,dep,kind)] mib (snd pind) in
sigma, List.hd l
let elimination_suffix = function
| InSProp -> "_sind"
| InProp -> "_ind"
| InSet -> "_rec"
| InType -> "_rect"
let case_suffix = "_case"
let make_elimination_ident id s = add_suffix id (elimination_suffix s)
let lookup_eliminator env ind_sp s =
let kn,i = ind_sp in
let mpu = KerName.modpath @@ MutInd.user kn in
let mpc = KerName.modpath @@ MutInd.canonical kn in
let ind_id = (lookup_mind kn env).mind_packets.(i).mind_typename in
let id = add_suffix ind_id (elimination_suffix s) in
let l = Label.of_id id in
let knu = KerName.make mpu l in
let knc = KerName.make mpc l in
let cst = Constant.make knu knc in
if mem_constant cst env then GlobRef.ConstRef cst
else
try Nametab.locate (qualid_of_ident id)
with Not_found ->
user_err ~hdr:"default_elim"
(strbrk "Cannot find the elimination combinator " ++
Id.print id ++ strbrk ", the elimination of the inductive definition " ++
Nametab.pr_global_env Id.Set.empty (GlobRef.IndRef ind_sp) ++
strbrk " on sort " ++ Sorts.pr_sort_family s ++
strbrk " is probably not allowed.")