module Ref = NReference let cn_to_s = function | Cic.Anonymous -> "_" | Cic.Name s -> s ;; type ctx = | Ce of NCic.hypothesis | Fix of Ref.reference * string * NCic.term let splat mk_pi ctx t = List.fold_left (fun t c -> match c with | Ce (name, NCic.Def (bo,ty)) -> NCic.LetIn (name, ty, bo, t) | Ce (name, NCic.Decl ty) when mk_pi -> NCic.Prod (name, ty, t) | Ce (name, NCic.Decl ty) -> NCic.Lambda (name, ty, t) | Fix (_,name,ty) when mk_pi -> NCic.Prod (name, ty, t) | Fix (_,name,ty) -> NCic.Lambda (name,ty,t)) t ctx ;; let context_tassonomy ctx = let rec split inner acc acc1 = function | Ce _ :: tl when inner -> split inner (acc+1) (acc1+1) tl | Fix _ ::tl -> split false acc (acc1+1) tl | _ as l -> acc, List.length l, acc1 in split true 0 1 ctx ;; let splat_args_for_rel ctx t = let bound, free, primo_ce_dopo_fix = context_tassonomy ctx in if free = 0 then t else let rec aux = function | 0 -> [] | n -> (match List.nth ctx (n+bound) with | Fix (refe, _, _) when (n+bound) < primo_ce_dopo_fix -> NCic.Const refe | Fix _ | Ce _ -> NCic.Rel (n+bound)) :: aux (n-1) in NCic.Appl (t:: aux free) ;; let splat_args ctx t n_fix = let bound, free, primo_ce_dopo_fix = context_tassonomy ctx in if ctx = [] then t else let rec aux = function | 0 -> [] | n -> (match List.nth ctx (n-1) with | Ce _ when n <= bound -> NCic.Rel n | Fix (refe, _, _) when n < primo_ce_dopo_fix -> splat_args_for_rel ctx (NCic.Const refe) | Fix _ | Ce _ -> NCic.Rel (n - n_fix) ) :: aux (n-1) in NCic.Appl (t:: aux (List.length ctx)) ;; exception Nothing_to_do;; let fix_outty curi tyno t context outty = let leftno,rightno = match fst (CicEnvironment.get_obj CicUniv.oblivion_ugraph curi) with Cic.InductiveDefinition (tyl,_,leftno,_) -> let _,_,arity,_ = List.nth tyl tyno in let rec count_prods leftno context arity = match leftno, CicReduction.whd context arity with 0, Cic.Sort _ -> 0 | 0, Cic.Prod (name,so,ty) -> 1 + count_prods 0 (Some (name, Cic.Decl so)::context) ty | n, Cic.Prod (name,so,ty) -> count_prods (leftno - 1) (Some (name, Cic.Decl so)::context) ty | _,_ -> assert false in (*prerr_endline (UriManager.string_of_uri curi); prerr_endline ("LEFTNO: " ^ string_of_int leftno ^ " " ^ CicPp.ppterm arity);*) leftno, count_prods leftno [] arity | _ -> assert false in let ens,args = let tty,_= CicTypeChecker.type_of_aux' [] context t CicUniv.oblivion_ugraph in match CicReduction.whd context tty with Cic.MutInd (_,_,ens) -> ens,[] | Cic.Appl (Cic.MutInd (_,_,ens)::args) -> ens,fst (HExtlib.split_nth leftno args) | _ -> assert false in let rec aux n irl context outsort = match n, CicReduction.whd context outsort with 0, Cic.Prod _ -> raise Nothing_to_do | 0, _ -> let irl = List.rev irl in let ty = CicSubstitution.lift rightno (Cic.MutInd (curi,tyno,ens)) in let ty = if args = [] && irl = [] then ty else Cic.Appl (ty::(List.map (CicSubstitution.lift rightno) args)@irl) in let he = CicSubstitution.lift (rightno + 1) outty in let t = if irl = [] then he else Cic.Appl (he::List.map (CicSubstitution.lift 1) irl) in Cic.Lambda (Cic.Anonymous, ty, t) | n, Cic.Prod (name,so,ty) -> let ty' = aux (n - 1) (Cic.Rel n::irl) (Some (name, Cic.Decl so)::context) ty in Cic.Lambda (name,so,ty') | _,_ -> assert false in (*prerr_endline ("RIGHTNO = " ^ string_of_int rightno ^ " OUTTY = " ^ CicPp.ppterm outty);*) let outsort = fst (CicTypeChecker.type_of_aux' [] context outty CicUniv.oblivion_ugraph) in try aux rightno [] context outsort with Nothing_to_do -> outty (*prerr_endline (CicPp.ppterm outty ^ " <==> " ^ CicPp.ppterm outty');*) ;; (* we are lambda-lifting also variables that do not occur *) (* ctx does not distinguish successive blocks of cofix, since there may be no * lambda separating them *) let convert_term uri t = let rec aux octx (ctx : ctx list) n_fix uri = function | Cic.CoFix (k, fl) -> let buri = UriManager.uri_of_string (UriManager.buri_of_uri uri^"/"^ UriManager.name_of_uri uri ^ string_of_int (List.length ctx)^".con") in let bctx, fixpoints_tys, tys, _ = List.fold_right (fun (name,ty,_) (ctx, fixpoints, tys, idx) -> let ty, fixpoints_ty = aux octx ctx n_fix uri ty in let r = Ref.reference_of_ouri buri(Ref.CoFix idx) in Fix (r,name,ty) :: ctx, fixpoints_ty @ fixpoints,ty::tys,idx+1) fl ([], [], [], 0) in let bctx = bctx @ ctx in let n_fl = List.length fl in let boctx,_ = List.fold_left (fun (types,len) (n,ty,_) -> (Some (Cic.Name n,(Cic.Decl (CicSubstitution.lift len ty)))::types, len+1)) (octx,0) fl in let fl, fixpoints = List.fold_right2 (fun (name,_,bo) ty (l,fixpoints) -> let bo, fixpoints_bo = aux boctx bctx n_fl buri bo in (([],name,~-1,splat true ctx ty, splat false ctx bo)::l), fixpoints_bo @ fixpoints) fl tys ([],fixpoints_tys) in let obj = NUri.nuri_of_ouri buri,0,[],[], NCic.Fixpoint (false, fl, (`Generated, `Definition)) in splat_args ctx (NCic.Const (Ref.reference_of_ouri buri (Ref.CoFix k))) n_fix, fixpoints @ [obj] | Cic.Fix (k, fl) -> let buri = UriManager.uri_of_string (UriManager.buri_of_uri uri^"/"^ UriManager.name_of_uri uri ^ string_of_int (List.length ctx)^".con") in let bad_bctx, fixpoints_tys, tys, _ = List.fold_right (fun (name,recno,ty,_) (bctx, fixpoints, tys, idx) -> let ty, fixpoints_ty = aux octx ctx n_fix uri ty in let r = (* recno is dummy here, must be lifted by the ctx len *) Ref.reference_of_ouri buri (Ref.Fix (idx,recno)) in Fix (r,name,ty) :: bctx, fixpoints_ty@fixpoints,ty::tys,idx+1) fl ([], [], [], 0) in let _, free, _ = context_tassonomy (bad_bctx @ ctx) in let bctx = List.map (function | Fix (Ref.Ref (_,_,Ref.Fix (idx, recno)),name, ty) -> Fix (Ref.reference_of_ouri buri(Ref.Fix (idx,recno+free)),name,ty) | _ -> assert false) bad_bctx @ ctx in let n_fl = List.length fl in let boctx,_ = List.fold_left (fun (types,len) (n,_,ty,_) -> (Some (Cic.Name n,(Cic.Decl (CicSubstitution.lift len ty)))::types, len+1)) (octx,0) fl in let rno_k = ref 0 in let fl, fixpoints,_ = List.fold_right2 (fun (name,rno,_,bo) ty (l,fixpoints,idx) -> let bo, fixpoints_bo = aux boctx bctx n_fl buri bo in let rno = rno + free in if idx = k then rno_k := rno; (([],name,rno,splat true ctx ty, splat false ctx bo)::l), fixpoints_bo @ fixpoints,idx+1) fl tys ([],fixpoints_tys,0) in let obj = NUri.nuri_of_ouri buri,max_int,[],[], NCic.Fixpoint (true, fl, (`Generated, `Definition)) in splat_args ctx (NCic.Const (Ref.reference_of_ouri buri (Ref.Fix (k,!rno_k)))) n_fix, fixpoints @ [obj] | Cic.Rel n -> let bound, _, primo_ce_dopo_fix = context_tassonomy ctx in (match List.nth ctx (n-1) with | Fix (r,_,_) when n < primo_ce_dopo_fix -> splat_args_for_rel ctx (NCic.Const r), [] | Ce _ when n <= bound -> NCic.Rel n, [] | Fix _ (* BUG 3 fix nested *) | Ce _ -> NCic.Rel (n-n_fix), []) | Cic.Lambda (name, (s as old_s), t) -> let s, fixpoints_s = aux octx ctx n_fix uri s in let ctx = Ce (cn_to_s name, NCic.Decl s) :: ctx in let octx = Some (name, Cic.Decl old_s) :: octx in let t, fixpoints_t = aux octx ctx n_fix uri t in NCic.Lambda (cn_to_s name, s, t), fixpoints_s @ fixpoints_t | Cic.Prod (name, (s as old_s), t) -> let s, fixpoints_s = aux octx ctx n_fix uri s in let ctx = Ce (cn_to_s name, NCic.Decl s) :: ctx in let octx = Some (name, Cic.Decl old_s) :: octx in let t, fixpoints_t = aux octx ctx n_fix uri t in NCic.Prod (cn_to_s name, s, t), fixpoints_s @ fixpoints_t | Cic.LetIn (name, (te as old_te), (ty as old_ty), t) -> let te, fixpoints_s = aux octx ctx n_fix uri te in let ty, fixpoints_ty = aux octx ctx n_fix uri ty in let ctx = Ce (cn_to_s name, NCic.Def (te, ty)) :: ctx in let octx = Some (name, Cic.Def (old_te, old_ty)) :: octx in let t, fixpoints_t = aux octx ctx n_fix uri t in NCic.LetIn (cn_to_s name, ty, te, t), fixpoints_s @ fixpoints_t @ fixpoints_ty | Cic.Cast (t,ty) -> let t, fixpoints_t = aux octx ctx n_fix uri t in let ty, fixpoints_ty = aux octx ctx n_fix uri ty in NCic.LetIn ("cast", ty, t, NCic.Rel 1), fixpoints_t @ fixpoints_ty | Cic.Sort Cic.Prop -> NCic.Sort NCic.Prop,[] | Cic.Sort Cic.CProp -> NCic.Sort NCic.CProp,[] | Cic.Sort (Cic.Type _) -> NCic.Sort (NCic.Type 0),[] | Cic.Sort Cic.Set -> NCic.Sort (NCic.Type 0),[] (* calculate depth in the univ_graph*) | Cic.Appl l -> let l, fixpoints = List.fold_right (fun t (l,acc) -> let t, fixpoints = aux octx ctx n_fix uri t in (t::l,fixpoints@acc)) l ([],[]) in (match l with | (NCic.Appl l1)::l2 -> NCic.Appl (l1@l2), fixpoints | _ -> NCic.Appl l, fixpoints) | Cic.Const (curi, ens) -> aux_ens octx ctx n_fix uri ens (match fst(CicEnvironment.get_obj CicUniv.oblivion_ugraph curi) with | Cic.Constant (_,Some _,_,_,_) -> NCic.Const (Ref.reference_of_ouri curi Ref.Def) | Cic.Constant (_,None,_,_,_) -> NCic.Const (Ref.reference_of_ouri curi Ref.Decl) | _ -> assert false) | Cic.MutInd (curi, tyno, ens) -> aux_ens octx ctx n_fix uri ens (NCic.Const (Ref.reference_of_ouri curi (Ref.Ind tyno))) | Cic.MutConstruct (curi, tyno, consno, ens) -> aux_ens octx ctx n_fix uri ens (NCic.Const (Ref.reference_of_ouri curi (Ref.Con (tyno,consno)))) | Cic.MutCase (curi, tyno, outty, t, branches) -> let outty = fix_outty curi tyno t octx outty in let r = Ref.reference_of_ouri curi (Ref.Ind tyno) in let outty, fixpoints_outty = aux octx ctx n_fix uri outty in let t, fixpoints_t = aux octx ctx n_fix uri t in let branches, fixpoints = List.fold_right (fun t (l,acc) -> let t, fixpoints = aux octx ctx n_fix uri t in (t::l,fixpoints@acc)) branches ([],[]) in NCic.Match (r,outty,t,branches), fixpoints_outty@fixpoints_t@fixpoints | Cic.Implicit _ | Cic.Meta _ | Cic.Var _ -> assert false and aux_ens octx ctx n_fix uri ens he = match ens with [] -> he,[] | _::_ -> let ens,objs = List.fold_right (fun (_,t) (l,objs) -> let t,o = aux octx ctx n_fix uri t in t::l, o@objs ) ens ([],[]) in NCic.Appl (he::ens),objs in aux [] [] 0 uri t ;; let cook mode vars t = let t = CicSubstitution.lift (List.length vars) t in snd (List.fold_right (fun uri (n,t) -> let t = CicSubstitution.subst_vars [uri,Cic.Rel 1] t in let bo,ty = match fst (CicEnvironment.get_obj CicUniv.oblivion_ugraph uri) with Cic.Variable (_,bo,ty,_,_) -> bo,ty | _ -> assert false in let id = Cic.Name (UriManager.name_of_uri uri) in let t = match bo,ty,mode with None,ty,`Lambda -> Cic.Lambda (id,ty,t) | None,ty,`Pi -> Cic.Prod (id,ty,t) | Some bo,ty,_ -> Cic.LetIn (id,bo,ty,t) in n+1,t ) vars (1,t)) ;; let convert_obj_aux uri = function | Cic.Constant (name, None, ty, vars, _) -> let ty = cook `Pi vars ty in let nty, fixpoints = convert_term uri ty in assert(fixpoints = []); NCic.Constant ([], name, None, nty, (`Provided,`Theorem,`Regular)), fixpoints | Cic.Constant (name, Some bo, ty, vars, _) -> let bo = cook `Lambda vars bo in let ty = cook `Pi vars ty in let nbo, fixpoints_bo = convert_term uri bo in let nty, fixpoints_ty = convert_term uri ty in assert(fixpoints_ty = []); NCic.Constant ([], name, Some nbo, nty, (`Provided,`Theorem,`Regular)), fixpoints_bo @ fixpoints_ty | Cic.InductiveDefinition (itl,vars,leftno,_) -> let ind = let _,x,_,_ = List.hd itl in x in let itl, fix_itl = List.fold_right (fun (name, _, ty, cl) (itl,acc) -> let ty = cook `Pi vars ty in let ty, fix_ty = convert_term uri ty in let cl, fix_cl = List.fold_right (fun (name, ty) (cl,acc) -> let ty = cook `Pi vars ty in let ty, fix_ty = convert_term uri ty in ([], name, ty)::cl, acc @ fix_ty) cl ([],[]) in ([], name, ty, cl)::itl, fix_ty @ fix_cl @ acc) itl ([],[]) in NCic.Inductive(ind, leftno + List.length vars, itl, (`Provided, `Regular)), fix_itl | Cic.Variable _ | Cic.CurrentProof _ -> assert false ;; let convert_obj uri obj = let o, fixpoints = convert_obj_aux uri obj in let obj = NUri.nuri_of_ouri uri,max_int, [], [], o in fixpoints @ [obj] ;;