module A = Cic2acic
module Ut = CicUtil
module E = CicEnvironment
+module PEH = ProofEngineHelpers
module PER = ProofEngineReduction
+module P = ProceduralPreprocess
module Cl = ProceduralClassify
module M = ProceduralMode
module T = ProceduralTypes
max_depth: int option;
depth: int;
context: C.context;
- intros: string list;
- ety: C.annterm option
+ intros: string list
}
(* helpers ******************************************************************)
-let id x = x
-
-let comp f g x = f (g x)
-
let cic = D.deannotate_term
let split2_last l1 l2 =
| C.AMeta _ -> "meta"
| C.AImplicit _ -> "implict"
-let clear st = {st with intros = []; ety = None}
+let clear st = {st with intros = []}
let next st = {(clear st) with depth = succ st.depth}
-let set_ety st ety =
- if st.ety = None then {st with ety = ety} else st
-
-let add st entry intro ety =
- let st = set_ety st ety in
+let add st entry intro =
{st with context = entry :: st.context; intros = intro :: st.intros}
let test_depth st =
| C.AConst (_, uri, []) ->
UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
| _ -> false
+
+let is_fwd_rewrite_right hd tl =
+ if is_rewrite_right hd then match List.nth tl 3 with
+ | C.ARel _ -> true
+ | _ -> false
+ else false
+
+let is_fwd_rewrite_left hd tl =
+ if is_rewrite_left hd then match List.nth tl 3 with
+ | C.ARel _ -> true
+ | _ -> false
+ else false
(*
let get_ind_name uri tno xcno =
try
with Not_found -> `Type (CicUniv.fresh())
with Invalid_argument _ -> failwith "A2P.get_sort"
+let get_type msg st bo =
+try
+ let ty, _ = TC.type_of_aux' [] st.context (cic bo) Un.empty_ugraph in
+ ty
+with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
+
(* proof construction *******************************************************)
let unused_premise = "UNUSED"
let defined_premise = "DEFINED"
-let assumed_premise = "ASSUMED"
-
-let expanded_premise = "EXPANDED"
-
-let convert st v =
+let convert st ?name v =
match get_inner_types st v with
+ | None -> []
| Some (st, et) ->
let cst, cet = cic st, cic et in
if PER.alpha_equivalence cst cet then [] else
- [T.Change (st, et, "")]
- | None -> []
-
-let eta_expand n t =
- let ty = C.AImplicit ("", None) in
- let name i = Printf.sprintf "%s%u" expanded_premise i in
- let lambda i t = C.ALambda ("", C.Name (name i), ty, t) in
- let arg i n = T.mk_arel (n - i) (name i) in
- let rec aux i f a =
- if i >= n then f, a else aux (succ i) (comp f (lambda i)) (arg i n :: a)
- in
- let absts, args = aux 0 id [] in
- match Cn.lift 1 n t with
- | C.AAppl (id, ts) -> absts (C.AAppl (id, ts @ args))
- | t -> absts (C.AAppl ("", t :: args))
-
-let appl_expand n = function
- | C.AAppl (id, ts) ->
- let before, after = T.list_split (List.length ts + n) ts in
- C.AAppl ("", C.AAppl (id, before) :: after)
- | _ -> assert false
+ let e = Cn.mk_pattern 0 (T.mk_arel 1 "") in
+ match name with
+ | None -> [T.Change (st, et, None, e, "")]
+ | Some id -> [T.Change (st, et, Some (id, id), e, ""); T.ClearBody (id, "")]
let get_intro name t =
try
try
if st.intros = [] then script else
let count = List.length st.intros in
- let p0 = T.Whd (count, "") in
- let p1 = T.Intros (Some count, List.rev st.intros, "") in
- match st.ety with
- | Some ety when Cn.need_whd count ety -> p0 :: p1 :: script
- | _ -> p1 :: script
+ T.Intros (Some count, List.rev st.intros, "") :: script
with Invalid_argument _ -> failwith "A2P.mk_intros"
let rec mk_atomic st dtext what =
- if T.is_atomic what then [], what else
- let name = defined_premise in
- mk_fwd_proof st dtext name what, T.mk_arel 0 name
-
-and mk_fwd_rewrite st dtext name tl direction =
- let what, where = List.nth tl 5, List.nth tl 3 in
- let rewrite premise =
- let script, what = mk_atomic st dtext what in
- T.Rewrite (direction, what, Some (premise, name), dtext) :: script
- in
+ if T.is_atomic what then
+ match what with
+ | C.ARel (_, _, _, name) -> convert st ~name what, what
+ | _ -> [], what
+ else
+ let name = defined_premise in
+ let script = convert st ~name what in
+ script @ mk_fwd_proof st dtext name what, T.mk_arel 0 name
+
+and mk_fwd_rewrite st dtext name tl direction =
+ assert (List.length tl = 6);
+ let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
+ let e = Cn.mk_pattern 1 predicate in
match where with
- | C.ARel (_, _, _, binder) -> rewrite binder
- | _ ->
- assert (get_inner_sort st where = `Prop);
- let pred, old = List.nth tl 2, List.nth tl 1 in
- let pred_name = defined_premise in
- let pred_text = "extracted" in
- let p1 = T.LetIn (pred_name, pred, pred_text) in
- let cut_name = assumed_premise in
- let cut_type = C.AAppl ("", [T.mk_arel 0 pred_name; old]) in
- let cut_text = "" in
- let p2 = T.Cut (cut_name, cut_type, cut_text) in
- let qs = [rewrite cut_name; mk_proof (next st) where] in
- [T.Branch (qs, ""); p2; p1]
+ | C.ARel (_, _, _, premise) ->
+ let script, what = mk_atomic st dtext what in
+ T.Rewrite (direction, what, Some (premise, name), e, dtext) :: script
+ | _ -> assert false
+
+and mk_rewrite st dtext script t what qs tl direction =
+ assert (List.length tl = 5);
+ let predicate = List.nth tl 2 in
+ let e = Cn.mk_pattern 1 predicate in
+ List.rev script @ convert st t @
+ [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
and mk_fwd_proof st dtext name = function
- | C.AAppl (_, hd :: tl) as v ->
- if is_rewrite_right hd then mk_fwd_rewrite st dtext name tl true else
- if is_rewrite_left hd then mk_fwd_rewrite st dtext name tl false else
- let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
+ | C.ALetIn (_, n, v, t) ->
+ let entry = Some (n, C.Def (cic v, None)) in
+ let intro = get_intro n t in
+ let qt = mk_fwd_proof (add st entry intro) dtext name t in
+ let qv = mk_fwd_proof st "" intro v in
+ List.append qt qv
+ | C.AAppl (_, hd :: tl) as v ->
+ if is_fwd_rewrite_right hd tl then mk_fwd_rewrite st dtext name tl true else
+ if is_fwd_rewrite_left hd tl then mk_fwd_rewrite st dtext name tl false else
+ let ty = get_type "TC1" st hd in
begin match get_inner_types st v with
| Some (ity, _) when M.bkd st.context ty ->
let qs = [[T.Id ""]; mk_proof (next st) v] in
| _ ->
let (classes, rc) as h = Cl.classify st.context ty in
let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
- [T.LetIn (name, v, dtext ^ text)]
- end
- | C.AMutCase (id, uri, tyno, outty, arg, cases) as v ->
- begin match Cn.mk_ind st.context id uri tyno outty arg cases with
- | None -> [T.LetIn (name, v, dtext)]
- | Some v -> mk_fwd_proof st dtext name v
+ [T.LetIn (name, v, dtext ^ text)]
end
- | v ->
- [T.LetIn (name, v, dtext)]
+ | C.AMutCase _ -> assert false
+ | C.ACast _ -> assert false
+ | v ->
+ match get_inner_types st v with
+ | Some (ity, _) ->
+ let qs = [[T.Id ""]; mk_proof (next st) v] in
+ [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
+ | _ ->
+ [T.LetIn (name, v, dtext)]
and mk_proof st = function
- | C.ALambda (_, name, v, t) as what ->
+ | C.ALambda (_, name, v, t) ->
let entry = Some (name, C.Decl (cic v)) in
let intro = get_intro name t in
- let ety = match get_inner_types st what with
- | Some (_, ety) -> Some ety
- | None -> None
- in
- mk_proof (add st entry intro ety) t
- | C.ALetIn (_, name, v, t) as what ->
+ mk_proof (add st entry intro) t
+ | C.ALetIn (_, name, v, t) as what ->
let proceed, dtext = test_depth st in
let script = if proceed then
let entry = Some (name, C.Def (cic v, None)) in
let intro = get_intro name t in
- let q = mk_proof (next (add st entry intro None)) t in
+ let q = mk_proof (next (add st entry intro)) t in
List.rev_append (mk_fwd_proof st dtext intro v) q
else
[T.Apply (what, dtext)]
in
mk_intros st script
- | C.ARel _ as what ->
+ | C.ARel _ as what ->
let _, dtext = test_depth st in
let text = "assumption" in
let script = [T.Apply (what, dtext ^ text)] in
mk_intros st script
- | C.AMutConstruct _ as what ->
+ | C.AMutConstruct _ as what ->
let _, dtext = test_depth st in
let script = [T.Apply (what, dtext)] in
mk_intros st script
- | C.AAppl (_, hd :: tl) as t ->
+ | C.AAppl (_, hd :: tl) as t ->
let proceed, dtext = test_depth st in
let script = if proceed then
- let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
+ let ty = get_type "TC2" st hd in
let (classes, rc) as h = Cl.classify st.context ty in
- let decurry = List.length classes - List.length tl in
- if decurry < 0 then mk_proof (clear st) (appl_expand decurry t) else
- if decurry > 0 then mk_proof (clear st) (eta_expand decurry t) else
+ let premises, _ = PEH.split_with_whd (st.context, ty) in
+ assert (List.length classes - List.length tl = 0);
let synth = I.S.singleton 0 in
let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
match rc with
- | Some (i, j) when i > 1 && i <= List.length classes ->
+ | Some (i, j) when i > 1 && i <= List.length classes && M.is_eliminator premises ->
let classes, tl, _, what = split2_last classes tl in
let script, what = mk_atomic st dtext what in
let synth = I.S.add 1 synth in
let qs = mk_bkd_proofs (next st) synth classes tl in
if is_rewrite_right hd then
- List.rev script @ convert st t @
- [T.Rewrite (false, what, None, dtext); T.Branch (qs, "")]
+ mk_rewrite st dtext script t what qs tl false
else if is_rewrite_left hd then
- List.rev script @ convert st t @
- [T.Rewrite (true, what, None, dtext); T.Branch (qs, "")]
+ mk_rewrite st dtext script t what qs tl true
else
- let using = Some hd in
+ let l = succ (List.length tl) in
+ let predicate = List.nth tl (l - i) in
+ let e = Cn.mk_pattern j predicate in
+ let using = Some hd in
List.rev script @ convert st t @
- [T.Elim (what, using, dtext ^ text); T.Branch (qs, "")]
+ [T.Elim (what, using, e, dtext ^ text); T.Branch (qs, "")]
| _ ->
let qs = mk_bkd_proofs (next st) synth classes tl in
let script, hd = mk_atomic st dtext hd in
[T.Apply (t, dtext)]
in
mk_intros st script
- | C.AMutCase (id, uri, tyno, outty, arg, cases) ->
- begin match Cn.mk_ind st.context id uri tyno outty arg cases with
- | None ->
- let text = Printf.sprintf "%s" "UNEXPANDED: mutcase" in
- let script = [T.Note text] in
- mk_intros st script
- | Some t -> mk_proof st t
- end
- | t ->
+ | C.AMutCase _ -> assert false
+ | C.ACast _ -> assert false
+ | t ->
let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
let script = [T.Note text] in
mk_intros st script
let mk_obj st = function
| C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
- let ast = mk_proof (set_ety st (Some t)) v in
+ let ast = mk_proof st v in
let count = T.count_steps 0 ast in
let text = Printf.sprintf "tactics: %u" count in
T.Theorem (s, t, text) :: ast @ [T.Qed ""]
max_depth = depth;
depth = 0;
context = [];
- intros = [];
- ety = None
+ intros = []
} in
HLog.debug "Level 2 transformation";
let steps = mk_obj st aobj in