module A = Cic2acic
module Ut = CicUtil
module E = CicEnvironment
+module PEH = ProofEngineHelpers
module PER = ProofEngineReduction
+module Pp = CicPp
module P = ProceduralPreprocess
module Cl = ProceduralClassify
-module M = ProceduralMode
module T = ProceduralTypes
module Cn = ProceduralConversion
(* helpers ******************************************************************)
-let identity x = x
-
-let comp f g x = f (g x)
-
let cic = D.deannotate_term
let split2_last l1 l2 =
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 expanded_premise = "EXPANDED"
-
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
- let e = Cn.mk_pattern [] (T.mk_arel 1 "") in
+ 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 eta_expand n t =
- let id = Ut.id_of_annterm t in
- let ty = C.AImplicit ("", None) in
- let name i = Printf.sprintf "%s%u" expanded_premise i in
- let lambda i t = C.ALambda (id, C.Name (name i), ty, t) in
- let arg i n = T.mk_arel (n - i) (name (n - i - 1)) 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 identity [] 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 (id, C.AAppl ("", before) :: after)
- | _ -> assert false
-
-let get_intro name t =
-try
-match name with
+let get_intro = function
| C.Anonymous -> unused_premise
- | C.Name s ->
- if DTI.does_not_occur 1 (cic t) then unused_premise else s
-with Invalid_argument _ -> failwith "A2P.get_intro"
+ | C.Name s -> s
let mk_intros st script =
try
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
- 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 =
- let what, where = List.nth tl 5, List.nth tl 3 in
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
+let rec mk_arg st = function
+ | C.ARel (_, _, _, name) as what -> convert st ~name what, what
+ | what -> [], what
+
+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 (_, _, _, premise) ->
- let script, what = mk_atomic st dtext what in
+ let script, what = mk_arg st 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.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 ->
+ | 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, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
+ let ty = get_type "TC1" st hd in
begin match get_inner_types st v with
- | Some (ity, _) when M.bkd st.context ty ->
+ | Some (ity, _) ->
let qs = [[T.Id ""]; mk_proof (next st) v] in
[T.Branch (qs, ""); T.Cut (name, ity, dtext)]
- | _ ->
+ | _ ->
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
- end
- | C.ACast (_, v, _) ->
- mk_fwd_proof st dtext name v
- | v ->
+ | 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.LetIn (name, v, dtext)]
and mk_proof st = function
- | C.ALambda (_, name, v, t) ->
+ | C.ALambda (_, name, v, t) ->
let entry = Some (name, C.Decl (cic v)) in
- let intro = get_intro name t in
+ let intro = get_intro name in
mk_proof (add st entry intro) t
- | C.ALetIn (_, name, v, t) as what ->
+ | 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 intro = get_intro name 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 premises, _ = P.split 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
+ if decurry <> 0 then begin
+ let msg = Printf.sprintf "Decurry: %i\nTerm: %s\nContext: %s"
+ decurry (Pp.ppterm (cic t)) (Pp.ppcontext st.context)
+ in
+ HLog.warn msg; assert false
+ end;
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 && M.is_eliminator premises ->
+ | Some (i, j) ->
let classes, tl, _, what = split2_last classes tl in
- let script, what = mk_atomic st dtext what in
+ let script, what = mk_arg st 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
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
- List.rev script @ convert st t @
- [T.Rewrite (false, what, None, e, dtext); T.Branch (qs, "")]
+ mk_rewrite st dtext script t what qs tl false
else if is_rewrite_left hd then
- let rps, predicate = [List.nth tl 4], List.nth tl 2 in
- let e = Cn.mk_pattern rps predicate in
- List.rev script @ convert st t @
- [T.Rewrite (true, what, None, e, 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 0 (T.mk_arel 1 "") (* 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, "")]
+ | None ->
let qs = mk_bkd_proofs (next st) synth classes tl in
- let script, hd = mk_atomic st dtext hd in
+ let script, hd = mk_arg st hd in
List.rev script @ convert st t @
[T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
else
[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
- | C.ACast (_, t, _) ->
- mk_proof st t
- | 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
and mk_bkd_proofs st synth classes ts =
try
let _, dtext = test_depth st in
- let aux inv v =
+ let aux (inv, _) v =
if I.overlaps synth inv then None else
if I.S.is_empty inv then Some (mk_proof st v) else
Some [T.Apply (v, dtext ^ "dependent")]
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