*)
module C = Cic
-module D = Deannotate
-module DTI = DoubleTypeInference
+module I = CicInspect
+module S = CicSubstitution
module TC = CicTypeChecker
module Un = CicUniv
module UM = UriManager
module A = Cic2acic
module Ut = CicUtil
module E = CicEnvironment
+module Pp = CicPp
+module PEH = ProofEngineHelpers
+module HEL = HExtlib
+module DTI = DoubleTypeInference
-module Cl = CicClassify
+module Cl = ProceduralClassify
module T = ProceduralTypes
module Cn = ProceduralConversion
+module H = ProceduralHelpers
type status = {
sorts : (C.id, A.sort_kind) Hashtbl.t;
max_depth: int option;
depth: int;
context: C.context;
- intros: string list;
- ety: C.annterm option
+ intros: string option list;
+ clears: string list;
+ clears_note: string;
+ case: int list;
+ skip_thm_and_qed : bool;
}
(* helpers ******************************************************************)
-let id x = x
-
-let comp f g x = f (g x)
-
-let cic = D.deannotate_term
-
let split2_last l1 l2 =
try
let n = pred (List.length l1) in
- let before1, after1 = T.list_split n l1 in
- let before2, after2 = T.list_split n l2 in
+ let before1, after1 = HEL.split_nth n l1 in
+ let before2, after2 = HEL.split_nth n l2 in
before1, before2, List.hd after1, List.hd after2
with Invalid_argument _ -> failwith "A2P.split2_last"
-
+
let string_of_head = function
| C.ASort _ -> "sort"
| C.AConst _ -> "const"
| 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 push st = {st with case = 1 :: st.case}
+
+let inc st =
+ {st with case = match st.case with
+ | [] -> assert false
+ | hd :: tl -> succ hd :: tl
+ }
+
+let case st str =
+ let case = String.concat "." (List.rev_map string_of_int st.case) in
+ Printf.sprintf "case %s: %s" case str
+
let test_depth st =
try
let msg = Printf.sprintf "Depth %u: " st.depth in
| C.AConst (_, uri, []) ->
UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
| _ -> false
-(*
-let get_ind_name uri tno xcno =
-try
- let ts = match E.get_obj Un.empty_ugraph uri with
- | C.InductiveDefinition (ts, _, _,_), _ -> ts
- | _ -> assert false
- in
- let tname, cs = match List.nth ts tno with
- | (name, _, _, cs) -> name, cs
- in
- match xcno with
- | None -> tname
- | Some cno -> fst (List.nth cs (pred cno))
-with Invalid_argument _ -> failwith "A2P.get_ind_name"
-*)
+
+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_inner_types st v =
try
let id = Ut.id_of_annterm v in
| {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
with Not_found -> None
with Invalid_argument _ -> failwith "A2P.get_inner_types"
-
+(*
let get_inner_sort st v =
try
let id = Ut.id_of_annterm v in
try Hashtbl.find st.sorts id
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 (H.cic bo) Un.empty_ugraph in
+ ty
+with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
+
+let get_entry st id =
+ let rec aux = function
+ | [] -> assert false
+ | Some (C.Name name, e) :: _ when name = id -> e
+ | _ :: tl -> aux tl
+ in
+ aux st.context
-(* proof construction *******************************************************)
+let get_ind_names uri tno =
+try
+ let ts = match E.get_obj Un.empty_ugraph uri with
+ | C.InductiveDefinition (ts, _, _, _), _ -> ts
+ | _ -> assert false
+ in
+ match List.nth ts tno with
+ | (_, _, _, cs) -> List.map fst cs
+with Invalid_argument _ -> failwith "A2P.get_ind_names"
-let unused_premise = "UNUSED"
+(* proof construction *******************************************************)
-let defined_premise = "DEFINED"
+let used_premise = C.Name "USED"
-let assumed_premise = "ASSUMED"
+let mk_exp_args hd tl classes synth =
+ let meta id = C.AImplicit (id, None) in
+ let map v (cl, b) =
+ if I.overlaps synth cl && b then v else meta ""
+ in
+ let rec aux = function
+ | [] -> []
+ | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
+ in
+ let args = T.list_rev_map2 map tl classes in
+ let args = aux args in
+ if args = [] then hd else C.AAppl ("", hd :: args)
+
+let mk_convert st ?name sty ety note =
+ let e = Cn.hole "" in
+ let csty, cety = H.cic sty, H.cic ety in
+ let _note = Printf.sprintf "%s\nSINTH: %s\nEXP: %s"
+ note (Pp.ppterm csty) (Pp.ppterm cety)
+ in
+ if Ut.alpha_equivalence csty cety then [(* T.Note note *)] else
+ match name with
+ | None -> [T.Change (sty, ety, None, e, ""(*note*))]
+ | Some (id, i) ->
+ begin match get_entry st id with
+ | C.Def _ -> assert false (* [T.ClearBody (id, note)] *)
+ | C.Decl _ -> [T.Change (ety, sty, Some (id, Some id), e, "" (* note *))]
+ end
+
+let convert st ?name v =
+ match get_inner_types st v with
+ | None -> [(*T.Note "NORMAL: NO INNER TYPES"*)]
+ | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
+
+let convert_elim st ?name t v pattern =
+ match t, get_inner_types st t, get_inner_types st v with
+ | _, None, _
+ | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
+ | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
+ let where = List.hd (List.rev tl) in
+ let cty = Cn.elim_inferred_type
+ st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
+ in
+ mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
+ | _, Some _, Some _ -> assert false
+
+let get_intro = function
+ | C.Anonymous -> None
+ | C.Name s -> Some s
+
+let mk_intros st what script =
+ let intros st script =
+ if st.intros = [] then script else
+ let count = List.length st.intros in
+ T.Intros (Some count, List.rev st.intros, "") :: script
+ in
+ let clears st script =
+ if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
+ in
+ intros st (clears st (convert st what @ script))
-let expanded_premise = "EXPANDED"
+let mk_arg st = function
+ | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
+ | _ -> []
-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)
+let mk_fwd_rewrite st dtext name tl direction t =
+ 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 (_, _, i, premise) as v ->
+ let where = Some (premise, name) in
+(* let _script = convert_elim st ~name:(premise, i) t v e in *)
+ let script = mk_arg st what @ mk_arg st v (* @ script *) in
+ let st = {st with context = Cn.clear st.context premise} in
+ st, T.Rewrite (direction, what, where, e, dtext) :: script
+ | _ -> assert false
+
+let mk_rewrite st dtext where qs tl direction t =
+ assert (List.length tl = 5);
+ let predicate = List.nth tl 2 in
+ let e = Cn.mk_pattern 1 predicate in
+ let script = [] (* convert_elim st t t e *) in
+ script @ [T.Rewrite (direction, where, None, e, dtext); T.Branch (qs, "")]
+
+let rec proc_lambda st name v t =
+ let dno = DTI.does_not_occur 1 (H.cic t) in
+ let dno = dno && match get_inner_types st t with
+ | None -> true
+ | Some (it, et) ->
+ DTI.does_not_occur 1 (H.cic it) && DTI.does_not_occur 1 (H.cic et)
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 get_intro name t =
-try
-match name with
- | 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"
-
-let mk_intros st script =
-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
-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
+ let name = match dno, name with
+ | true, _ -> C.Anonymous
+ | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
+ | false, name -> name
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]
-
-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
- begin match get_inner_types st v with
+ let entry = Some (name, C.Decl (H.cic v)) in
+ let intro = get_intro name in
+ proc_proof (add st entry intro) t
+
+and proc_letin st what name v t =
+ let intro = get_intro name in
+ let proceed, dtext = test_depth st in
+ let script = if proceed then
+ let st, hyp, rqv = 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)]
- | None ->
- let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph 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
- | v ->
- [T.LetIn (name, v, dtext)]
-
-and mk_proof st = function
- | C.ALambda (_, name, v, t) as what ->
- 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
+ let st, rqv = match v with
+ | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
+ mk_fwd_rewrite st dtext intro tl true v
+ | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
+ mk_fwd_rewrite st dtext intro tl false v
+ | v ->
+ let qs = [proc_proof (next st) v; [T.Id ""]] in
+ st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
+ in
+ st, C.Decl (H.cic ity), rqv
+ | None ->
+ st, C.Def (H.cic v, None), [T.LetIn (intro, v, dtext)]
in
- mk_proof (add st entry intro ety) 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
- List.rev_append (mk_fwd_proof st dtext intro v) q
- else
- [T.Apply (what, dtext)]
+ let entry = Some (name, hyp) in
+ let qt = proc_proof (next (add st entry intro)) t in
+ List.rev_append rqv qt
+ else
+ [T.Apply (what, dtext)]
+ in
+ mk_intros st what script
+
+and proc_rel st what =
+ let _, dtext = test_depth st in
+ let text = "assumption" in
+ let script = [T.Apply (what, dtext ^ text)] in
+ mk_intros st what script
+
+and proc_mutconstruct st what =
+ let _, dtext = test_depth st in
+ let script = [T.Apply (what, dtext)] in
+ mk_intros st what script
+
+and proc_appl st what hd tl =
+ let proceed, dtext = test_depth st in
+ let script = if proceed then
+ let ty = get_type "TC2" st hd in
+ let classes, rc = Cl.classify st.context ty in
+ let goal_arity = match get_inner_types st what with
+ | None -> 0
+ | Some (ity, _) -> snd (PEH.split_with_whd (st.context, H.cic ity))
in
- mk_intros st script
- | 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 ->
- let _, dtext = test_depth st in
- let script = [T.Apply (what, dtext)] in
- mk_intros st script
- | 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 (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 synth = Cl.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 ->
- let classes, tl, _, what = split2_last classes tl in
- let script, what = mk_atomic st dtext what in
- let synth = Cl.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 @
- [T.Rewrite (false, what, None, dtext); T.Branch (qs, "")]
- else if is_rewrite_left hd then
- List.rev script @
- [T.Rewrite (true, what, None, dtext); T.Branch (qs, "")]
- else
- let using = Some hd in
- List.rev script @
- [T.Elim (what, using, 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
- List.rev script @
- [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
- else
- [T.Apply (t, dtext)]
+ let parsno, argsno = List.length classes, List.length tl in
+ let decurry = parsno - argsno in
+ let diff = goal_arity - decurry in
+ if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
+ let rec mk_synth a n =
+ if n < 0 then a else mk_synth (I.S.add n a) (pred n)
in
- mk_intros st script
- | 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 =
+ let synth = mk_synth I.S.empty decurry in
+ let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
+ let script = List.rev (mk_arg st hd) in
+ match rc with
+ | Some (i, j, uri, tyno) ->
+ let classes, tl, _, where = split2_last classes tl in
+ let script = List.rev (mk_arg st where) @ script in
+ let synth = I.S.add 1 synth in
+ let names = get_ind_names uri tyno in
+ let qs = proc_bkd_proofs (next st) synth names classes tl in
+ if is_rewrite_right hd then
+ script @ mk_rewrite st dtext where qs tl false what
+ else if is_rewrite_left hd then
+ script @ mk_rewrite st dtext where qs tl true what
+ else
+ let predicate = List.nth tl (parsno - i) in
+ let e = Cn.mk_pattern j predicate in
+ let using = Some hd in
+ (* convert_elim st what what e @ *) script @
+ [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
+ | None ->
+ let qs = proc_bkd_proofs (next st) synth [] classes tl in
+ let hd = mk_exp_args hd tl classes synth in
+ script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
+ else
+ [T.Apply (what, dtext)]
+ in
+ mk_intros st what script
+
+and proc_other st what =
+ let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
+ let script = [T.Note text] in
+ mk_intros st what script
+
+and proc_proof st t =
+ let f st =
+ let xtypes, note = match get_inner_types st t with
+ | Some (it, et) -> Some (H.cic it, H.cic et),
+ (Printf.sprintf "\nInferred: %s\nExpected: %s"
+ (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
+ | None -> None, "\nNo types"
+ in
+ let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
+ let note = Pp.ppcontext st.context ^ note in
+ {st with context = context; clears = clears; clears_note = note; }
+ in
+ match t with
+ | C.ALambda (_, name, w, t) -> proc_lambda st name w t
+ | C.ALetIn (_, name, v, t) as what -> proc_letin (f st) what name v t
+ | C.ARel _ as what -> proc_rel (f st) what
+ | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
+ | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
+ | what -> proc_other (f st) what
+
+and proc_bkd_proofs st synth names classes ts =
try
- let _, dtext = test_depth st in
- let aux inv v =
- if Cl.overlaps synth inv then None else
- if Cl.S.is_empty inv then Some (mk_proof st v) else
- Some [T.Apply (v, dtext ^ "dependent")]
+ let get_note =
+ let names = ref (names, push st) in
+ fun f ->
+ match !names with
+ | [], st -> fun _ -> f st
+ | "" :: tl, st -> names := tl, st; fun _ -> f st
+ | hd :: tl, st ->
+ let note = case st hd in
+ names := tl, inc st;
+ fun b -> if b then T.Note note :: f st else f st
in
- T.list_map2_filter aux classes ts
-with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
+ let _, dtext = test_depth st in
+ let aux (inv, _) v =
+ if I.overlaps synth inv then None else
+ if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
+ Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
+ in
+ let ps = T.list_map2_filter aux classes ts in
+ let b = List.length ps > 1 in
+ List.rev_map (fun f -> f b) ps
+
+with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
(* object costruction *******************************************************)
List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
-let mk_obj st = function
+let proc_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 count = T.count_steps 0 ast in
- let text = Printf.sprintf "tactics: %u" count in
- T.Theorem (s, t, text) :: ast @ [T.Qed ""]
+ let ast = proc_proof st v in
+ let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
+ let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
+ if st.skip_thm_and_qed then ast
+ else T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
| _ ->
failwith "not a theorem"
(* interface functions ******************************************************)
-let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
+let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth
+?(skip_thm_and_qed=false) prefix aobj =
let st = {
- sorts = ids_to_inner_sorts;
- types = ids_to_inner_types;
- prefix = prefix;
- max_depth = depth;
- depth = 0;
- context = [];
- intros = [];
- ety = None
+ sorts = ids_to_inner_sorts;
+ types = ids_to_inner_types;
+ prefix = prefix;
+ max_depth = depth;
+ depth = 0;
+ context = [];
+ intros = [];
+ clears = [];
+ clears_note = "";
+ case = [];
+ skip_thm_and_qed = skip_thm_and_qed;
} in
- HLog.debug "Level 2 transformation";
- let steps = mk_obj st aobj in
- HLog.debug "grafite rendering";
+ HLog.debug "Procedural: level 2 transformation";
+ let steps = proc_obj st aobj in
+ HLog.debug "Procedural: grafite rendering";
List.rev (T.render_steps [] steps)
projects / helm.git / blobdiff