* http://cs.unibo.it/helm/.
*)
-module C = Cic
-module I = CicInspect
-module S = CicSubstitution
-module TC = CicTypeChecker
-module Un = CicUniv
-module UM = UriManager
-module Obj = LibraryObjects
-module HObj = HelmLibraryObjects
-module A = Cic2acic
-module Ut = CicUtil
-module E = CicEnvironment
-module Pp = CicPp
-module PEH = ProofEngineHelpers
-module HEL = HExtlib
-module DTI = DoubleTypeInference
-module NU = CicNotationUtil
-module L = Librarian
-
-module Cl = ProceduralClassify
-module T = ProceduralTypes
-module Cn = ProceduralConversion
-module H = ProceduralHelpers
-module X = ProceduralTeX
-
-type status = {
- sorts : (C.id, A.sort_kind) Hashtbl.t;
- types : (C.id, A.anntypes) Hashtbl.t;
- max_depth: int option;
- depth: int;
- context: C.context;
- case: int list
-}
+module P1 = Procedural1
+module X = ProceduralTeX
let tex_formatter = ref None
-let debug = ref false
-
-(* helpers ******************************************************************)
-
-let split2_last l1 l2 =
-try
- let n = pred (List.length l1) 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.AMutInd _ -> "mutind"
- | C.AMutConstruct _ -> "mutconstruct"
- | C.AVar _ -> "var"
- | C.ARel _ -> "rel"
- | C.AProd _ -> "prod"
- | C.ALambda _ -> "lambda"
- | C.ALetIn _ -> "letin"
- | C.AFix _ -> "fix"
- | C.ACoFix _ -> "cofix"
- | C.AAppl _ -> "appl"
- | C.ACast _ -> "cast"
- | C.AMutCase _ -> "mutcase"
- | C.AMeta _ -> "meta"
- | C.AImplicit _ -> "implict"
-
-let next st = {st with depth = succ st.depth}
-
-let add st entry = {st with context = entry :: st.context}
-
-let push st = {st with case = 1 :: st.case}
-
-let inc st =
- {st with case = match st.case with
- | [] -> []
- | 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
- match st.max_depth with
- | None -> true, ""
- | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
-with Invalid_argument _ -> failwith "A2P.test_depth"
-
-let is_rewrite_right = function
- | C.AConst (_, uri, []) ->
- UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
- | _ -> false
-
-let is_rewrite_left = function
- | 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_inner_types st v =
-try
- let id = Ut.id_of_annterm v in
- try match Hashtbl.find st.types id with
- | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
- | {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_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
-
-let string_of_atomic = function
- | C.ARel (_, _, _, s) -> s
- | C.AVar (_, uri, _) -> H.name_of_uri uri None None
- | C.AConst (_, uri, _) -> H.name_of_uri uri None None
- | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
- | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
- | _ -> ""
-
-let get_sub_names head l =
- let s = string_of_atomic head in
- if s = "" then [] else
- let map (names, i) _ =
- let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
- in
- let names, _ = List.fold_left map ([], 1) l in
- List.rev names
-
-let get_type msg st t = H.get_type msg st.context (H.cic t)
-
-let clear_absts m =
- let rec aux k n = function
- | C.ALambda (id, s, v, t) when k > 0 ->
- C.ALambda (id, s, v, aux (pred k) n t)
- | C.ALambda (_, _, _, t) when n > 0 ->
- aux 0 (pred n) (Cn.lift 1 (-1) t)
- | t when n > 0 ->
- Printf.eprintf "A2P.clear_absts: %u %s\n" n (Pp.ppterm (H.cic t));
- assert false
- | t -> t
- in
- aux m
-
-(* proof construction *******************************************************)
-
-let anonymous_premise = C.Name "UNNAMED"
-
-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 script =
- if !debug then
- let sname = match name with None -> "" | Some (id, _) -> id in
- let note = Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
- note sname (Pp.ppterm csty) (Pp.ppterm cety)
- in
- [T.Note note]
- else []
- in
- assert (Ut.is_sober st.context csty);
- assert (Ut.is_sober st.context cety);
- if Ut.alpha_equivalence csty cety then script else
- let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
- match name with
- | None -> T.Change (sty, ety, None, e, "") :: script
- | Some (id, i) ->
- begin match get_entry st id with
- | C.Def _ -> assert false (* T.ClearBody (id, "") :: script *)
- | C.Decl _ ->
- T.Change (ety, sty, Some (id, Some id), e, "") :: script
- end
-
-let convert st ?name v =
- match get_inner_types st v with
- | None ->
- if !debug then [T.Note "NORMAL: NO INNER TYPES"] else []
- | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
-
-let get_intro = function
- | C.Anonymous -> None
- | C.Name s -> Some s
-
-let mk_preamble st what script =
- convert st what @ script
-
-let mk_arg st = function
- | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
- | _ -> []
-
-let mk_fwd_rewrite st dtext name tl direction v t ity =
- let compare premise = function
- | None -> true
- | Some s -> s = premise
- in
- 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
- if (Cn.does_not_occur e) then st, [] else
- match where with
- | C.ARel (_, _, i, premise) as w ->
- let script name =
- let where = Some (premise, name) in
- let script = mk_arg st what @ mk_arg st w in
- T.Rewrite (direction, what, where, e, dtext) :: script
- in
- if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
- {st with context = Cn.clear st.context premise}, script name
- else begin
- assert (Ut.is_sober st.context (H.cic ity));
- let ity = H.acic_bc st.context ity in
- let br1 = [T.Id ""] in
- let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
- let text = "non-linear rewrite" in
- st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
- end
- | _ -> 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 = [T.Branch (qs, "")] in
- if (Cn.does_not_occur e) then script else
- T.Rewrite (direction, where, None, e, dtext) :: script
-
-let rec proc_lambda st what name v t =
- let name = match name with
- | C.Anonymous -> H.mk_fresh_name st.context anonymous_premise
- | name -> name
- in
- let entry = Some (name, C.Decl (H.cic v)) in
- let intro = get_intro name in
- let script = proc_proof (add st entry) t in
- let script = T.Intros (Some 1, [intro], "") :: script in
- mk_preamble st what script
-
-and proc_letin st what name v w 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 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 t ity
- | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
- mk_fwd_rewrite st dtext intro tl false v t ity
- | v ->
- assert (Ut.is_sober st.context (H.cic ity));
- let ity = H.acic_bc st.context ity in
- 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, H.cic w), [T.LetIn (intro, v, dtext)]
- in
- let entry = Some (name, hyp) in
- let qt = proc_proof (next (add st entry)) t in
- List.rev_append rqv qt
- else
- [T.Apply (what, dtext)]
- in
- mk_preamble 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_preamble st what script
-
-and proc_mutconstruct st what =
- let _, dtext = test_depth st in
- let script = [T.Apply (what, dtext)] in
- mk_preamble st what script
-
-and proc_const st what =
- let _, dtext = test_depth st in
- let script = [T.Apply (what, dtext)] in
- mk_preamble st what script
-
-and proc_appl st what hd tl =
- let proceed, dtext = test_depth st in
- let script = if proceed then
- let ty = match get_inner_types st hd with
- | Some (ity, _) -> H.cic ity
- | None -> get_type "TC2" st hd
- in
- let classes, rc = Cl.classify st.context ty in
- let goal_arity, goal = match get_inner_types st what with
- | None -> 0, None
- | Some (ity, ety) ->
- snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
- in
- 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 classes = Cl.adjust st.context tl ?goal classes in
- let rec mk_synth a n =
- if n < 0 then a else mk_synth (I.S.add n a) (pred n)
- in
- 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 classes2, tl2, _, where = split2_last classes tl in
- let script2 = List.rev (mk_arg st where) @ script in
- let synth2 = I.S.add 1 synth in
- let names = H.get_ind_names uri tyno in
- let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
- if List.length qs <> List.length names then
- 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 if is_rewrite_right hd then
- script2 @ mk_rewrite st dtext where qs tl2 false what
- else if is_rewrite_left hd then
- script2 @ mk_rewrite st dtext where qs tl2 true what
- else
- let predicate = List.nth tl2 (parsno - i) in
- let e = Cn.mk_pattern j predicate in
- let using = Some hd in
- script2 @
- [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
- | None ->
- let names = get_sub_names hd tl in
- let qs = proc_bkd_proofs (next st) synth names 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_preamble st what script
-
-and proc_case st what uri tyno u v ts =
- let proceed, dtext = test_depth st in
- let script = if proceed then
- let synth, classes = I.S.empty, Cl.make ts in
- let names = H.get_ind_names uri tyno in
- let qs = proc_bkd_proofs (next st) synth names classes ts in
- let lpsno, _ = H.get_ind_type uri tyno in
- let ps, sort_disp = H.get_ind_parameters st.context (H.cic v) in
- let _, rps = HEL.split_nth lpsno ps in
- let rpsno = List.length rps in
- let predicate = clear_absts rpsno (1 - sort_disp) u in
- let e = Cn.mk_pattern rpsno predicate in
- let text = "" in
- let script = List.rev (mk_arg st v) in
- script @ [T.Cases (v, e, dtext ^ text); T.Branch (qs, "")]
- else
- [T.Apply (what, dtext)]
- in
- mk_preamble st what script
-
-and proc_other st what =
- let _, dtext = test_depth st in
- let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
- let script = [T.Apply (what, dtext ^ text)] in
- mk_preamble 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
- {st with context = context}
- in
- match t with
- | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
- | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
- | C.ARel _ as what -> proc_rel (f st) what
- | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
- | C.AConst _ as what -> proc_const (f st) what
- | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
- | C.AMutCase (_, uri, i, u, v, ts) as what -> proc_case (f st) what uri i u v ts
- | what -> proc_other (f st) what
-
-and proc_bkd_proofs st synth names classes ts =
-try
- let get_names b = ref (names, if b then push st else st) in
- let get_note f b names =
- match !names with
- | [], st -> f st
- | "" :: tl, st -> names := tl, st; f st
- | hd :: tl, st ->
- let note = case st hd in
- names := tl, inc st;
- if b then T.Note note :: f st else f st
- in
- 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 (get_note (fun _ -> [T.Apply (v, dtext ^ "dependent")]))
- in
- let ps = T.list_map2_filter aux classes ts in
- let b = List.length ps > 1 in
- let names = get_names b in
- List.rev_map (fun f -> f b names) ps
-
-with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
-
-(* object costruction *******************************************************)
-
-let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
-
-let def_flavours = [`Definition]
-
-let get_flavour ?flavour attrs =
- let rec aux = function
- | [] -> List.hd th_flavours
- | `Flavour fl :: _ -> fl
- | _ :: tl -> aux tl
- in
- match flavour with
- | Some fl -> fl
- | None -> aux attrs
-
-let proc_obj ?flavour ?(info="") st = function
- | C.AConstant (_, _, s, Some v, t, [], attrs) ->
- begin match get_flavour ?flavour attrs with
- | flavour when List.mem flavour th_flavours ->
- 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 "%s\n%s%s: %u\n%s: %u\n%s"
- "COMMENTS" info "Tactics" steps "Final nodes" nodes "END"
- in
- T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text]
- | flavour when List.mem flavour def_flavours ->
- [T.Statement (flavour, Some s, t, Some v, "")]
- | _ ->
- failwith "not a theorem, definition, axiom or inductive type"
- end
- | C.AConstant (_, _, s, None, t, [], attrs) ->
- [T.Statement (`Axiom, Some s, t, None, "")]
- | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
- [T.Inductive (types, lpsno, "")]
- | _ ->
- failwith "not a theorem, definition, axiom or inductive type"
-
(* interface functions ******************************************************)
let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types
projects / helm.git / blobdiff