From 1b36fc4540d93ff21c1afcf485e47e3fe3f26ddb Mon Sep 17 00:00:00 2001 From: Ferruccio Guidi Date: Wed, 11 Mar 2009 12:31:32 +0000 Subject: [PATCH] .... --- .../acic_procedural/acic2Procedural.ml | 482 +--------------- .../acic_procedural/procedural-1.ml | 515 ++++++++++++++++++ .../acic_procedural/procedural-1.mli | 44 ++ 3 files changed, 561 insertions(+), 480 deletions(-) create mode 100644 helm/software/components/acic_procedural/procedural-1.ml create mode 100644 helm/software/components/acic_procedural/procedural-1.mli diff --git a/helm/software/components/acic_procedural/acic2Procedural.ml b/helm/software/components/acic_procedural/acic2Procedural.ml index 0edb5c8b0..043bd6e3a 100644 --- a/helm/software/components/acic_procedural/acic2Procedural.ml +++ b/helm/software/components/acic_procedural/acic2Procedural.ml @@ -23,489 +23,11 @@ * 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 diff --git a/helm/software/components/acic_procedural/procedural-1.ml b/helm/software/components/acic_procedural/procedural-1.ml new file mode 100644 index 000000000..b3e112850 --- /dev/null +++ b/helm/software/components/acic_procedural/procedural-1.ml @@ -0,0 +1,515 @@ +(* Copyright (C) 2003-2005, HELM Team. + * + * This file is part of HELM, an Hypertextual, Electronic + * Library of Mathematics, developed at the Computer Science + * Department, University of Bologna, Italy. + * + * HELM is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * HELM is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with HELM; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + * + * For details, see the HELM World-Wide-Web page, + * 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 +} + +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" + +let init ~ids_to_inner_sorts ~ids_to_inner_types ?depth context = + { + sorts = ids_to_inner_sorts; + types = ids_to_inner_types; + max_depth = depth; + depth = 0; + context = context; + case = [] + } diff --git a/helm/software/components/acic_procedural/procedural-1.mli b/helm/software/components/acic_procedural/procedural-1.mli new file mode 100644 index 000000000..8cbcb1c7e --- /dev/null +++ b/helm/software/components/acic_procedural/procedural-1.mli @@ -0,0 +1,44 @@ +(* Copyright (C) 2003-2005, HELM Team. + * + * This file is part of HELM, an Hypertextual, Electronic + * Library of Mathematics, developed at the Computer Science + * Department, University of Bologna, Italy. + * + * HELM is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * HELM is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with HELM; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + * + * For details, see the HELM World-Wide-Web page, + * http://cs.unibo.it/helm/. + *) + +val procedural_of_acic_object: + ids_to_inner_sorts:(Cic.id, Cic2acic.sort_kind) Hashtbl.t -> + ids_to_inner_types:(Cic.id, Cic2acic.anntypes) Hashtbl.t -> ?info:string -> + ?depth:int -> ?flavour:Cic.object_flavour -> string -> Cic.annobj -> + (Cic.annterm, Cic.annterm, + Cic.annterm GrafiteAst.reduction, Cic.annterm CicNotationPt.obj, string) + GrafiteAst.statement list + +val procedural_of_acic_term: + ids_to_inner_sorts:(Cic.id, Cic2acic.sort_kind) Hashtbl.t -> + ids_to_inner_types:(Cic.id, Cic2acic.anntypes) Hashtbl.t -> + ?depth:int -> string -> Cic.context -> Cic.annterm -> + (Cic.annterm, Cic.annterm, + Cic.annterm GrafiteAst.reduction, Cic.annterm CicNotationPt.obj, string) + GrafiteAst.statement list + +val tex_formatter: Format.formatter option ref + +val debug: bool ref -- 2.39.2