(* Copyright (C) 2019, 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
* 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/.
- *)
+*)
+open Continuationals.Stack
module Ast = NotationPt
open NTactics
+open NTacStatus
+
+type just = [ `Term of NTacStatus.tactic_term | `Auto of NnAuto.auto_params ]
+
+let mk_just status goal =
+ function
+ `Auto (l,params) -> NnAuto.auto_lowtac ~params:(l,params) status goal
+ | `Term t -> apply_tac t
+
+exception NotAProduct
+exception FirstTypeWrong
+exception NotEquivalentTypes
+
+let extract_first_goal_from_status status =
+ let s = status#stack in
+ match s with
+ | [] -> fail (lazy "There's nothing to prove")
+ | (g1, _, k, tag1) :: tl ->
+ let goals = filter_open g1 in
+ let (loc::tl) = goals in
+ let goal = goal_of_loc (loc) in
+ goal ;;
+ (*
+ let (_,_,metasenv,_,_) = status#obj in
+ match metasenv with
+ | [] -> fail (lazy "There's nothing to prove")
+ | (hd,_) :: tl -> hd
+ *)
+
+let extract_conclusion_type status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,gty = term_of_cic_term status gty ctx in
+ gty
+;;
+
+let alpha_eq_tacterm_kerterm ty t status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,cicterm = disambiguate status ctx ty `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ let (_,_,metasenv,subst,_) = status#obj in
+ let status,ty = term_of_cic_term status cicterm ctx in
+ if NCicReduction.alpha_eq status metasenv subst ctx t ty then
+ true
+ else
+ false
+;;
+
+let are_convertible ty1 ty2 status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,cicterm1 = disambiguate status ctx ty1 `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ let status,cicterm2 = disambiguate status ctx ty2 `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ NTacStatus.are_convertible status ctx cicterm1 cicterm2
+
+(* LCF-like tactic that checks whether the conclusion of the sequent of the given goal is a product, checks that
+ the type of the conclusion's bound variable is the same as t1 and then uses an exact_tac with
+ \lambda id: t1. ?. If a t2 is given it checks that t1 ~_{\beta} t2 and uses and exact_tac with \lambda id: t2. ?
+*)
+let lambda_abstract_tac id t1 t2 status goal =
+ match extract_conclusion_type status goal with
+ | NCic.Prod (_,t,_) ->
+ if alpha_eq_tacterm_kerterm t1 t status goal then
+ match t2 with
+ | None ->
+ let (_,_,t1) = t1 in
+ exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit
+ `JustOne))) (*status*)
+ | Some t2 ->
+ let status,res = are_convertible t1 t2 status goal in
+ if res then
+ let (_,_,t2) = t2 in
+ exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t2),Ast.Implicit
+ `JustOne))) (*status*)
+ else
+ raise NotEquivalentTypes
+ else
+ raise FirstTypeWrong
+ | _ -> raise NotAProduct
+
+let assume name ty eqty (*status*) =
+(* let goal = extract_first_goal_from_status status in *)
+ distribute_tac (fun status goal ->
+ try exec (lambda_abstract_tac name ty eqty status goal) status goal
+ with
+ | NotAProduct -> fail (lazy "You can't assume without an universal quantification")
+ | FirstTypeWrong -> fail (lazy "The assumed type is wrong")
+ | NotEquivalentTypes -> fail (lazy "The two given types are not equivalent")
+ )
+;;
+
+let suppose t1 id t2 (*status*) =
+(* let goal = extract_first_goal_from_status status in *)
+ distribute_tac (fun status goal ->
+ try exec (lambda_abstract_tac id t1 t2 status goal) status goal
+ with
+ | NotAProduct -> fail (lazy "You can't suppose without a logical implication")
+ | FirstTypeWrong -> fail (lazy "The supposed proposition is different from the premise")
+ | NotEquivalentTypes -> fail (lazy "The two given propositions are not equivalent")
+ )
+;;
+
+let assert_tac t1 t2 status goal continuation =
+ let t = extract_conclusion_type status goal in
+ if alpha_eq_tacterm_kerterm t1 t status goal then
+ match t2 with
+ | None -> continuation
+ | Some t2 ->
+ let status,res = are_convertible t1 t2 status goal in
+ if res then continuation
+ else
+ raise NotEquivalentTypes
+ else
+ raise FirstTypeWrong
+
+let mustdot status =
+ let s = status#stack in
+ match s with
+ | [] -> fail (lazy "No goals to dot")
+ | (_, _, k, _) :: tl ->
+ if List.length k > 0 then
+ true
+ else
+ false
+
+let bydone just status =
+ let goal = extract_first_goal_from_status status in
+ let mustdot = mustdot status in
+(*
+ let goal,mustdot =
+ let s = status#stack in
+ match s with
+ | [] -> fail (lazy "Invalid use of done")
+ | (g1, _, k, tag1) :: tl ->
+ let goals = filter_open g1 in
+ let (loc::tl) = goals in
+ let goal = goal_of_loc (loc) in
+ if List.length k > 0 then
+ goal,true
+ else
+ goal,false
+ in
+
+ *)
+(*
+ let goals = filter_open g1 in
+ let (loc::tl) = goals in
+ let goal = goal_of_loc (loc) in
+ if tag1 == `BranchTag then
+ if List.length (shift_goals s) > 0 then (* must simply shift *)
+ (
+ prerr_endline (pp status#stack);
+ prerr_endline "Head goals:";
+ List.map (fun goal -> prerr_endline (string_of_int goal)) (head_goals status#stack);
+ prerr_endline "Shift goals:";
+ List.map (fun goal -> prerr_endline (string_of_int goal)) (shift_goals status#stack);
+ prerr_endline "Open goals:";
+ List.map (fun goal -> prerr_endline (string_of_int goal)) (open_goals status#stack);
+ if tag2 == `BranchTag && g2 <> [] then
+ goal,true,false,false
+ else if tag2 == `BranchTag then
+ goal,false,true,true
+ else
+ goal,false,true,false
+ )
+ else
+ (
+ if tag2 == `BranchTag then
+ goal,false,true,true
+ else
+ goal,false,true,false
+ )
+ else
+ goal,false,false,false (* It's a strange situation, there's is an underlying level on the
+ stack but the current one was not created by a branch? Should be
+ an error *)
+ | (g, _, _, tag) :: [] ->
+ let (loc::tl) = filter_open g in
+ let goal = goal_of_loc (loc) in
+ if tag == `BranchTag then
+(* let goals = filter_open g in *)
+ goal,false,true,false
+ else
+ goal,false,false,false
+ in
+ *)
+ let l = [mk_just status goal just] in
+ let l =
+ if mustdot then List.append l [dot_tac] else l
+ in
+ (*
+ let l =
+ if mustmerge then List.append l [merge_tac] else l
+ in
+ let l =
+ if mustmergetwice then List.append l [merge_tac] else l
+ in
+ *)
+ block_tac l status
+(*
+ let (_,_,metasenv,subst,_) = status#obj in
+ let goal,last =
+ match metasenv with
+ | [] -> fail (lazy "There's nothing to prove")
+ | (_,_) :: (hd,_) :: tl -> hd,false
+ | (hd,_) :: tl -> hd,true
+ in
+ if last then
+ mk_just status goal just status
+ else
+ block_tac [ mk_just status goal just; shift_tac ] status
+*)
+;;
+
+let we_need_to_prove t id t1 status =
+ let goal = extract_first_goal_from_status status in
+ match id with
+ | None ->
+ (
+ match t1 with
+ | None -> (* We need to prove t *)
+ (
+ try assert_tac t None status goal (id_tac status)
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ )
+ | Some t1 -> (* We need to prove t or equivalently t1 *)
+ (
+ try assert_tac t (Some t1) status goal (change_tac ~where:("",0,(None,[],Some
+ Ast.UserInput)) ~with_what:t1 status)
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ )
+ | Some id ->
+ (
+ match t1 with
+ (* We need to prove t (id) *)
+ | None -> block_tac [cut_tac t; branch_tac; shift_tac; intro_tac id; merge_tac;
+ dot_tac
+ ] status
+ (* We need to prove t (id) or equivalently t1 *)
+ | Some t1 -> block_tac [cut_tac t; branch_tac ; change_tac ~where:("",0,(None,[],Some
+ Ast.UserInput))
+ ~with_what:t1; shift_tac; intro_tac id; merge_tac;
+ dot_tac
+ ]
+ status
+ )
+;;
+
+let by_just_we_proved just ty id ty' status =
+ let goal = extract_first_goal_from_status status in
+ let wrappedjust = just in
+ let just = mk_just status goal just in
+ match id with
+ | None ->
+ (match ty' with
+ | None -> (* just we proved P done *)
+ (
+ try
+ assert_tac ty None status goal (bydone wrappedjust status)
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ | Some ty' -> (* just we proved P that is equivalent to P' done *)
+ (
+ try
+ assert_tac ty' None status goal (block_tac [change_tac ~where:("",0,(None,[],Some
+ Ast.UserInput))
+ ~with_what:ty; bydone wrappedjust]
+ status )
+ with
+ | FirstTypeWrong -> fail (lazy "The second proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ )
+ | Some id ->
+ (
+ match ty' with
+ | None -> block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac id; merge_tac ] status
+ | Some ty' -> block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac id; change_tac
+ ~where:("",0,(None,[id,Ast.UserInput],None)) ~with_what:ty';
+ merge_tac] status
+ )
+;;
+
+let existselim just id1 t1 t2 id2 (*status*) =
+ distribute_tac (fun status goal ->
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just status goal just in
+ exec (block_tac [
+ cut_tac ("",0,(Ast.Appl [Ast.Ident ("ex",None); t1; Ast.Binder (`Lambda,(Ast.Ident
+ (id1,None), Some t1),t2)]));
+ branch_tac ~force:false;
+ just;
+ shift_tac;
+ case1_tac "_";
+ intros_tac ~names_ref:(ref []) [id1;id2];
+ merge_tac
+ ]) status goal
+ )
+;;
+
+let andelim just t1 id1 t2 id2 (*status*) =
+(* let goal = extract_first_goal_from_status status in *)
+ distribute_tac (fun status goal ->
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just status goal just in
+ exec (block_tac [
+ cut_tac ("",0,(Ast.Appl [Ast.Ident ("And",None); t1 ; t2]));
+ branch_tac ~force:false;
+ just;
+ shift_tac;
+ case1_tac "_";
+ intros_tac ~names_ref:(ref []) [id1;id2];
+ merge_tac
+ ]) status goal
+ )
+;;
+
+let type_of_tactic_term status ctx t =
+ let status,cicterm = disambiguate status ctx t `XTNone in
+ let (_,cicty) = typeof status ctx cicterm in
+ cicty
+
+let swap_first_two_goals_tac status =
+ let gstatus =
+ match status#stack with
+ | [] -> assert false
+ | (g,t,k,tag) :: s ->
+ match g with
+ | (loc1) :: (loc2) :: tl ->
+ ([loc2;loc1] @+ tl,t,k,tag) :: s
+ | _ -> assert false
+ in
+ status#set_stack gstatus
+
+let thesisbecomes t1 t2 = we_need_to_prove t1 None t2
+;;
+
+let obtain id t1 status =
+ let goal = extract_first_goal_from_status status in
+ let cicgty = get_goalty status goal in
+ let ctx = ctx_of cicgty in
+ let cicty = type_of_tactic_term status ctx t1 in
+ let _,ty = term_of_cic_term status cicty ctx in
+ let (_,_,t1) = t1 in
+ block_tac [ cut_tac ("",0,(Ast.Appl [Ast.Ident ("eq",None); Ast.NCic ty; t1; Ast.Implicit
+ `JustOne]));
+ swap_first_two_goals_tac;
+ branch_tac; shift_tac; shift_tac; intro_tac id; merge_tac; dot_tac;
+ ]
+ status
+;;
+
+let conclude t1 =
+ distribute_tac (fun status goal ->
+ let cicgty = get_goalty status goal in
+ let ctx = ctx_of cicgty in
+ let _,gty = term_of_cic_term status cicgty ctx in
+ match gty with
+ NCic.Appl [_;_;plhs;_] ->
+ if alpha_eq_tacterm_kerterm t1 plhs status goal then
+ exec id_tac status goal
+ else
+ fail (lazy "The given conclusion is different from the left-hand side of the current conclusion")
+ | _ -> fail (lazy "Your conclusion needs to be an equality")
+ )
+;;
+
+let rewritingstep rhs just last_step status =
+ let goal = extract_first_goal_from_status status in
+ let cicgty = get_goalty status goal in
+ let ctx = ctx_of cicgty in
+ let _,gty = term_of_cic_term status cicgty ctx in
+ let cicty = type_of_tactic_term status ctx rhs in
+ let _,ty = term_of_cic_term status cicty ctx in
+ let just' = (* Extraction of the ""justification"" from the ad hoc justification *)
+ match just with
+ `Auto (univ, params) ->
+ let params =
+ if not (List.mem_assoc "timeout" params) then
+ ("timeout","3")::params
+ else params
+ in
+ let params' =
+ if not (List.mem_assoc "paramodulation" params) then
+ ("paramodulation","1")::params
+ else params
+ in
+ if params = params' then NnAuto.auto_lowtac ~params:(univ, params) status goal
+ else
+ first_tac [NnAuto.auto_lowtac ~params:(univ, params) status goal; NnAuto.auto_lowtac
+ ~params:(univ, params') status goal]
+ | `Term just -> apply_tac just
+ | `SolveWith term -> NnAuto.demod_tac ~params:(Some [term], ["all","1";"steps","1"; "use_ctx","false"])
+ | `Proof -> id_tac
+ in
+ let plhs,prhs,prepare =
+ match gty with (* Extracting the lhs and rhs of the previous equality *)
+ NCic.Appl [_;_;plhs;prhs] -> plhs,prhs,(fun continuation -> continuation status)
+ | _ -> fail (lazy "You are not building an equaility chain")
+ in
+ let continuation =
+ if last_step then
+ (*CSC:manca controllo sul fatto che rhs sia convertibile con prhs*)
+ let todo = [just'] in
+ let todo = if mustdot status then List.append todo [dot_tac] else todo
+ in
+ block_tac todo
+ else
+ let (_,_,rhs) = rhs in
+ block_tac [apply_tac ("",0,Ast.Appl [Ast.Ident ("trans_eq",None); Ast.NCic ty; Ast.NCic plhs;
+ rhs; Ast.NCic prhs]); branch_tac; just'; merge_tac]
+ in
+ prepare continuation
+;;
+
+(*
+ let goal = extract_first_goal_from_status status in
+ let cicgty = get_goalty status goal in
+ let ctx = ctx_of cicgty in
+ let _,gty = term_of_cic_term status cicgty ctx in
+ let cicty = type_of_tactic_term status ctx rhs in
+ let _,ty = term_of_cic_term status cicty ctx in
+ let just' = (* Extraction of the ""justification"" from the ad hoc justification *)
+ match just with
+ `Auto (univ, params) ->
+ let params =
+ if not (List.mem_assoc "timeout" params) then
+ ("timeout","3")::params
+ else params
+ in
+ let params' =
+ if not (List.mem_assoc "paramodulation" params) then
+ ("paramodulation","1")::params
+ else params
+ in
+ if params = params' then NnAuto.auto_lowtac ~params:(univ, params) status goal
+ else
+ first_tac [NnAuto.auto_lowtac ~params:(univ, params) status goal; NnAuto.auto_lowtac
+ ~params:(univ, params') status goal]
+ | `Term just -> apply_tac just
+ | `SolveWith term -> NnAuto.demod_tac ~params:(Some [term], ["all","1";"steps","1"; "use_ctx","false"])
+ | `Proof -> id_tac
+ in
+ let plhs,prhs,prepare =
+ match lhs with
+ None -> (* = E2 *)
+ let plhs,prhs =
+ match gty with (* Extracting the lhs and rhs of the previous equality *)
+ NCic.Appl [_;_;plhs;prhs] -> plhs,prhs
+ | _ -> fail (lazy "You are not building an equaility chain")
+ in
+ plhs,prhs,
+ (fun continuation -> continuation status)
+ | Some (None,lhs) -> (* conclude *)
+ let plhs,prhs =
+ match gty with
+ NCic.Appl [_;_;plhs;prhs] -> plhs,prhs
+ | _ -> fail (lazy "You are not building an equaility chain")
+ in
+ (*TODO*)
+ (*CSC: manca check plhs convertibile con lhs *)
+ plhs,prhs,
+ (fun continuation -> continuation status)
+ | Some (Some name,lhs) -> (* obtain *)
+ NCic.Rel 1, NCic.Rel 1, (* continuation for this case is gonna be ignored, so it doesn't
+ matter what the values of these two are *)
+ (fun continuation ->
+ let (_,_,lhs) = lhs in
+ block_tac [ cut_tac ("",0,(Ast.Appl [Ast.Ident ("eq",None); Ast.NCic ty; lhs; Ast.Implicit
+ `JustOne]));
+ swap_first_two_goals_tac;
+ branch_tac; shift_tac; shift_tac; intro_tac name; merge_tac; dot_tac;
+(*
+ change_tac ~where:("",0,(None,[],Some Ast.Appl[Ast.Implicit `JustOne;Ast.Implicit
+ `JustOne; Ast.UserInput; Ast.Implicit `JustOne]))
+ ~with_what:rhs
+*)
+ ]
+ status
+ )
+ in
+ let continuation =
+ if last_step then
+ (*CSC:manca controllo sul fatto che rhs sia convertibile con prhs*)
+ let todo = [just'] in
+ let todo = if mustdot status then List.append todo [dot_tac] else todo
+ in
+ block_tac todo
+ else
+ let (_,_,rhs) = rhs in
+ block_tac [apply_tac ("",0,Ast.Appl [Ast.Ident ("trans_eq",None); Ast.NCic ty; Ast.NCic plhs;
+ rhs; Ast.NCic prhs]); branch_tac; just'; merge_tac]
+ in
+ prepare continuation
+;;
+ *)
+
+let we_proceed_by_cases_on t1 t2 status =
+ let goal = extract_first_goal_from_status status in
+ try
+ assert_tac t2 None status goal (block_tac [cases_tac ~what:t1 ~where:("",0,(None,[],Some
+ Ast.UserInput));
+ dot_tac] status)
+ with
+ | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
+
+let we_proceed_by_induction_on t1 t2 status =
+ let goal = extract_first_goal_from_status status in
+ try
+ assert_tac t2 None status goal (block_tac [elim_tac ~what:t1 ~where:("",0,(None,[],Some
+ Ast.UserInput));
+ dot_tac] status)
+ with
+ | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
+;;
+
+let byinduction t1 id = suppose t1 id None ;;
+
+let case id l =
+ distribute_tac (fun status goal ->
+ let rec aux l =
+ match l with
+ [] -> [id_tac]
+ | (id,ty)::tl ->
+ (try_tac (assume id ("",0,ty) None)) :: (aux tl)
+ in
+(* if l == [] then exec (try_tac (intro_tac "H")) status goal *)
+(* else *)
+ exec (block_tac (aux l)) status goal
+ )
+;;
-let assume name ty =
- exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (name,None),Some ty),Ast.Implicit `JustOne)))
+let print_stack status = prerr_endline ("PRINT STACK: " ^ (pp status#stack)); id_tac status ;;
-let suppose t id t1 =
- let t1 = match t1 with None -> t | Some t1 -> t1 in
- exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit `JustOne)))
+(* vim: ts=2: sw=0: et:
+ * *)
projects / helm.git / blobdiff