(* 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 =
- function
- `Auto (l,params) -> distribute_tac (fun status goal -> NnAuto.auto_lowtac
- ~params:(l,params) status goal)
- | `Term t -> apply_tac t
+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
+ match goals with
+ [] -> fail (lazy "No goals under focus")
+ | loc::_tl ->
+ let goal = goal_of_loc (loc) in
+ goal ;;
+
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 gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ term_of_cic_term status gty ctx
;;
-let same_type_as_conclusion 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 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
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,cicterm1 = disambiguate status ctx ty1 `XTNone in
+ let status,cicterm2 = disambiguate status ctx ty2 `XTNone in
+ NTacStatus.are_convertible status ctx cicterm1 cicterm2
+
+let clear_volatile_params_tac status =
+ match status#stack with
+ [] -> fail (lazy "Empty stack")
+ | (g,t,k,tag,p)::tl ->
+ let rec remove_volatile = function
+ [] -> []
+ | (k,_v as hd')::tl' ->
+ let re = Str.regexp "volatile_.*" in
+ if Str.string_match re k 0 then
+ remove_volatile tl'
+ else
+ hd'::(remove_volatile tl')
+ in
+ let newp = remove_volatile p in
+ status#set_stack ((g,t,k,tag,newp)::tl)
+;;
+
+let add_parameter_tac key value status =
+ match status#stack with
+ [] -> status
+ | (g,t,k,tag,p) :: tl -> status#set_stack ((g,t,k,tag,(key,value)::p)::tl)
+;;
+
(* 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. ?
+ 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 same_type_as_conclusion t1 t status goal then
- match t2 with
- | None ->
- let (_,_,t1) = t1 in
- exec (exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit
- `JustOne)))) status goal
-
- | Some t2 ->
- let status,res = are_convertible t1 t2 status goal in
- if res then
- let (_,_,t2) = t2 in
- exec (exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t2),Ast.Implicit
- `JustOne)))) status goal
- else
- raise NotEquivalentTypes
- else
- raise FirstTypeWrong
- | _ -> raise NotAProduct
-
-let assume name ty eqty =
- distribute_tac (fun status goal ->
- try lambda_abstract_tac name ty eqty 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 lambda_abstract_tac id t1 status goal =
+ match extract_conclusion_type status goal with
+ | status,NCic.Prod (_,t,_) ->
+ if alpha_eq_tacterm_kerterm t1 t status goal then
+ let (_,_,t1) = t1 in
+ block_tac [exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit
+ `JustOne))); clear_volatile_params_tac;
+ add_parameter_tac "volatile_newhypo" id] status
+ else
+ raise FirstTypeWrong
+ | _ -> raise NotAProduct
+
+let assume name ty status =
+ let goal = extract_first_goal_from_status status in
+ try lambda_abstract_tac name ty 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 =
- distribute_tac (fun status goal ->
- try lambda_abstract_tac id t1 t2 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 suppose t1 id status =
+ let goal = extract_first_goal_from_status status in
+ try lambda_abstract_tac id t1 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 same_type_as_conclusion t1 t status goal then
- match t2 with
- | None -> exec continuation status goal
- | Some t2 ->
- let status,res = are_convertible t1 t2 status goal in
- if res then
- exec continuation status goal
- else
- raise NotEquivalentTypes
+ let status,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 branch_dot_tac status =
+ match status#stack with
+ ([],t,k,tag,p) :: tl ->
+ if List.length t > 0 then
+ status#set_stack (([List.hd t],List.tl t,k,tag,p)::tl)
else
- raise FirstTypeWrong
-
-let we_need_to_prove t id t1 =
- distribute_tac (fun status goal ->
- match id with
- | None ->
- (
- match t1 with
- | None -> (* We need to prove t *)
- (
- try
- assert_tac t None status goal id_tac
- 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)
- 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
- | None -> (* We need to prove t (id) *)
- exec (block_tac [cut_tac t; branch_tac ~force:false; shift_tac; intro_tac id;
- (*merge_tac*)]) status goal
- | Some t1 -> (* We need to prove t (id) or equivalently t1 *)
- exec (block_tac [cut_tac t; branch_tac ~force:false; change_tac ~where:("",0,(None,[],Some Ast.UserInput))
- ~with_what:t1; shift_tac; intro_tac id; merge_tac]) status goal
- )
+ status
+ | _ -> status
+;;
+
+let status_parameter key status =
+ match status#stack with
+ [] -> ""
+ | (_g,_t,_k,_tag,p)::_ -> try List.assoc key p with _ -> ""
+;;
+
+let beta_rewriting_step t status =
+ let ctx = status_parameter "volatile_context" status in
+ if ctx <> "beta_rewrite" then
+ (
+ let newhypo = status_parameter "volatile_newhypo" status in
+ if newhypo = "" then
+ fail (lazy "Invalid use of 'that is equivalent to'")
+ else
+ change_tac ~where:("",0,(None,[newhypo,Ast.UserInput],None)) ~with_what:t status
+ )
+ else
+ change_tac ~where:("",0,(None,[],Some
+ Ast.UserInput)) ~with_what:t status
+;;
+
+let done_continuation status =
+ let rec continuation l =
+ match l with
+ [] -> []
+ | (_,t,_,tag,p)::tl ->
+ if tag = `BranchTag then
+ if List.length t > 0 then
+ let continue =
+ let ctx =
+ try List.assoc "context" p
+ with Not_found -> ""
+ in
+ ctx <> "induction" && ctx <> "cases"
+ in
+ if continue then [clear_volatile_params_tac;branch_dot_tac] else
+ [clear_volatile_params_tac]
+ else
+ [merge_tac] @ (continuation tl)
+ else
+ []
+ in
+ continuation status#stack
+;;
+
+let bydone just status =
+ let goal = extract_first_goal_from_status status in
+ let continuation = done_continuation status in
+ let l = [mk_just status goal just] @ continuation in
+ block_tac l status
+;;
+
+let push_goals_tac status =
+ match status#stack with
+ [] -> fail (lazy "Error pushing goals")
+ | (g1,t1,k1,tag1,p1) :: (g2,t2,k2,tag2,p2) :: tl ->
+ if List.length g2 > 0 then
+ status#set_stack ((g1,t1 @+ g2,k1,tag1,p1) :: ([],t2,k2,tag2,p2) :: tl)
+ else status (* Nothing to push *)
+ | _ -> status
+
+let we_need_to_prove t id status =
+ let goal = extract_first_goal_from_status status in
+ match id with
+ | None ->
+ (
+ try assert_tac t None status goal (add_parameter_tac "volatile_context" "beta_rewrite" status)
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ )
+ | Some id ->
+ (
+ block_tac [clear_volatile_params_tac; cut_tac t; branch_tac; shift_tac; intro_tac id; merge_tac; branch_tac;
+ push_goals_tac; add_parameter_tac "volatile_context" "beta_rewrite"
+ ] status
)
;;
-let by_just_we_proved just ty id ty' =
- distribute_tac (fun status goal ->
- let just = mk_just just in
- match id with
- | None ->
- (match ty' with
- | None -> (* just we proved P done *)
- (
- try
- assert_tac ty None status goal just
- 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' (Some ty) status goal (block_tac [change_tac
- ~where:("",0,(None,[],Some Ast.UserInput)) ~with_what:ty; just])
- 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 -> exec (block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac
- id; merge_tac ]) status goal
- | Some ty' -> exec (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 goal
- )
+let by_just_we_proved just ty id status =
+ let goal = extract_first_goal_from_status status in
+ let just = mk_just status goal just in
+ match id with
+ | None ->
+ assert_tac ty None status goal (block_tac [clear_volatile_params_tac; add_parameter_tac
+ "volatile_context" "beta_rewrite"] status)
+ | Some id ->
+ (
+ block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac id; merge_tac;
+ clear_volatile_params_tac; add_parameter_tac "volatile_newhypo" id] status
)
;;
-let thesisbecomes t1 t2 = we_need_to_prove t1 None t2 ;;
+let existselim just id1 t1 t2 id2 status =
+ let goal = extract_first_goal_from_status status in
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just status goal just in
+ (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;
+ clear_volatile_params_tac
+ ]) status
+;;
-let bydone just =
- mk_just just
+let andelim just t1 id1 t2 id2 status =
+ let goal = extract_first_goal_from_status status in
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just status goal just in
+ (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;
+ clear_volatile_params_tac
+ ]) status
;;
-let existselim just id1 t1 t2 id2 =
- let (_,_,t1) = t1 in
- let (_,_,t2) = t2 in
- let just = mk_just just in
- 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
- ]
-
-let andelim just t1 id1 t2 id2 =
- let (_,_,t1) = t1 in
- let (_,_,t2) = t2 in
- let just = mk_just just in
- 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
- ]
+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,p) :: s ->
+ match g with
+ | (loc1) :: (loc2) :: tl ->
+ ([loc2;loc1] @+ tl,t,k,tag,p) :: s
+ | _ -> assert false
+ in
+ status#set_stack gstatus
+
+let thesisbecomes t1 = we_need_to_prove t1 None
;;
+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; branch_tac; push_goals_tac;
+ add_parameter_tac "volatile_context" "rewrite"
+ ]
+ status
+;;
+let conclude 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 _,gty = term_of_cic_term status cicgty ctx in
+ match gty with
+ (* The first term of this Appl should probably be "eq" *)
+ NCic.Appl [_;_;plhs;_] ->
+ if alpha_eq_tacterm_kerterm t1 plhs status goal then
+ add_parameter_tac "volatile_context" "rewrite" status
+ 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 lhs rhs just last_step = fail (lazy "Not implemented");
- (*
- let aux ((proof,goal) as status) =
- let (curi,metasenv,_subst,proofbo,proofty, attrs) = proof in
- let _,context,gty = CicUtil.lookup_meta goal metasenv in
- let eq,trans =
- match LibraryObjects.eq_URI () with
- None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
- | Some uri ->
- Cic.MutInd (uri,0,[]), Cic.Const (LibraryObjects.trans_eq_URI ~eq:uri,[])
+let rewritingstep rhs just last_step status =
+ let ctx = status_parameter "volatile_context" status in
+ if ctx = "rewrite" then
+ (
+ 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
+ let todo = [just'] @ (done_continuation status) 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
+ )
+ else
+ fail (lazy "You are not building an equality chain")
+;;
+
+let rec pp_metasenv_names (metasenv:NCic.metasenv) =
+ match metasenv with
+ [] -> ""
+ | hd :: tl ->
+ let n,conj = hd in
+ let meta_attrs,_,_ = conj in
+ let rec find_name_aux meta_attrs = match meta_attrs with
+ [] -> "Anonymous"
+ | hd :: tl -> match hd with
+ `Name n -> n
+ | _ -> find_name_aux tl
+ in
+ let name = find_name_aux meta_attrs
+ in
+ "[Goal: " ^ (string_of_int n) ^ ", Name: " ^ name ^ "]; " ^ (pp_metasenv_names tl)
+;;
+
+let print_goals_names_tac s (status:#NTacStatus.tac_status) =
+ let (_,_,metasenv,_,_) = status#obj in
+ prerr_endline (s ^" -> Metasenv: " ^ (pp_metasenv_names metasenv)); status
+
+(* Useful as it does not change the order in the list *)
+let rec list_change_assoc k v = function
+ [] -> []
+ | (k',_v' as hd) :: tl -> if k' = k then (k',v) :: tl else hd :: (list_change_assoc k v tl)
+;;
+
+let add_names_to_goals_tac (cl:NCic.constructor list ref) (status:#NTacStatus.tac_status) =
+ let add_name_to_goal name goal metasenv =
+ let (mattrs,ctx,t) = try List.assoc goal metasenv with _ -> assert false in
+ let mattrs = (`Name name) :: (List.filter (function `Name _ -> false | _ -> true) mattrs) in
+ let newconj = (mattrs,ctx,t) in
+ list_change_assoc goal newconj metasenv
in
- let ty,_ =
- CicTypeChecker.type_of_aux' metasenv context rhs CicUniv.oblivion_ugraph in
- let just' =
- match just with
- `Auto (univ, params) ->
- let params =
- if not (List.exists (fun (k,_) -> k = "timeout") params) then
- ("timeout","3")::params
- else params
- in
- let params' =
- if not (List.exists (fun (k,_) -> k = "paramodulation") params) then
- ("paramodulation","1")::params
- else params
- in
- if params = params' then
- Tactics.auto ~dbd ~params:(univ, params) ~automation_cache
- else
- Tacticals.first
- [Tactics.auto ~dbd ~params:(univ, params) ~automation_cache ;
- Tactics.auto ~dbd ~params:(univ, params') ~automation_cache]
- | `Term just -> Tactics.apply just
- | `SolveWith term ->
- Tactics.demodulate ~automation_cache ~dbd
- ~params:(Some [term],
- ["all","1";"steps","1"; "use_context","false"])
- | `Proof ->
- Tacticals.id_tac
+ let new_goals =
+ (* It's important that this tactic is called before branching and right after the creation of
+ * the new goals, when they are still under focus *)
+ match status#stack with
+ [] -> fail (lazy "Can not add names to an empty stack")
+ | (g,_,_,_,_) :: _tl ->
+ let rec sublist n = function
+ [] -> []
+ | hd :: tl -> if n = 0 then [] else hd :: (sublist (n-1) tl)
+ in
+ List.map (fun _,sw -> goal_of_switch sw) (sublist (List.length !cl) g)
+ in
+ let rec add_names_to_goals g cl metasenv =
+ match g,cl with
+ [],[] -> metasenv
+ | hd::tl, (_,consname,_)::tl' ->
+ add_names_to_goals tl tl' (add_name_to_goal consname hd metasenv)
+ | _,_ -> fail (lazy "There are less goals than constructors")
in
- let plhs,prhs,prepare =
- match lhs with
- None ->
- let plhs,prhs =
- match gty with
- Cic.Appl [_;_;plhs;prhs] -> plhs,prhs
- | _ -> assert false
+ let (olduri,oldint,metasenv,oldsubst,oldkind) = status#obj in
+ let newmetasenv = add_names_to_goals new_goals !cl metasenv
+ in status#set_obj(olduri,oldint,newmetasenv,oldsubst,oldkind)
+;;
+(*
+ let (olduri,oldint,metasenv,oldsubst,oldkind) = status#obj in
+ let remove_name_from_metaattrs =
+ List.filter (function `Name _ -> false | _ -> true) in
+ let rec add_names_to_metasenv cl metasenv =
+ match cl,metasenv with
+ [],_ -> metasenv
+ | hd :: tl, mhd :: mtl ->
+ let _,consname,_ = hd in
+ let gnum,conj = mhd in
+ let mattrs,ctx,t = conj in
+ let mattrs = [`Name consname] @ (remove_name_from_metaattrs mattrs)
in
- plhs,prhs,
- (fun continuation ->
- ProofEngineTypes.apply_tactic continuation status)
- | Some (None,lhs) ->
- let plhs,prhs =
- match gty with
- Cic.Appl [_;_;plhs;prhs] -> plhs,prhs
- | _ -> assert false
+ let newconj = mattrs,ctx,t in
+ let newmeta = gnum,newconj in
+ newmeta :: (add_names_to_metasenv tl mtl)
+ | _,[] -> assert false
+ in
+ let newmetasenv = add_names_to_metasenv !cl metasenv in
+ status#set_obj (olduri,oldint,newmetasenv,oldsubst,oldkind)
+*)
+
+let unfocus_branch_tac status =
+ match status#stack with
+ [] -> status
+ | (g,t,k,tag,p) :: tl -> status#set_stack (([],g @+ t,k,tag,p)::tl)
+;;
+
+let we_proceed_by_induction_on t1 t2 status =
+ let goal = extract_first_goal_from_status status in
+ let txt,len,t1 = t1 in
+ let t1 = txt, len, Ast.Appl [t1; Ast.Implicit `Vector] in
+ let indtyinfo = ref None in
+ let sort = ref (NCic.Rel 1) in
+ let cl = ref [] in (* this is a ref on purpose, as the block of code after sort_of_goal_tac in
+ block_tac acts as a block of asynchronous code, in which cl gets modified with the info retrieved
+ with analize_indty_tac, and later used to label each new goal with a costructor name. Using a
+ plain list this doesn't seem to work, as add_names_to_goals_tac would immediately act on an empty
+ list, instead of acting on the list of constructors *)
+ try
+ assert_tac t2 None status goal (block_tac [
+ analyze_indty_tac ~what:t1 indtyinfo;
+ sort_of_goal_tac sort;
+ (fun status ->
+ let ity = HExtlib.unopt !indtyinfo in
+ let NReference.Ref (uri, _) = ref_of_indtyinfo ity in
+ let name =
+ NUri.name_of_uri uri ^ "_" ^
+ snd (NCicElim.ast_of_sort
+ (match !sort with NCic.Sort x -> x | _ -> assert false))
+ in
+ let eliminator =
+ let l = [Ast.Ident (name,None)] in
+ (* Generating an implicit for each argument of the inductive type, plus one the
+ * predicate, plus an implicit for each constructor of the inductive type *)
+ let l = l @ HExtlib.mk_list (Ast.Implicit `JustOne) (ity.leftno+1+ity.consno) in
+ let _,_,t1 = t1 in
+ let l = l @ [t1] in
+ Ast.Appl l
+ in
+ cl := ity.cl;
+ exact_tac ("",0,eliminator) status);
+ add_names_to_goals_tac cl;
+ branch_tac;
+ push_goals_tac;
+ unfocus_branch_tac;
+ add_parameter_tac "context" "induction"
+ ] status)
+ with
+ | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
+;;
+
+let we_proceed_by_cases_on ((txt,len,ast1) as t1) t2 status =
+ let goal = extract_first_goal_from_status status in
+ let npt1 = txt, len, Ast.Appl [ast1; Ast.Implicit `Vector] in
+ let indtyinfo = ref None in
+ let cl = ref [] in
+ try
+ assert_tac t2 None status goal (block_tac [
+ analyze_indty_tac ~what:npt1 indtyinfo;
+ cases_tac ~what:t1 ~where:("",0,(None,[],Some
+ Ast.UserInput));
+ (
+ fun status ->
+ let ity = HExtlib.unopt !indtyinfo in
+ cl := ity.cl; add_names_to_goals_tac cl status
+ );
+ branch_tac; push_goals_tac;
+ unfocus_branch_tac;
+ add_parameter_tac "context" "cases"
+ ] status)
+ with
+ | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
+;;
+
+let byinduction t1 id status =
+ let ctx = status_parameter "context" status in
+ if ctx <> "induction" then fail (lazy "You can't use this tactic outside of an induction context")
+ else suppose t1 id status
+;;
+
+let name_of_conj conj =
+ let mattrs,_,_ = conj in
+ let rec search_name mattrs =
+ match mattrs with
+ [] -> "Anonymous"
+ | hd::tl ->
+ match hd with
+ `Name n -> n
+ | _ -> search_name tl
+ in
+ search_name mattrs
+
+let rec loc_of_goal goal l =
+ match l with
+ [] -> fail (lazy "Reached the end")
+ | hd :: tl ->
+ let _,sw = hd in
+ let g = goal_of_switch sw in
+ if g = goal then hd
+ else loc_of_goal goal tl
+;;
+
+let has_focused_goal status =
+ match status#stack with
+ [] -> false
+ | ([],_,_,_,_) :: _tl -> false
+ | _ -> true
+;;
+
+let focus_on_case_tac case status =
+ let (_,_,metasenv,_,_) = status#obj in
+ let rec goal_of_case case metasenv =
+ match metasenv with
+ [] -> fail (lazy "The given case does not exist")
+ | (goal,conj) :: tl ->
+ if name_of_conj conj = case then goal
+ else goal_of_case case tl
+ in
+ let goal_to_focus = goal_of_case case metasenv in
+ let gstatus =
+ match status#stack with
+ [] -> fail (lazy "There is nothing to prove")
+ | (g,t,k,tag,p) :: s ->
+ let loc =
+ try
+ loc_of_goal goal_to_focus t
+ with _ -> fail (lazy "The given case is not part of the current induction/cases analysis
+ context")
+ in
+ let curloc = if has_focused_goal status then
+ let goal = extract_first_goal_from_status status in
+ [loc_of_goal goal g]
+ else []
+ in
+ (((g @- curloc) @+ [loc]),(curloc @+ (t @- [loc])),k,tag,p) :: s
+ in
+ status#set_stack gstatus
+;;
+
+let case id l status =
+ let ctx = status_parameter "context" status in
+ if ctx <> "induction" && ctx <> "cases" then fail (lazy "You can't use case outside of an
+ induction/cases analysis context")
+else
+ (
+ if has_focused_goal status then fail (lazy "Finish the current case before switching")
+ else
+ (
+(*
+ let goal = extract_first_goal_from_status status in
+ let (_,_,metasenv,_,_) = status#obj in
+ let conj = NCicUtils.lookup_meta goal metasenv in
+ let name = name_of_conj conj in
+*)
+ let continuation =
+ let rec aux l =
+ match l with
+ [] -> [id_tac]
+ | (id,ty)::tl ->
+ (try_tac (assume id ("",0,ty))) :: (aux tl)
+ in
+ aux l
in
- (*CSC: manca check plhs convertibile con lhs *)
- plhs,prhs,
- (fun continuation ->
- ProofEngineTypes.apply_tactic continuation status)
- | Some (Some name,lhs) ->
- let newmeta = CicMkImplicit.new_meta metasenv [] in
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context in
- let plhs = lhs in
- let prhs = Cic.Meta(newmeta,irl) in
- plhs,prhs,
- (fun continuation ->
- let metasenv = (newmeta, context, ty)::metasenv in
- let mk_fresh_name_callback =
- fun metasenv context _ ~typ ->
- FreshNamesGenerator.mk_fresh_name ~subst:[] metasenv context
- (Cic.Name name) ~typ
- in
- let proof = curi,metasenv,_subst,proofbo,proofty, attrs in
- let proof,goals =
- ProofEngineTypes.apply_tactic
- (Tacticals.thens
- ~start:(Tactics.cut ~mk_fresh_name_callback
- (Cic.Appl [eq ; ty ; lhs ; prhs]))
- ~continuations:[Tacticals.id_tac ; continuation]) (proof,goal)
- in
- let goals =
- match just,goals with
- `Proof, [g1;g2;g3] -> [g2;g3;newmeta;g1]
- | _, [g1;g2] -> [g2;newmeta;g1]
- | _, l ->
- prerr_endline (String.concat "," (List.map string_of_int l));
- prerr_endline (CicMetaSubst.ppmetasenv [] metasenv);
- assert false
- in
- proof,goals)
- in
- let continuation =
- if last_step then
- (*CSC:manca controllo sul fatto che rhs sia convertibile con prhs*)
- just'
- else
- Tacticals.thens
- ~start:(Tactics.apply ~term:(Cic.Appl [trans;ty;plhs;rhs;prhs]))
- ~continuations:[just' ; Tacticals.id_tac]
- in
- prepare continuation
- in
- ProofEngineTypes.mk_tactic aux
+(* if name = id then block_tac continuation status *)
+(* else *)
+ block_tac ([focus_on_case_tac id] @ continuation) status
+ )
+ )
;;
- *)
+
+let print_stack status = prerr_endline ("PRINT STACK: " ^ (pp status#stack)); id_tac status ;;
+
+(* vim: ts=2: sw=0: et:
+ * *)
projects / helm.git / blobdiff