-type binder_type =
- Declaration
- | Definition
-;;
+(* Copyright (C) 2000, 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/.
+ *)
-type metas_context = (int * Cic.term) list;;
+open ProofEngineHelpers
+open ProofEngineTypes
-type context = (binder_type * Cic.name * Cic.term) list;;
+ (* proof assistant status *)
-type sequent = context * Cic.term;;
+let proof = ref (None : proof option)
+let goal = ref (None : goal option)
-let proof = ref (None : (metas_context * Cic.term * Cic.term) option);;
-(*CSC: Quando facciamo Clear di una ipotesi, cosa succede? *)
-(* Note: the sequent is redundant: it can be computed from the type of the *)
-(* metavariable and its context in the proof. We keep it just for efficiency *)
-(* because computing the context of a term may be quite expensive. *)
-let goal = ref (None : (int * sequent) option);;
-
-exception NotImplemented
-
-(*CSC: Funzione che deve sparire!!! *)
-let cic_context_of_context =
- List.map
- (function
- Declaration,_,t -> t
- | Definition,_,_ -> raise NotImplemented
- )
-;;
-
-let refine_meta meta term newmetasenv =
- let (metasenv,bo,ty) =
- match !proof with
- None -> assert false
- | Some (metasenv,bo,ty) -> metasenv,bo,ty
- in
- let metasenv' = newmetasenv @ (List.remove_assoc meta metasenv) in
- let bo' =
- let rec aux =
- let module C = Cic in
- function
- C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta meta' when meta=meta' -> term
- | C.Meta _ as t -> t
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- aux bo
- in
- proof := Some (metasenv',bo',ty)
-;;
-
-let new_meta () =
- let metasenv =
- match !proof with
- None -> assert false
- | Some (metasenv,_,_) -> metasenv
- in
- let rec aux =
- function
- None,[] -> 1
- | Some n,[] -> n
- | None,(n,_)::tl -> aux (Some n,tl)
- | Some m,(n,_)::tl -> if n > m then aux (Some n,tl) else aux (Some m,tl)
- in
- 1 + aux (None,metasenv)
-;;
+let apply_tactic ~tactic:tactic =
+ match !proof,!goal with
+ None,_
+ | _,None -> assert false
+ | Some proof', Some goal' ->
+ let (newproof, newgoals) = tactic ~status:(proof', goal') in
+ proof := Some newproof;
+ goal :=
+ (match newgoals, newproof with
+ goal::_, _ -> Some goal
+ | [], (_,(goal,_,_)::_,_,_) ->
+ (* the tactic left no open goal ; let's choose the first open goal *)
+(*CSC: here we could implement and use a proof-tree like notion... *)
+ Some goal
+ | _, _ -> None)
(* metas_in_term term *)
(* Returns the ordered list of the metas that occur in [term]. *)
function
C.Rel _
| C.Var _ -> []
- | C.Meta n -> [n]
+ | C.Meta (n,_) -> [n]
| C.Sort _
| C.Implicit -> []
| C.Cast (te,ty) -> (aux te) @ (aux ty)
| C.LetIn (_,s,t) -> (aux s) @ (aux t)
| C.Appl l -> List.fold_left (fun i t -> i @ (aux t)) [] l
| C.Const _
- | C.Abst _
| C.MutInd _
| C.MutConstruct _ -> []
| C.MutCase (sp,cookingsno,i,outt,t,pl) ->
he::(elim_duplicates (List.filter (function el -> he <> el) tl))
in
elim_duplicates metas
-;;
(* perforate context term ty *)
(* replaces the term [term] in the proof with a new metavariable whose type *)
(* are efficiency reasons. *)
let perforate context term ty =
let module C = Cic in
- let newmeta = new_meta () in
- match !proof with
- None -> assert false
- | Some (metasenv,bo,gty) ->
+ match !proof with
+ None -> assert false
+ | Some (uri,metasenv,bo,gty as proof') ->
+ let newmeta = new_meta proof' in
(* We push the new meta at the end of the list for pretty-printing *)
(* purposes: in this way metas are ordered. *)
- let metasenv' = metasenv@[newmeta,ty] in
- let rec aux =
- function
- (* Is == strong enough? *)
- t when t == term -> C.Meta newmeta
- | C.Rel _ as t -> t
- | C.Var _ as t -> t
- | C.Meta _ as t -> t
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (aux te, aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t)
- | C.Appl l -> C.Appl (List.map aux l)
- | C.Const _ as t -> t
- | C.Abst _ as t -> t
- | C.MutInd _ as t -> t
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux outt, aux t,
- List.map aux pl)
- | C.Fix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux ty, aux bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux ty, aux bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- let bo' = aux bo in
+ let metasenv' = metasenv@[newmeta,context,ty] in
+ let irl = identity_relocation_list_for_metavariable context in
+(*CSC: Bug: se ci sono due term uguali nella prova dovrei bucarne uno solo!!!*)
+ let bo' =
+ ProofEngineReduction.replace (==) term (C.Meta (newmeta,irl)) bo
+ in
(* It may be possible that some metavariables occurred only in *)
(* the term we are perforating and they now occurs no more. We *)
(* get rid of them, collecting the really useful metavariables *)
(* in metasenv''. *)
+(*CSC: Bug: una meta potrebbe non comparire in bo', ma comparire nel tipo *)
+(*CSC: di una metavariabile che compare in bo'!!!!!!! *)
let newmetas = metas_in_term bo' in
let metasenv'' =
- List.filter (function (n,_) -> List.mem n newmetas) metasenv'
+ List.filter (function (n,_,_) -> List.mem n newmetas) metasenv'
in
- proof := Some (metasenv'',bo',gty) ;
- goal := Some (newmeta,(context,ty)) ;
- newmeta
-;;
+ proof := Some (uri,metasenv'',bo',gty) ;
+ goal := Some newmeta
+
(************************************************************)
(* Some easy tactics. *)
(************************************************************)
-exception Fail of string;;
+(*CSC: generatore di nomi? Chiedere il nome? *)
+let fresh_name =
+ let next_fresh_index = ref 0
+in
+ function () ->
+ incr next_fresh_index ;
+ "fresh_name" ^ string_of_int !next_fresh_index
-let intros () =
- let module C = Cic in
- let module R = CicReduction in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (metasenv,_,_) -> metasenv
- in
- let (metano,context,ty) =
- match !goal with
- None -> assert false
- | Some (metano,(context,ty)) -> metano,context,ty
- in
- let newmeta = new_meta () in
- let rec collect_context =
- function
- C.Cast (te,_) -> collect_context te
- | C.Prod (n,s,t) ->
- let (ctx,ty,bo) = collect_context t in
- ((Declaration,n,s)::ctx,ty,C.Lambda(n,s,bo))
- | C.LetIn (n,s,t) ->
- let (ctx,ty,bo) = collect_context t in
- ((Definition,n,s)::ctx,ty,C.LetIn(n,s,bo))
- | _ as t -> [], t, (C.Meta newmeta)
+let reduction_tactic reduction_function term =
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ (* We don't know if [term] is a subterm of [ty] or a subterm of *)
+ (* the type of one metavariable. So we replace it everywhere. *)
+ (*CSC: Il vero problema e' che non sapendo dove sia il term non *)
+ (*CSC: sappiamo neppure quale sia il suo contesto!!!! Insomma, *)
+ (*CSC: e' meglio prima cercare il termine e scoprirne il *)
+ (*CSC: contesto, poi ridurre e infine rimpiazzare. *)
+ let replace context where=
+(*CSC: Per il momento se la riduzione fallisce significa solamente che *)
+(*CSC: siamo nel contesto errato. Metto il try, ma che schifo!!!! *)
+(*CSC: Anche perche' cosi' catturo anche quelle del replace che non dovrei *)
+ try
+ let term' = reduction_function context term in
+ ProofEngineReduction.replace ~equality:(==) ~what:term ~with_what:term'
+ ~where:where
+ with
+ _ -> where
+ in
+ let ty' = replace context ty in
+ let context' =
+ List.fold_right
+ (fun entry context ->
+ match entry with
+ Some (name,Cic.Def t) ->
+ (Some (name,Cic.Def (replace context t)))::context
+ | Some (name,Cic.Decl t) ->
+ (Some (name,Cic.Decl (replace context t)))::context
+ | None -> None::context
+ ) context []
in
- let revcontext',ty',bo' = collect_context ty in
- let context'' = (List.rev revcontext') @ context in
- refine_meta metano bo' [newmeta,ty'] ;
- goal := Some (newmeta,(context'',ty'))
-;;
+ let metasenv' =
+ List.map
+ (function
+ (n,_,_) when n = metano -> (metano,context',ty')
+ | _ as t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty) ;
+ goal := Some metano
-(* The term bo must be closed in the current context *)
-let exact bo =
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (metasenv,_,_) -> metasenv
- in
- let (metano,context,ty) =
- match !goal with
- None -> assert false
- | Some (metano,(context,ty)) ->
- assert (ty = List.assoc metano metasenv) ;
- (* Invariant: context is the actual context of the meta in the proof *)
- metano,context,ty
- in
- (*CSC: deve sparire! *)
- let context = cic_context_of_context context in
- if R.are_convertible (T.type_of_aux' metasenv context bo) ty then
- refine_meta metano bo []
- else
- raise (Fail "The type of the provided term is not the one expected.")
-;;
+(* Reduces [term] using [reduction_function] in the current scratch goal [ty] *)
+let reduction_tactic_in_scratch reduction_function term ty =
+ let metasenv =
+ match !proof with
+ None -> []
+ | Some (_,metasenv,_,_) -> metasenv
+ in
+ let metano,context,_ =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let term' = reduction_function context term in
+ ProofEngineReduction.replace
+ ~equality:(==) ~what:term ~with_what:term' ~where:ty
+
+let whd = reduction_tactic CicReduction.whd
+let reduce = reduction_tactic ProofEngineReduction.reduce
+let simpl = reduction_tactic ProofEngineReduction.simpl
+
+let whd_in_scratch = reduction_tactic_in_scratch CicReduction.whd
+let reduce_in_scratch =
+ reduction_tactic_in_scratch ProofEngineReduction.reduce
+let simpl_in_scratch =
+ reduction_tactic_in_scratch ProofEngineReduction.simpl
+
+(* It is just the opposite of whd. The code should probably be merged. *)
+let fold term =
+ let curi,metasenv,pbo,pty =
+ match !proof with
+ None -> assert false
+ | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
+ in
+ let metano,context,ty =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let term' = CicReduction.whd context term in
+ (* We don't know if [term] is a subterm of [ty] or a subterm of *)
+ (* the type of one metavariable. So we replace it everywhere. *)
+ (*CSC: ma si potrebbe ovviare al problema. Ma non credo *)
+ (*CSC: che si guadagni nulla in fatto di efficienza. *)
+ let replace =
+ ProofEngineReduction.replace
+ ~equality:
+ (ProofEngineReduction.syntactic_equality ~alpha_equivalence:false)
+ ~what:term' ~with_what:term
+ in
+ let ty' = replace ty in
+ let context' =
+ List.map
+ (function
+ Some (n,Cic.Decl t) -> Some (n,Cic.Decl (replace t))
+ | Some (n,Cic.Def t) -> Some (n,Cic.Def (replace t))
+ | None -> None
+ ) context
+ in
+ let metasenv' =
+ List.map
+ (function
+ (n,_,_) when n = metano -> (metano,context',ty')
+ | _ as t -> t
+ ) metasenv
+ in
+ proof := Some (curi,metasenv',pbo,pty) ;
+ goal := Some metano
+
+(************************************************************)
+(* Tactics defined elsewhere *)
+(************************************************************)
+
+ (* primitive tactics *)
+
+let apply term = apply_tactic (PrimitiveTactics.apply_tac ~term)
+let intros () =
+ apply_tactic (PrimitiveTactics.intros_tac ~name:(fresh_name ()))
+let cut term = apply_tactic (PrimitiveTactics.cut_tac ~term)
+let letin term = apply_tactic (PrimitiveTactics.letin_tac ~term)
+let exact term = apply_tactic (PrimitiveTactics.exact_tac ~term)
+let elim_intros_simpl term =
+ apply_tactic (PrimitiveTactics.elim_intros_simpl_tac ~term)
+let change ~goal_input:what ~input:with_what =
+ apply_tactic (PrimitiveTactics.change_tac ~what ~with_what)
+
+ (* structural tactics *)
+
+let clearbody hyp = apply_tactic (ProofEngineStructuralRules.clearbody ~hyp)
+let clear hyp = apply_tactic (ProofEngineStructuralRules.clear ~hyp)
+
+ (* other tactics *)
+
+let elim_type term = apply_tactic (Ring.elim_type_tac ~term)
+let ring () = apply_tactic Ring.ring_tac
+let fourier () = apply_tactic FourierR.fourier_tac
+let rewrite_simpl term = apply_tactic (FourierR.rewrite_simpl_tac ~term)
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