package lambdapi
Proof assistant for the λΠ-calculus modulo rewriting
Install
Dune Dependency
Authors
Maintainers
Sources
lambdapi-2.6.0.tbz
sha256=d01e5f13db2eaba6e4fe330667149e0059d4886c651ff9d6b672db2dfc9765ed
sha512=33b68c972aca37985ed73c527076198e7d4961c7e27c89cdabfe4d1cff97cd41ccfb85ae9499eb98ad9a0aefd920bc55555df6393fc441ac2429e4d99cddafa8
doc/src/lambdapi.tool/indexing.ml.html
Source file indexing.ml
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open Core open Term open Common open Pos type sym_name = Common.Path.t * string let name_of_sym s = (s.sym_path, s.sym_name) (* discrimination tree *) (* substitution trees would be best *) (* - all variables are indexed equally, ignoring the name - let-ins are expanded when indexed, but not when computing subterms to index - patterns (e.g. $x.[t1 .. tn]) are indexed as HOLES, ignoring the arguments t1 .. tn - we consider t1 ... tn as subterms when computing the subterms to index - flexible terms, i.e. applyed HOLES (i.e. applied patterns $x.[t1 .. tn]) are not indexed as subterms - when computing the subterms to index, when entering a product the bound variable is replaced with a pattern to simulate modus-ponens e.g. "pi x : T. x + x" has as subterm "$x + $x" *) module Pure = struct type 'a index = | Leaf of 'a list | Choice of 'a node list and 'a node = | IHOLE of 'a index | IRigid of rigid * 'a index and rigid = | IVar | IKind | IType | ISymb of sym_name | IAppl | IAbst | IProd type 'a db = 'a list Lplib.Extra.StrMap.t * 'a index let empty : 'a db = Lplib.Extra.StrMap.empty, Choice [] let rec node_of_stack t s v = match unfold t with | Kind -> IRigid(IKind, index_of_stack s v) | Type -> IRigid(IType, index_of_stack s v) | Vari _ -> IRigid(IVar, index_of_stack s v) | Symb sym -> IRigid(ISymb (name_of_sym sym), index_of_stack s v) | Appl(t1,t2) -> IRigid(IAppl, index_of_stack (t1::t2::s) v) | Abst(t1,bind) -> let _, t2 = Bindlib.unbind bind in IRigid(IAbst, index_of_stack (t1::t2::s) v) | Prod(t1,bind) -> let _, t2 = Bindlib.unbind bind in IRigid(IProd, index_of_stack (t1::t2::s) v) | Patt (_var,_varname,_args) -> IHOLE (index_of_stack s v) | LLet (_typ, bod, bind) -> (* Let-ins are expanded during indexing *) node_of_stack (Bindlib.subst bind bod) s v | Meta _ | Plac _ -> assert false (* not for meta-closed terms *) | Wild -> assert false (* used only by tactics and reduction *) | TRef _ -> assert false (* destroyed by unfold *) | TEnv _ (* used in rewriting rules RHS *) -> assert false (* use term_of_rhs *) and index_of_stack stack v = match stack with | [] -> Leaf [v] | t::s -> Choice [node_of_stack t s v] exception NoMatch (* match a rigid with a term, either raising NoMatch or returning the (ordered) list of immediate subterms of the term *) let rec match_rigid r term = match r,unfold term with | IKind, Kind -> [] | IType, Type -> [] | IVar, Vari _ -> [] | ISymb n, Symb sym when n = name_of_sym sym -> [] | IAppl, Appl(t1,t2) -> [t1;t2] | IAbst, Abst(t1,bind) -> let _, t2 = Bindlib.unbind bind in [t1;t2] | IProd, Prod(t1,bind) -> let _, t2 = Bindlib.unbind bind in [t1;t2] | _, LLet (_typ, bod, bind) -> match_rigid r (Bindlib.subst bind bod) | _, (Meta _ | Plac _ | Wild | TRef _ | TEnv _) -> assert false | _, _ -> raise NoMatch (* match anything with a flexible term *) let rec match_flexible = function IHOLE i -> [i] | IRigid(r,i) -> match r with | IVar | IKind | IType | ISymb _ -> [i] | IAppl | IAbst | IProd -> List.concat (List.map match_flexible_index (match_flexible_index i)) and match_flexible_index = function Leaf _ -> assert false (* ill-typed term *) | Choice nodes -> List.concat (List.map match_flexible nodes) let rec insert_index index stack v = match index,stack with | Leaf vs, [] -> Leaf(v::vs) | Choice l, t::s -> let rec aux = function | [] -> [node_of_stack t s v] | n::nl -> try insert_node n t s v :: nl with NoMatch -> n :: aux nl in Choice(aux l) | _, _ -> assert false (* ill-typed term *) and insert_node node term s v = match node,term with (* Patterns are holes, holes are patterns *) | IHOLE i, Patt _ -> IHOLE (insert_index i s v) | IRigid(r,i), t -> let s' = match_rigid r t in IRigid(r,insert_index i (s'@s) v) | _, _ -> raise NoMatch let insert (namemap,index) term v = namemap, insert_index index [term] v let insert_name (namemap,index) name v = let vs = match Lplib.Extra.StrMap.find_opt name namemap with None -> [] | Some l -> l in Lplib.Extra.StrMap.add name (v::vs) namemap, index let rec search_index ~generalize index stack = match index,stack with | Leaf vs, [] -> vs | Choice l, t::s -> List.fold_right (fun n res -> search_node ~generalize n t s @ res) l [] | _, _ -> assert false (* ill-typed term *) and search_node ~generalize node term s = match node,term with | _, Patt _ -> List.concat (List.map (fun i -> search_index ~generalize i s) (match_flexible node)) | IHOLE i, _ when generalize -> search_index ~generalize i s | IHOLE i, t -> search_node ~generalize (IRigid(IVar,i)) t s | IRigid(r,i), t -> match match_rigid r t with | s' -> search_index ~generalize i (s'@s) | exception NoMatch -> [] (* when [~generalize] is false, all holes in the index are matched only by variables, i.e. the pattern is not matched up to generalization *) let search ~generalize (_,index) term = search_index ~generalize index [term] let locate_name (namemap,_) name = match Lplib.Extra.StrMap.find_opt name namemap with None -> [] | Some l -> l let dump_to ~filename i = let ch = open_out_bin filename in Marshal.to_channel ch i [] ; close_out ch let restore_from ~filename = let ch = open_in_bin filename in let i = Marshal.from_channel ch in close_in ch ; i end module DB = struct (* fix codomain type *) type side = Parsing.SearchQuerySyntax.side = Lhs | Rhs type inside = Parsing.SearchQuerySyntax.inside = Exact | Inside type 'inside where = 'inside Parsing.SearchQuerySyntax.where = | Spine of 'inside | Conclusion of 'inside | Hypothesis of 'inside (* the "name" in the sym_name of rules is just the printed position of the rule; the associated position is never None *) type position = | Name | Type of inside where | Xhs of inside * side type item = sym_name * Common.Pos.pos option let pp_side fmt = function | Lhs -> Lplib.Base.out fmt "lhs" | Rhs -> Lplib.Base.out fmt "rhs" let pp_inside fmt = function | Exact -> Lplib.Base.out fmt "as the exact" | Inside -> Lplib.Base.out fmt "inside the" let pp_where fmt = function | Spine ins -> Lplib.Base.out fmt "%a spine of" pp_inside ins | Hypothesis ins -> Lplib.Base.out fmt "%a hypothesis of" pp_inside ins | Conclusion ins -> Lplib.Base.out fmt "%a conclusion of" pp_inside ins module ItemSet = struct include Map.Make(struct type t = item let compare = compare end) let of_list l = List.fold_left (fun m (k,v) -> update k (function | None -> Some v | Some l -> Some (v@l)) m) empty l end type answer = ((*generalized:*)bool * term * position) list type ho_pp = { run : 'a. 'a Lplib.Base.pp -> 'a Lplib.Base.pp } let identity_escaper : ho_pp = { run = fun x -> x } let html_escaper : ho_pp = { run = fun pp fmt x -> let res = Dream.html_escape (Format.asprintf "%a" pp x) in Format.pp_print_string fmt res } let generic_pp_of_position_list ~escaper ~sep = Lplib.List.pp (fun ppf position -> Print.without_qualifying (fun () -> match position with | _,_,Name -> Lplib.Base.out ppf "Name" | generalize,term,Type where -> Lplib.Base.out ppf "%a occurs %s%a the type" (escaper.run Print.term) term (if generalize then "generalized " else "") pp_where where | generalize,term,Xhs (inside,side) -> Lplib.Base.out ppf "%a occurs %s %a %a" (escaper.run Print.term) term (if generalize then "generalized" else "") pp_inside inside pp_side side)) sep let generic_pp_of_item_list ~escape ~escaper ~separator ~sep ~delimiters ~lis:(lisb,lise) ~pres:(preb,pree) fmt l = if l = [] then Lplib.Base.out fmt "Nothing found" else Lplib.List.pp (fun ppf (((p,n),pos),(positions : answer)) -> Lplib.Base.out ppf "%s%a.%s@%a%s%a%s%s%a%s%s@." lisb (escaper.run Core.Print.path) p n (escaper.run Common.Pos.pp) pos separator (generic_pp_of_position_list ~escaper ~sep) positions separator preb (Common.Pos.print_file_contents ~escape ~delimiters) pos pree lise) "" fmt l let html_of_item_list = generic_pp_of_item_list ~escape:Dream.html_escape ~escaper:html_escaper ~separator:"<br>\n" ~sep:" and<br>\n" ~delimiters:("<p>","</p>") ~lis:("<li>","</li>") ~pres:("<pre>","</pre>") let pp_item_list = generic_pp_of_item_list ~escape:(fun x -> x) ~escaper:identity_escaper ~separator:"\n" ~sep:" and\n" ~delimiters:("","") ~lis:("* ","") ~pres:("","") let pp_item_set fmt set = pp_item_list fmt (ItemSet.bindings set) let html_of_item_set fmt set = Lplib.Base.out fmt "<ul>%a</ul>" html_of_item_list (ItemSet.bindings set) (* disk persistence *) let dbpath = match Sys.getenv_opt "HOME" with | Some s -> s ^ "/.LPSearch.db" | None -> ".LPSearch.db" let rwpaths = ref [] let restore_from_disk () = try Pure.restore_from ~filename:dbpath with Sys_error msg -> Common.Error.wrn None "%s.\n\ Type \"lambdapi index --help\" to learn how to create the index." msg ; Pure.empty let db : (item * position list) Pure.db Lazy.t ref = ref (lazy (restore_from_disk ())) let empty () = db := lazy Pure.empty let insert k v = let db' = Pure.insert (Lazy.force !db) k v in db := lazy db' let insert_name k v = let db' = Pure.insert_name (Lazy.force !db) k v in db := lazy db' let set_of_list ~generalize k l = ItemSet.of_list (List.map (fun (i,pos) -> i, List.map (fun x -> generalize,k,x) pos) l) let search ~generalize k = set_of_list ~generalize k (Pure.search ~generalize (Lazy.force !db) k) let dump () = Pure.dump_to ~filename:dbpath (Lazy.force !db) let locate_name name = let k = Term.mk_Wild (* dummy, unused *) in set_of_list ~generalize:false k (Pure.locate_name (Lazy.force !db) name) end let find_sym ~prt:_prt ~prv:_prv _sig_state {elt=(mp,name); pos} = let pos,mp = match mp with [] -> let res = DB.locate_name name in if DB.ItemSet.cardinal res > 1 then Common.Error.fatal pos "Overloaded symbol %s, search for \"name = %s\" to know how \ to disambiguate it" name name ; (match DB.ItemSet.choose_opt res with | None -> Common.Error.fatal pos "Unknown symbol %s." name | Some (((mp,_),sympos),[_,_,DB.Name]) -> sympos,mp | Some _ -> assert false) (* locate only returns DB.Name*) | _::_ -> None,mp in Core.Term.create_sym mp Core.Term.Public Core.Term.Defin Core.Term.Sequen false (Common.Pos.make pos name) None Core.Term.mk_Type [] let search_pterm ~generalize ~mok env pterm = let sig_state = Core.Sig_state.dummy in let env = ("V#",(Bindlib.new_var mk_Vari "V#" ,Bindlib.box Term.mk_Type,None))::env in let query = Parsing.Scope.scope_search_pattern ~find_sym ~mok sig_state env pterm in DB.search ~generalize query module QNameMap = Map.Make(struct type t = sym_name let compare = Stdlib.compare end) let no_implicits_in_term t = let res = ref true in Core.LibTerm.iter (function | Plac _ -> res := false | Wild | TRef _ -> assert false | _ -> ()) t ; !res let check_rule : Parsing.Syntax.p_rule -> sym_rule = fun (r as rr) -> let ss = Core.Sig_state.dummy in let pr = Parsing.Scope.scope_rule ~find_sym false ss r in let s = pr.elt.pr_sym in let r = Parsing.Scope.rule_of_pre_rule pr in if no_implicits_in_term (snd (Bindlib.unmbind r.rhs)) then s, r else Common.Error.fatal (rr.pos) "The rule has implicit terms in the right-hand-side: %a" (Parsing.Pretty.rule "") rr let load_meta_rules () = let rules = ref [] in List.iter (fun rwpath -> let cmdstream = Parsing.Parser.Lp.parse_file rwpath in Stream.iter (fun {elt ; _ } -> match elt with Parsing.Syntax.P_rules r -> rules := List.rev_append r !rules | _ -> ()) cmdstream) !DB.rwpaths ; let rules = List.rev !rules in let handle_rule map r = let (s,r) = check_rule r in let h = function Some rs -> Some(r::rs) | None -> Some[r] in SymMap.update s h map in let map = List.fold_left handle_rule SymMap.empty rules in SymMap.iter Tree.update_dtree map; SymMap.fold (fun sym _rs map' -> QNameMap.add (name_of_sym sym) (Timed.(!(sym.sym_dtree))) map') map QNameMap.empty let meta_rules = lazy (load_meta_rules ()) let normalize typ = let dtree sym = try QNameMap.find (name_of_sym sym) (Lazy.force meta_rules) with Not_found -> Core.Tree_type.empty_dtree in Core.Eval.snf ~dtree ~tags:[`NoExpand] [] typ let rec is_flexible t = match Core.Term.unfold t with | Patt _ -> true | Appl(t,_) -> is_flexible t | LLet(_,_,b) -> let _, t = Bindlib.unbind b in is_flexible t | Vari _ | Type | Kind | Symb _ | Prod _ | Abst _ -> false | Meta _ | Plac _ | Wild | TRef _ | TEnv _ -> assert false let enter = DB.(function | Hypothesis _ -> Hypothesis Inside | Spine _ | Conclusion _ -> Conclusion Inside) let enter_pi_source = DB.(function | Spine _ -> Hypothesis Exact | Hypothesis _ -> Hypothesis Inside | Conclusion _ -> Conclusion Inside) let enter_pi_target ~is_prod = DB.(function | Spine _ when is_prod -> Spine Inside | Spine _ -> Conclusion Exact | Hypothesis _ -> Hypothesis Inside | Conclusion _ -> Conclusion Inside) let subterms_to_index ~is_spine t = let rec aux ~where t = let t = Core.Term.unfold t in [where,t] @ match t with | Vari _ | Type | Kind | Symb _ -> [] | Abst(t,b) -> let _, t2 = Bindlib.unbind b in aux ~where:(enter where) t @ aux ~where:(enter where) t2 | Prod(t,b) -> (match where with | Spine _ -> let t2 = Bindlib.subst b (Core.Term.mk_Patt (None,"dummy",[||])) in aux ~where:(enter_pi_source where) t @ aux ~where:(enter_pi_target ~is_prod:(Core.Term.is_prod t2) where) t2 | _ -> let _, t2 = Bindlib.unbind b in aux ~where:(enter_pi_source where) t @ aux ~where:(enter_pi_target ~is_prod:false where) t2) | Appl(t1,t2) -> aux ~where:(enter where) t1 @ aux ~where:(enter where) t2 | Patt (_var,_varname,args) -> List.concat (List.map (aux ~where:(enter where)) (Array.to_list args)) | LLet (t1,t2,b) -> (* we do not expand the let-in when indexing subterms *) let _, t3 = Bindlib.unbind b in aux ~where:(enter where) t1 @ aux ~where:(enter where) t2 @ aux ~where:(enter where) t3 | Meta _ | Plac _ | Wild | TRef _ | TEnv _ -> assert false in aux ~where:(if is_spine then Spine Exact else Conclusion Exact) t let insert_rigid t v = if not (is_flexible t) then begin DB.insert t v (* assert (List.mem v (DB.search t)); *) end let index_term_and_subterms ~is_spine t item = let tn = normalize t in (* Format.printf "%a : %a REWRITTEN TO %a@." pp_item (item Exact) Core.Print.term t Core.Print.term tn ; *) let cmp (where1,t1) (where2,t2) = let res = compare where1 where2 in if res = 0 then Core.Term.cmp t1 t2 else res in let subterms = List.sort_uniq cmp (subterms_to_index ~is_spine tn) in List.iter (fun (where,s) -> insert_rigid s (item where)) subterms let index_rule sym ({Core.Term.lhs=lhsargs ; rule_pos ; _} as rule) = let rule_pos = match rule_pos with | None -> assert false (* this probably may happen, but it is BAD! I leave the assert false to detect when it happens and let the team decide what to do *) | Some pos -> pos in let lhs = Core.Term.add_args (Core.Term.mk_Symb sym) lhsargs in let rhs = Core.Term.term_of_rhs rule in let get_inside = function | DB.Conclusion ins -> ins | _ -> assert false in let filename = Option.get rule_pos.fname in let path = Library.path_of_file Parsing.LpLexer.escape filename in let rule_name = (path,Common.Pos.to_string ~print_fname:false rule_pos) in index_term_and_subterms ~is_spine:false lhs (fun where -> ((rule_name,Some rule_pos),[Xhs(get_inside where,Lhs)])) ; index_term_and_subterms ~is_spine:false rhs (fun where -> ((rule_name,Some rule_pos),[Xhs(get_inside where,Rhs)])) let index_sym sym = let qname = name_of_sym sym in (* Name *) DB.insert_name (snd qname) ((qname,sym.sym_decl_pos),[Name]) ; (* Type + InType *) let typ = Timed.(!(sym.Core.Term.sym_type)) in index_term_and_subterms ~is_spine:true typ (fun where -> ((qname,sym.sym_decl_pos),[Type where])) ; (* InBody??? sym.sym_def : term option ref but all the subterms are too much; collect only the constants? *) (* Rules *) List.iter (index_rule sym) Timed.(!(sym.Core.Term.sym_rules)) let index_sign ~rules:rwrules sign = DB.rwpaths := rwrules ; let syms = Timed.(!(sign.Core.Sign.sign_symbols)) in let rules = Timed.(!(sign.Core.Sign.sign_deps)) in Lplib.Extra.StrMap.iter (fun _ sym -> index_sym sym) syms ; Common.Path.Map.iter (fun path rules -> Lplib.Extra.StrMap.iter (fun name rules -> let sym = Core.Sign.find_sym path name in List.iter (index_rule sym) rules) rules) rules (* let's flatten the interface *) include DB module QueryLanguage = struct open Parsing.SearchQuerySyntax let match_opt p x = match p,x with | None, _ -> true | Some x', x -> x=x' let match_where p x = match p with | None -> true | Some p -> match p,x with | Spine insp, Spine ins | Conclusion insp, Conclusion ins | Hypothesis insp, Hypothesis ins -> match_opt insp ins | _, _ -> false let filter_constr constr _ positions = match constr with | QType wherep -> List.exists (function | _,_,Type where -> match_where wherep where | _ -> false) positions | QXhs (insp,sidep) -> List.exists (function | _,_,Xhs (ins,side) -> match_opt insp ins && match_opt sidep side | _ -> false) positions let answer_base_query ~mok env = function | QName s -> locate_name s | QSearch (patt,generalize,constr) -> let res = search_pterm ~generalize ~mok env patt in (match constr with | None -> res | Some constr -> ItemSet.filter (filter_constr constr) res) let perform_op = function | Intersect -> ItemSet.merge (fun _ positions1 positions2 -> match positions1, positions2 with | Some l1, Some l2 -> Some (l1@l2) | _,_ -> None) | Union -> ItemSet.union (fun _ positions1 positions2 -> Some (positions1 @ positions2)) let filter set f = let f ((p',_),_) _ = match f with | Path p -> let string_of_path x = Format.asprintf "%a" Common.Path.pp x in Lplib.String.is_prefix p (string_of_path p') in ItemSet.filter f set let answer_query ~mok env = let rec aux = function | QBase bq -> answer_base_query ~mok env bq | QOpp (q1,op,q2) -> perform_op op (aux q1) (aux q2) | QFilter (q,f) -> filter (aux q) f in aux end (* let's flatten the interface *) include QueryLanguage module UserLevelQueries = struct let search_cmd_gen ~fail ~pp_results s = try let pstream = Parsing.Parser.Lp.parse_search_query_string "LPSearch" s in let pq = Stream.next pstream in let mok _ = None in let items = answer_query ~mok [] pq in Format.asprintf "%a@." pp_results items with | Stream.Failure -> fail (Format.asprintf "Syntax error: a query was expected") | Common.Error.Fatal(_,msg) -> fail (Format.asprintf "Error: %s@." msg) | exn -> fail (Format.asprintf "Error: %s@." (Printexc.to_string exn)) let search_cmd_html s = search_cmd_gen ~fail:(fun x -> "<font color=\"red\">" ^ x ^ "</font>") ~pp_results:html_of_item_set s let search_cmd_txt s = search_cmd_gen ~fail:(fun x -> Common.Error.fatal_no_pos "%s" x) ~pp_results:pp_item_set s end (* let's flatten the interface *) include UserLevelQueries
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