(* Copyright (C) 2004, 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://helm.cs.unibo.it/ *) let debug = false let debug_print s = if debug then begin prerr_endline ""; prerr_endline s; prerr_endline "" end (** if set to true each number will have a different insance number and can * thus be interpreted differently than others *) let use_fresh_num_instances = false (** does the lexer return COMMENT tokens? *) let return_comments = false open Printf open DisambiguateTypes exception Parse_error of Token.flocation * string let cic_lexer = CicTextualLexer2.cic_lexer ~comments:return_comments () let fresh_num_instance = let n = ref 0 in if use_fresh_num_instances then (fun () -> incr n; !n) else (fun () -> 0) let choice_of_uri uri = let term = CicUtil.term_of_uri uri in (uri, (fun _ _ _ -> term)) let grammar = Grammar.gcreate cic_lexer let term = Grammar.Entry.create grammar "term" let term0 = Grammar.Entry.create grammar "term0" let tactic = Grammar.Entry.create grammar "tactic" let tactical = Grammar.Entry.create grammar "tactical" let tactical0 = Grammar.Entry.create grammar "tactical0" let command = Grammar.Entry.create grammar "command" let script = Grammar.Entry.create grammar "script" let return_term loc term = CicAst.AttributedTerm (`Loc loc, term) let return_tactic loc tactic = TacticAst.LocatedTactic (loc, tactic) let return_tactical loc tactical = TacticAst.LocatedTactical (loc, tactical) let return_command loc cmd = cmd (* TODO ZACK FIXME uhm ... why we drop loc? *) let fail floc msg = let (x, y) = CicAst.loc_of_floc floc in failwith (Printf.sprintf "Error at characters %d - %d: %s" x y msg) let name_of_string = function | "_" -> Cic.Anonymous | s -> Cic.Name s let string_of_name = function | Cic.Anonymous -> "_" | Cic.Name s -> s let int_opt = function | None -> None | Some lexeme -> Some (int_of_string lexeme) (** the uri of an inductive type (a ".ind" uri) is not meaningful without an * xpointer. Still, it's likely that an user who wrote "cic:/blabla/foo.ind" * actually meant "cic:/blabla/foo.ind#xpointer(1/1)", i.e. the first inductive * type in a block of mutual inductive types. * * This function performs the expansion foo.ind -> foo#xpointer..., if needed *) let ind_expansion uri = let len = String.length uri in if len >= 4 && String.sub uri (len - 4) 4 = ".ind" then uri ^ "#xpointer(1/1)" else uri EXTEND GLOBAL: term term0 tactic tactical tactical0 command script; int: [ [ num = NUM -> try int_of_string num with Failure _ -> raise (Parse_error (loc, "integer literal expected")) ] ]; meta_subst: [ [ s = SYMBOL "_" -> None | t = term -> Some t ] ]; binder: [ [ SYMBOL <:unicode> (* λ *) -> `Lambda | SYMBOL <:unicode> (* Π *) -> `Pi | SYMBOL <:unicode> (* ∃ *) -> `Exists | SYMBOL <:unicode> (* ∀ *) -> `Forall ] ]; sort: [ [ "Prop" -> `Prop | "Set" -> `Set | "Type" -> `Type | "CProp" -> `CProp ] ]; typed_name: [ [ PAREN "("; i = IDENT; SYMBOL ":"; typ = term; PAREN ")" -> (Cic.Name i, Some typ) | i = IDENT -> (Cic.Name i, None) ] ]; subst: [ [ subst = OPT [ SYMBOL "\\subst"; (* to avoid catching frequent "a [1]" cases *) PAREN "["; substs = LIST1 [ i = IDENT; SYMBOL <:unicode> (* ≔ *); t = term -> (i, t) ] SEP SYMBOL ";"; PAREN "]" -> substs ] -> subst ] ]; substituted_name: [ (* a subs.name is an explicit substitution subject *) [ s = IDENT; subst = subst -> CicAst.Ident (s, subst) | s = URI; subst = subst -> CicAst.Uri (ind_expansion s, subst) ] ]; name: [ (* as substituted_name with no explicit substitution *) [ s = [ IDENT | SYMBOL ] -> s ] ]; pattern: [ [ n = name -> (n, []) | PAREN "("; head = name; vars = LIST1 typed_name; PAREN ")" -> (head, vars) ] ]; let_defs:[ [ defs = LIST1 [ name = IDENT; args = LIST1 [ PAREN "(" ; names = LIST1 IDENT SEP SYMBOL ","; SYMBOL ":"; ty = term; PAREN ")" -> (names, ty) ]; index_name = OPT [ IDENT "on"; idx = IDENT -> idx ]; ty = OPT [ SYMBOL ":" ; t = term -> t ]; SYMBOL <:unicode> (* ≝ *); t1 = term -> let rec list_of_binder binder ty final_term = function | [] -> final_term | name::tl -> CicAst.Binder (binder, (Cic.Name name, Some ty), list_of_binder binder ty final_term tl) in let rec binder_of_arg_list binder final_term = function | [] -> final_term | (l,ty)::tl -> list_of_binder binder ty (binder_of_arg_list binder final_term tl) l in let t1' = binder_of_arg_list `Lambda t1 args in let ty' = match ty with | None -> None | Some ty -> Some (binder_of_arg_list `Pi ty args) in let rec get_position_of name n = function | [] -> (None,n) | nam::tl -> if nam = name then (Some n,n) else (get_position_of name (n+1) tl) in let rec find_arg name n = function | [] -> (fail loc (sprintf "Argument %s not found" name)) | (l,_)::tl -> let (got,len) = get_position_of name 0 l in (match got with | None -> (find_arg name (n+len) tl) | Some where -> n + where) in let index = (match index_name with | None -> 0 | (Some name) -> find_arg name 0 args) in ((Cic.Name name,ty'), t1', index) ] SEP "and" -> defs ]]; constructor: [ [ name = IDENT; SYMBOL ":"; typ = term -> (name, typ) ] ]; term0: [ [ t = term; EOI -> return_term loc t ] ]; term: [ "letin" NONA [ "let"; var = typed_name; SYMBOL <:unicode> (* ≝ *); t1 = term; "in"; t2 = term -> return_term loc (CicAst.LetIn (var, t1, t2)) | "let"; ind_kind = [ "corec" -> `CoInductive | "rec"-> `Inductive ]; defs = let_defs; "in"; body = term -> return_term loc (CicAst.LetRec (ind_kind, defs, body)) ] | "binder" RIGHTA [ b = binder; (vars, typ) = [ vars = LIST1 IDENT SEP SYMBOL ","; typ = OPT [ SYMBOL ":"; t = term -> t ] -> (vars, typ) | PAREN "("; vars = LIST1 IDENT SEP SYMBOL ","; typ = OPT [ SYMBOL ":"; t = term -> t ]; PAREN ")" -> (vars, typ) ]; SYMBOL "."; body = term -> let binder = List.fold_right (fun var body -> let name = name_of_string var in CicAst.Binder (b, (name, typ), body)) vars body in return_term loc binder | t1 = term; SYMBOL <:unicode> (* → *); t2 = term -> return_term loc (CicAst.Binder (`Pi, (Cic.Anonymous, Some t1), t2)) ] | "logic_add" LEFTA [ (* nothing here by default *) ] | "logic_mult" LEFTA [ (* nothing here by default *) ] | "logic_inv" NONA [ (* nothing here by default *) ] | "relop" LEFTA [ t1 = term; SYMBOL "="; t2 = term -> return_term loc (CicAst.Appl [CicAst.Symbol ("eq", 0); t1; t2]) ] | "add" LEFTA [ (* nothing here by default *) ] | "mult" LEFTA [ (* nothing here by default *) ] | "power" LEFTA [ (* nothing here by default *) ] | "inv" NONA [ (* nothing here by default *) ] | "apply" LEFTA [ t1 = term; t2 = term -> let rec aux = function | CicAst.Appl (hd :: tl) -> aux hd @ tl | term -> [term] in CicAst.Appl (aux t1 @ [t2]) ] | "simple" NONA [ sort = sort -> CicAst.Sort sort | n = substituted_name -> return_term loc n | i = NUM -> return_term loc (CicAst.Num (i, (fresh_num_instance ()))) | IMPLICIT -> return_term loc CicAst.Implicit | m = META; substs = [ PAREN "["; substs = LIST0 meta_subst SEP SYMBOL ";" ; PAREN "]" -> substs ] -> let index = try int_of_string (String.sub m 1 (String.length m - 1)) with Failure "int_of_string" -> fail loc ("Invalid meta variable number: " ^ m) in return_term loc (CicAst.Meta (index, substs)) | outtyp = OPT [ PAREN "["; typ = term; PAREN "]" -> typ ]; "match"; t = term; indty_ident = OPT [ SYMBOL ":"; id = IDENT -> id ]; "with"; PAREN "["; patterns = LIST0 [ lhs = pattern; SYMBOL <:unicode> (* ⇒ *); rhs = term -> ((lhs: CicAst.case_pattern), rhs) ] SEP SYMBOL "|"; PAREN "]" -> return_term loc (CicAst.Case (t, indty_ident, outtyp, patterns)) | PAREN "("; t1 = term; SYMBOL ":"; t2 = term; PAREN ")" -> return_term loc (CicAst.Appl [CicAst.Symbol ("cast", 0); t1; t2]) | PAREN "("; t = term; PAREN ")" -> return_term loc t ] ]; tactic_where: [ [ where = OPT [ "in"; ident = IDENT -> ident ] -> where ] ]; tactic_term: [ [ t = term -> t ] ]; ident_list0: [ [ PAREN "["; idents = LIST0 IDENT SEP SYMBOL ";"; PAREN "]" -> idents ] ]; ident_list1: [ [ PAREN "["; idents = LIST1 IDENT SEP SYMBOL ";"; PAREN "]" -> idents ] ]; reduction_kind: [ [ [ IDENT "reduce" | IDENT "Reduce" ] -> `Reduce | [ IDENT "simplify" | IDENT "Simplify" ] -> `Simpl | [ IDENT "whd" | IDENT "Whd" ] -> `Whd ] ]; tactic: [ [ [ IDENT "absurd" | IDENT "Absurd" ]; t = tactic_term -> return_tactic loc (TacticAst.Absurd t) | [ IDENT "apply" | IDENT "Apply" ]; t = tactic_term -> return_tactic loc (TacticAst.Apply t) | [ IDENT "assumption" | IDENT "Assumption" ] -> return_tactic loc TacticAst.Assumption | [ IDENT "auto" | IDENT "Auto" ] -> return_tactic loc TacticAst.Auto | [ IDENT "change" | IDENT "Change" ]; t1 = tactic_term; "with"; t2 = tactic_term; where = tactic_where -> return_tactic loc (TacticAst.Change (t1, t2, where)) (* TODO Change_pattern *) | [ IDENT "contradiction" | IDENT "Contradiction" ] -> return_tactic loc TacticAst.Contradiction | [ IDENT "cut" | IDENT "Cut" ]; t = tactic_term -> return_tactic loc (TacticAst.Cut t) | [ IDENT "decompose" | IDENT "Decompose" ]; principles = ident_list1; where = IDENT -> return_tactic loc (TacticAst.Decompose (where, principles)) | [ IDENT "discriminate" | IDENT "Discriminate" ]; hyp = IDENT -> return_tactic loc (TacticAst.Discriminate hyp) | [ IDENT "elimType" | IDENT "ElimType" ]; t = tactic_term -> return_tactic loc (TacticAst.ElimType t) | [ IDENT "elim" | IDENT "Elim" ]; t1 = tactic_term; using = OPT [ "using"; using = tactic_term -> using ] -> return_tactic loc (TacticAst.Elim (t1, using)) | [ IDENT "exact" | IDENT "Exact" ]; t = tactic_term -> return_tactic loc (TacticAst.Exact t) | [ IDENT "exists" | IDENT "Exists" ] -> return_tactic loc TacticAst.Exists | [ IDENT "fold" | IDENT "Fold" ]; kind = reduction_kind; t = tactic_term -> return_tactic loc (TacticAst.Fold (kind, t)) | [ IDENT "fourier" | IDENT "Fourier" ] -> return_tactic loc TacticAst.Fourier | [ IDENT "hint" | IDENT "Hint" ] -> return_tactic loc TacticAst.Hint | [ IDENT "injection" | IDENT "Injection" ]; ident = IDENT -> return_tactic loc (TacticAst.Injection ident) | [ IDENT "intros" | IDENT "Intros" ]; num = OPT [ num = int -> num ]; idents = OPT ident_list0 -> let idents = match idents with None -> [] | Some idents -> idents in return_tactic loc (TacticAst.Intros (num, idents)) | [ IDENT "intro" | IDENT "Intro" ] -> return_tactic loc (TacticAst.Intros (Some 1, [])) | [ IDENT "left" | IDENT "Left" ] -> return_tactic loc TacticAst.Left | [ "let" | "Let" ]; t = tactic_term; "in"; where = IDENT -> return_tactic loc (TacticAst.LetIn (t, where)) | kind = reduction_kind; pat = OPT [ "in"; pat = [ IDENT "goal" -> `Goal | IDENT "hyp" -> `Everywhere ] -> pat ]; terms = LIST0 term SEP SYMBOL "," -> let tac = (match (pat, terms) with | None, [] -> TacticAst.Reduce (kind, None) | None, terms -> TacticAst.Reduce (kind, Some (terms, `Goal)) | Some pat, [] -> TacticAst.Reduce (kind, Some ([], pat)) | Some pat, terms -> TacticAst.Reduce (kind, Some (terms, pat))) in return_tactic loc tac | [ IDENT "reflexivity" | IDENT "Reflexivity" ] -> return_tactic loc TacticAst.Reflexivity | [ IDENT "replace" | IDENT "Replace" ]; t1 = tactic_term; "with"; t2 = tactic_term -> return_tactic loc (TacticAst.Replace (t1, t2)) (* TODO Rewrite *) (* TODO Replace_pattern *) | [ IDENT "right" | IDENT "Right" ] -> return_tactic loc TacticAst.Right | [ IDENT "ring" | IDENT "Ring" ] -> return_tactic loc TacticAst.Ring | [ IDENT "split" | IDENT "Split" ] -> return_tactic loc TacticAst.Split | [ IDENT "symmetry" | IDENT "Symmetry" ] -> return_tactic loc TacticAst.Symmetry | [ IDENT "transitivity" | IDENT "Transitivity" ]; t = tactic_term -> return_tactic loc (TacticAst.Transitivity t) ] ]; tactical0: [ [ t = tactical; SYMBOL "." -> return_tactical loc t ] ]; tactical: [ "command" NONA [ cmd = command -> return_tactical loc (TacticAst.Command cmd) ] | "sequence" LEFTA [ tactics = LIST1 NEXT SEP SYMBOL ";" -> return_tactical loc (TacticAst.Seq tactics) ] | "then" NONA [ tac = tactical; PAREN "["; tacs = LIST0 tactical SEP SYMBOL ";"; PAREN "]" -> return_tactical loc (TacticAst.Then (tac, tacs)) ] | "loops" RIGHTA [ [ IDENT "do" | IDENT "Do" ]; count = int; tac = tactical -> return_tactical loc (TacticAst.Do (count, tac)) | [ IDENT "repeat" | IDENT "Repeat" ]; tac = tactical -> return_tactical loc (TacticAst.Repeat tac) ] | "simple" NONA [ [ IDENT "tries" | IDENT "Tries" ]; PAREN "["; tacs = LIST0 tactical SEP SYMBOL ";"; PAREN "]" -> return_tactical loc (TacticAst.Tries tacs) | [ IDENT "try" | IDENT "Try" ]; tac = NEXT -> return_tactical loc (TacticAst.Try tac) | [ IDENT "fail" | IDENT "Fail" ] -> return_tactical loc TacticAst.Fail | [ IDENT "id" | IDENT "Id" ] -> return_tactical loc TacticAst.IdTac | PAREN "("; tac = tactical; PAREN ")" -> return_tactical loc tac | tac = tactic -> return_tactical loc (TacticAst.Tactic tac) ] ]; theorem_flavour: [ (* all flavours but Goal *) [ [ IDENT "definition" | IDENT "Definition" ] -> `Definition | [ IDENT "fact" | IDENT "Fact" ] -> `Fact | [ IDENT "lemma" | IDENT "Lemma" ] -> `Lemma | [ IDENT "remark" | IDENT "Remark" ] -> `Remark | [ IDENT "theorem" | IDENT "Theorem" ] -> `Theorem ] ]; inductive_spec: [ [ fst_name = IDENT; params = LIST0 [ PAREN "("; names = LIST1 IDENT SEP SYMBOL ","; SYMBOL ":"; typ = term; PAREN ")" -> (names, typ) ]; SYMBOL ":"; fst_typ = term; SYMBOL <:unicode>; OPT SYMBOL "|"; fst_constructors = LIST0 constructor SEP SYMBOL "|"; tl = OPT [ "with"; types = LIST1 [ name = IDENT; SYMBOL ":"; typ = term; SYMBOL <:unicode>; OPT SYMBOL "|"; constructors = LIST0 constructor SEP SYMBOL "|" -> (name, true, typ, constructors) ] SEP "with" -> types ] -> let params = List.fold_right (fun (names, typ) acc -> (List.map (fun name -> (name, typ)) names) @ acc) params [] in let fst_ind_type = (fst_name, true, fst_typ, fst_constructors) in let tl_ind_types = match tl with None -> [] | Some types -> types in let ind_types = fst_ind_type :: tl_ind_types in (params, ind_types) ] ]; print_kind: [ [ [ IDENT "Env" | IDENT "env" | IDENT "Environment" | IDENT "environment" ] -> `Env | [ IDENT "Coer" | IDENT "coer" | IDENT "Coercions" | IDENT "coercions" ] -> `Coer ] ]; command: [ [ [ IDENT "abort" | IDENT "Abort" ] -> return_command loc TacticAst.Abort | [ IDENT "proof" | IDENT "Proof" ] -> return_command loc TacticAst.Proof | [ IDENT "quit" | IDENT "Quit" ] -> return_command loc TacticAst.Quit | [ IDENT "qed" | IDENT "Qed" ] -> return_command loc (TacticAst.Qed None) | [ IDENT "print" | IDENT "Print" ]; print_kind = print_kind -> return_command loc (TacticAst.Print print_kind) | [ IDENT "save" | IDENT "Save" ]; name = IDENT -> return_command loc (TacticAst.Qed (Some name)) | flavour = theorem_flavour; name = OPT IDENT; SYMBOL ":"; typ = term; body = OPT [ SYMBOL <:unicode> (* ≝ *); body = term -> body ] -> return_command loc (TacticAst.Theorem (flavour, name, typ, body)) | "let"; ind_kind = [ "corec" -> `CoInductive | "rec"-> `Inductive ]; defs = let_defs -> let name,ty = match defs with | ((Cic.Name name,Some ty),_,_) :: _ -> name,ty | ((Cic.Name name,None),_,_) :: _ -> fail loc ("No type given for " ^ name) | _ -> assert false in let body = CicAst.Ident (name,None) in TacticAst.Theorem(`Definition, Some name, ty, Some (CicAst.LetRec (ind_kind, defs, body))) | [ IDENT "inductive" | IDENT "Inductive" ]; spec = inductive_spec -> let (params, ind_types) = spec in return_command loc (TacticAst.Inductive (params, ind_types)) | [ IDENT "coinductive" | IDENT "CoInductive" ]; spec = inductive_spec -> let (params, ind_types) = spec in let ind_types = (* set inductive flags to false (coinductive) *) List.map (fun (name, _, term, ctors) -> (name, false, term, ctors)) ind_types in return_command loc (TacticAst.Inductive (params, ind_types)) | [ IDENT "coercion" | IDENT "Coercion" ] ; name = IDENT -> return_command loc (TacticAst.Coercion (CicAst.Ident (name,Some []))) | [ IDENT "coercion" | IDENT "Coercion" ] ; name = URI -> return_command loc (TacticAst.Coercion (CicAst.Uri (name,Some []))) | [ IDENT "goal" | IDENT "Goal" ]; typ = term; body = OPT [ SYMBOL <:unicode> (* ≝ *); body = term -> body ] -> return_command loc (TacticAst.Theorem (`Goal, None, typ, body)) | [ IDENT "undo" | IDENT "Undo" ]; steps = OPT NUM -> return_command loc (TacticAst.Undo (int_opt steps)) | [ IDENT "redo" | IDENT "Redo" ]; steps = OPT NUM -> return_command loc (TacticAst.Redo (int_opt steps)) | [ IDENT "baseuri" | IDENT "Baseuri" ]; uri = OPT QSTRING -> return_command loc (TacticAst.Baseuri uri) | [ IDENT "basedir" | IDENT "Basedir" ]; uri = OPT QSTRING -> return_command loc (TacticAst.Basedir uri) | [ IDENT "check" | IDENT "Check" ]; t = term -> return_command loc (TacticAst.Check t) (* | [ IDENT "alias" | IDENT "Alias" ]; spec = alias_spec -> return_command loc (TacticAst.Alias spec) *) ] ]; script_entry: [ [ cmd = tactical0 -> Command cmd (* | s = COMMENT -> Comment (loc, s) *) ] ]; script: [ [ entries = LIST0 script_entry; EOI -> (loc, entries) ] ]; END let exc_located_wrapper f = try f () with | Stdpp.Exc_located (floc, Stream.Error msg) -> raise (Parse_error (floc, msg)) | Stdpp.Exc_located (floc, exn) -> raise (Parse_error (floc, (Printexc.to_string exn))) let parse_term stream = exc_located_wrapper (fun () -> (Grammar.Entry.parse term0 stream)) let parse_tactic stream = exc_located_wrapper (fun () -> (Grammar.Entry.parse tactic stream)) let parse_tactical stream = exc_located_wrapper (fun () -> (Grammar.Entry.parse tactical0 stream)) let parse_script stream = exc_located_wrapper (fun () -> (Grammar.Entry.parse script stream)) (**/**) (** {2 Interface for gTopLevel} *) module EnvironmentP3 = struct type t = environment let empty = "" let aliases_grammar = Grammar.gcreate cic_lexer let aliases = Grammar.Entry.create aliases_grammar "aliases" let to_string env = let aliases = Environment.fold (fun domain_item (dsc, _) acc -> let s = match domain_item with | Id id -> sprintf "alias id %s = %s" id dsc | Symbol (symb, instance) -> sprintf "alias symbol \"%s\" (instance %d) = \"%s\"" symb instance dsc | Num instance -> sprintf "alias num (instance %d) = \"%s\"" instance dsc in s :: acc) env [] in String.concat "\n" (List.sort compare aliases) EXTEND GLOBAL: aliases; aliases: [ (* build an environment from an aliases list *) [ aliases = LIST0 alias; EOI -> List.fold_left (fun env (domain_item, codomain_item) -> Environment.add domain_item codomain_item env) Environment.empty aliases ] ]; alias: [ (* return a pair from an alias *) [ IDENT "alias"; choice = [ IDENT "id"; id = IDENT; SYMBOL "="; uri = URI -> (Id id, choice_of_uri uri) | IDENT "symbol"; symbol = QSTRING; PAREN "("; IDENT "instance"; instance = NUM; PAREN ")"; SYMBOL "="; dsc = QSTRING -> (Symbol (symbol, int_of_string instance), DisambiguateChoices.lookup_symbol_by_dsc symbol dsc) | IDENT "num"; PAREN "("; IDENT "instance"; instance = NUM; PAREN ")"; SYMBOL "="; dsc = QSTRING -> (Num (int_of_string instance), DisambiguateChoices.lookup_num_by_dsc dsc) ] -> choice ] ]; END let of_string s = if s = empty then Environment.empty else exc_located_wrapper (fun () -> Grammar.Entry.parse aliases (Stream.of_string s)) end (* vim:set encoding=utf8: *)