+ 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<def>>; OPT SYMBOL "|";
+ fst_constructors = LIST0 constructor SEP SYMBOL "|";
+ tl = OPT [ "with";
+ types = LIST1 [
+ name = IDENT; SYMBOL ":"; typ = term; SYMBOL <:unicode<def>>;
+ 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<def>> (* ≝ *); 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<def>> (* ≝ *); 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) ] ];