+ tactic_where: [
+ [ where = OPT [ IDENT "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: [
+ [ "reduce" -> `Reduce
+ | "simpl" -> `Simpl
+ | "whd" -> `Whd ]
+ ];
+ tactic: [
+ [ [ IDENT "absurd" | IDENT "Absurd" ] -> return_tactic loc TacticAst.Absurd
+ | [ IDENT "apply" | IDENT "Apply" ];
+ t = tactic_term -> return_tactic loc (TacticAst.Apply t)
+ | [ IDENT "assumption" | IDENT "Assumption" ] ->
+ return_tactic loc TacticAst.Assumption
+ | [ 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 "elim" | IDENT "Elim" ]; IDENT "type";
+ 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 "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 "left" | IDENT "Left" ] -> return_tactic loc TacticAst.Left
+ | [ "let" | "Let" ];
+ t = tactic_term; IDENT "in"; where = IDENT ->
+ return_tactic loc (TacticAst.LetIn (t, where))
+ (* TODO Reduce *)
+ | [ 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 "." -> t ] ];
+ tactical:
+ [ "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
+(* | [ IDENT "goal" | IDENT "Goal" ] -> `Goal *)
+ ]
+ ];
+ theorem_cmd: [
+ [ flavour = theorem_flavour; name = OPT IDENT; SYMBOL ":"; typ = term;
+ body = OPT [ SYMBOL <:unicode<def>> (* ≝ *); body = term -> body ];
+ SYMBOL "." ->
+ (loc, flavour, name, typ, body)
+ | [ IDENT "goal" | IDENT "Goal" ]; typ = term;
+ body = OPT [ SYMBOL <:unicode<def>> (* ≝ *); body = term -> body ];
+ SYMBOL "." ->
+ (loc, `Goal, None, typ, body)
+ ]
+ ];
+ proof_cmd: [ [ [ IDENT "proof" | IDENT "Proof" ]; SYMBOL "." -> loc ] ];
+ qed_cmd: [
+ [ [ IDENT "qed" | IDENT "Qed" ]; SYMBOL "." -> (loc, None)
+ | [ IDENT "save" | IDENT "Save" ]; name = IDENT; SYMBOL "." ->
+ (loc, Some name)
+ ]
+ ];
+ command: [
+ [ (loc', flavour, name, typ, body) = theorem_cmd ->
+ return_command loc (CommandAst.Theorem (loc', flavour, name, typ, body))
+ | (loc') = proof_cmd -> return_command loc (CommandAst.Proof loc')
+ | (loc, name) = qed_cmd -> return_command loc (CommandAst.Qed (loc, name))
+ ]
+ ];
+ script_entry: [
+ [ theorem = theorem_cmd;
+ proof = OPT [
+ proof_cmd; tacticals = LIST1 tactical0; qed = qed_cmd ->
+ (tacticals, qed)
+ ] ->
+ let (loc', flavour, name', typ, body_verbatim) = theorem in
+ let name'' =
+ match proof with
+ | None | Some (_, (_, None)) -> None
+ | Some (_, (_, Some name)) -> Some name
+ in
+ let name =
+ match (name', name'') with
+ | Some name, None -> name
+ | None, Some name -> name
+ | None, None ->
+ Stdpp.raise_with_loc loc (Failure "theorem's name is missing")
+ | Some name', Some name'' when name' <> name'' ->
+ Stdpp.raise_with_loc loc (Failure (sprintf
+ "theorem's name mismatch: %s <> %s" name' name''))
+ | Some name, _ -> name
+ in
+ let body =
+ match (body_verbatim, proof) with
+ | Some term, None -> CommandAst.Script.Verbatim (loc', term)
+ | None, Some (tacticals, (loc'', _)) ->
+ CommandAst.Script.Tactics (loc'', tacticals)
+ | Some _, Some _ ->
+ Stdpp.raise_with_loc loc (Failure (sprintf
+ "theorem %s has too many proofs" name))
+ | None, None ->
+ Stdpp.raise_with_loc loc (Failure (sprintf
+ "theorem %s has no proof" name))
+ in
+ return_script loc (CommandAst.Script.Theorem (flavour, name, typ, body))
+ ]
+ ];
+ script: [ [ entries = LIST0 script_entry; EOI -> entries ] ];