Associativity and precedence specifications have been added.

CHANGES

@@ -3,10 +3,10 @@
 ** The acgc.opt/acgc compiler and the acg.opt/acg interpreter:
 + Some syntax changes:
   1. Prefix operators have the highest priority
-  2. Infix operators have a higher priority than application (*Note:
-     this may break existing code*)
+  2. application has precedence over infix operators
   3. An associativity property (none, left, right) can be set to infix
-     operators (left is the default), and a precedence level as well
+     operators (left is the default), and a precedence level as
+     well. See associativity and the precedence section in the README.
 + Removed the dependency to BOLT (replaced by Logs) and dypgen (replaced by menhir)
 
 * Version 1.4.0

CHANGES.md

@@ -3,8 +3,9 @@
 * Removed the dependency to BOLT (replaced by Logs) and dypgen (replaced by menhir)
 * Some syntax changes:
   1. Prefix operators have the highest priority
-  2. Infix operators have a higher priority than application (*Note: this may break existing code*)
-  3. An associativity property (none, left, right) can be set to infix operators (left is the default), and a precedence level as well
+  2. Application has precedence over infix operators
+  3. An associativity property (none, left, right) can be set to infix operators (left is the default), and a precedence level as well. See the associativity and the precedence section in the [README](README.me).
+* Removed the dependency to BOLT (replaced by Logs) and dypgen (replaced by menhir)
 
 # Version 1.4.0
 ## The acgc.opt/acgc compiler and the acg.opt/acg interpreter:

README

@@ -205,9 +205,9 @@ acgc.opt)
 
 
 
-************************************
-* Syntax of signature and lexicons *
-************************************
+************************
+* Syntax of signatures *
+************************
 
 (see the examples/tag.acg file for an example)
 
@@ -266,6 +266,43 @@ if SYM is a prefic symbol (highest priority)
 	BINDER x y z.t
 if BINDER is a binder
 
++ About associativity and precedence of operators
+
+Prefix operators have precedence over application, and application has
+precedence over infix operators. Relative precedence among infix
+operators can be defined.
+
+When no associativity specification is set, the default is left
+associative.
+
+When no precedece definition is given, the default is higher
+precedence over any infix operator defined so far.
+
+When declaring or defining an infix operator with the keyword 'infix',
+the optional specification for the associativity and the relative
+precedence can be set.
+
+A specification is given between square brackets. The syntax is as
+follows:
+
+    infix [specification] SYM …
+
+(the remaining part of the declaration is the same as without the specification)
+
+A specification is non-empty comma-separated list of:
+
++ an (optional) associativity specification, given by one of the
+  keywords 'Left', 'Right', or 'NonAssoc'. If not present, left
+  associativity is set by default to infix operators
+
++ an (optional) precedence declaration (if not present, the highest
+  precedence over all the infix operators defined so far is given). It
+  is defined as '< SYM' (where SYM is a symbol). It assigns to the
+  operator being declared or defined the greates precedence *below* the precedence of SYM.
+
+***********************
+* Syntax of  lexicons *
+***********************
 
 There are two ways to define a lexicon:
 1. By using the keyword `lexicon` or `nl_lexicon` as in :

README.md

@@ -187,6 +187,28 @@ end
   * `SYM t` if `SYM` is a prefix symbol (highest priority)
   *	`BINDER x y z.t` if `BINDER` is a binder
 
+* About associativity and precedence of operators
+
+  Prefix operators have precedence over application, and application has precedence over infix operators. Relative precedence among infix operators can be defined.
+
+  When no associativity specification is set, the default is left associative.
+
+  When no precedece definition is given, the default is higher precedence over any infix operator defined so far.
+
+  When declaring or defining an infix operator with the keyword 'infix', the optional specification for the associativity and the relative precedence can be set.
+
+  A specification is given between square brackets. The syntax is as follows:
+  ```
+  infix [specification] SYM …
+  ```
+  (the remaining part of the declaration is the same as without the specification)
+
+  A specification is non-empty comma-separated list of:
+
+  + an (optional) associativity specification, given by one of the keywords `Left`, `Right`, or `NonAssoc`. If not present, left associativity is set by default to infix operators
+
+  + an (optional) precedence declaration (if not present, the highest precedence over all the infix operators defined so far is given). It is defined as `< SYM` (where `SYM` is a symbol). It assigns to the operator being declared or defined the greates precedence *below* the precedence of `SYM`.
+
 
 ### Lexicons
 

examples/montague-fr.acg

@@ -41,7 +41,7 @@ signature francais =
 	string : type;
 	
 	(* the infix concatenation operator + *)
-	infix + : string -> string -> string;
+	infix [Right] + : string -> string -> string;
 
 	(* the empty string e *)
 	e : string;
@@ -65,7 +65,7 @@ lexicon realisation_francais (syntax) : francais =
 	   returns the concatenation subject+loves+object *)
 	AIMER := lambda o s.s + aime + o;
 
-        VOULOIR_CV := lambda vp. Lambda s. s + veut + (vp e);
+        VOULOIR_CV := lambda vp. Lambda s. s + veut + vp e;
         VOULOIR_SC := lambda sc s. s + veut + sc;
 
 	CHAQUE := lambda n P. P (chaque + n);
@@ -111,7 +111,7 @@ lexicon realisation_anglais (syntax) : anglais =
 	(* LOVE is interpreted as a function taking two arguments. The first one is the object and the second one is the subject. It returns the concatenation subject+loves+object *)
 	AIMER := lambda o s.s + loves + o;
 
-        VOULOIR_CV := lambda vp. Lambda s. s + wants + to + (vp e);
+        VOULOIR_CV := lambda vp. Lambda s. s + wants + to + vp e;
         VOULOIR_SC := lambda sc s. s + wants + sc;
 
 	CHAQUE := lambda n P. P (every + n);

examples/montague.acg

@@ -27,7 +27,7 @@ signature strings =
 	string : type;
 	
 	(* the infix concatenation operator + *)
-	infix + : string -> string -> string;
+	infix [Right] + : string -> string -> string;
 
 	(* the empty string e *)
 	e : string;

examples/tag.acg

@@ -108,7 +108,7 @@ signature strings =
     (* We can define infix and prefix symbols. 
        Note that as for now, the length of symbols can only be 1. *)
     
-    infix + = lambda a b. lambda z. a (b z) : string -> string -> string;
+    infix [Right] + = lambda a b. lambda z. a (b z) : string -> string -> string;
     
     every, dog, chases, a, cat, sleeps, slowly, new, big, black, seems,
     john, mary, bill, paul, claims, loves, to, love, who, said, liked,
@@ -152,6 +152,7 @@ lexicon tag_strings (derived_trees) : strings =
     
     WH1, N1, VP1 := lambda f. f;
     N2, S2, VP2 := lambda f g. f + g;
+    VP2 := (+);
     
 end
 
@@ -177,8 +178,8 @@ signature semantics =
     
     (* And finally, here are the logical constants *)
     
-    infix & : t -> t -> t;	
-    infix > : t -> t -> t;
+    infix [Right] & : t -> t -> t;	
+    infix [Right, < & ] > : t -> t -> t;
     binder All : (e => t) -> t;
     binder Ex : (e => t) -> t;
     
@@ -208,7 +209,9 @@ lexicon tag_semantics (derivation_trees) : semantics =
     C_to_love := lambda s a O S. s (S (a (lambda x. O (lambda y. love x y))));
     C_slowly := lambda vp r. vp (lambda x. slowly (r x));
     C_seems := lambda vp r. vp (lambda x. seem r x);
-    C_new := lambda a n. a (Lambda x. (new x) & (n x));
+    C_new := lambda a n. a (Lambda x. new x & n x);
+    (* Application has precedence over operators such as & *)
+    (* So we can drop the parenthesis *)
     C_big := lambda a n. a (Lambda x. (big x) & (n x));
     C_black := lambda a n. a (Lambda x. (black x) & (n x));
     C_claims := lambda sa a S comp. sa (S (a (lambda x. claim x comp)));

src/acg-data/error.ml

@@ -45,7 +45,7 @@ let bad_infix_usage () =  !infix_as_prefix
 type lex_error =
   | Unstarted_comment
   | Unstarted_bracket
-  | Mismatch_parentheses
+  | Mismatch_parentheses of char
   | Unclosed_comment
   | Expect of string
   | Bad_token
@@ -56,6 +56,7 @@ type parse_error =
   | Duplicated_type of string
   | Binder_expected of string
   | Unknown_constant of string
+  | Not_def_as_infix of string
   | Unknown_constant_nor_variable of string
   | Unknown_constant_nor_type of string
   | Unknown_type of string
@@ -131,7 +132,7 @@ let lex_error_to_string = function
   | Unstarted_comment -> "Syntax error: No comment opened before this closing of comment"
   | Unstarted_bracket -> "Syntax error: No bracket opened before this right bracket"
   | Unclosed_comment -> "Syntax error: Unclosed comment"
-  | Mismatch_parentheses -> "Syntax error: Unclosed parenthesis"
+  | Mismatch_parentheses c -> Printf.sprintf "Syntax error: Unclosed parenthesis '%c'" c
   | Expect s -> Printf.sprintf "Syntax error: %s expected" s
   | Bad_token -> "Lexing error: no such token allowed"
 
@@ -141,6 +142,7 @@ let parse_error_to_string = function
   | Duplicated_term te ->  Printf.sprintf "Syntax error: Term \"%s\" has already been defined" te
   | Binder_expected id -> Printf.sprintf "Syntax error: Unknown binder \"%s\"" id
   | Unknown_constant id -> Printf.sprintf "Syntax error: Unknown constant \"%s\"" id
+  | Not_def_as_infix id -> Printf.sprintf "Syntax error: \"%s\" is not an infix operator" id
   | Unknown_constant_nor_variable id -> Printf.sprintf "Syntax error: Unknown constant or variable \"%s\"" id
   | Unknown_constant_nor_type id -> Printf.sprintf "Syntax error: Unknown constant or type \"%s\"" id
   | Unknown_type id -> Printf.sprintf "Syntax error: Unknown atomic type \"%s\"" id
@@ -148,7 +150,7 @@ let parse_error_to_string = function
   | No_such_signature s -> Printf.sprintf "Syntax error: Signature id \"%s\" not in the current environment" s
   | No_such_lexicon s -> Printf.sprintf "Syntax error: Lexicon id \"%s\" not in the current environment" s
   | Not_associative s -> Printf.sprintf "Syntax error: Operator \"%s\" is not associative but is used without parenthesis" s
-  | Not_infix s -> Printf.sprintf "Syntax error: Operator \"%s\" is not infix bus is used as infix" s
+  | Not_infix s -> Printf.sprintf "Syntax error: Operator \"%s\" is not infix but is used as infix" s
   | Prefix_missing_arg s -> Printf.sprintf "Syntax error: The prefix operator \"%s\" is missing its argument" s
   | Infix_missing_first_arg s  -> Printf.sprintf "Syntax error: The infix operator \"%s\" is missing its first argument" s
   | Infix_missing_second_arg s  -> Printf.sprintf "Syntax error: The infix operator \"%s\" is missing its first argument" s

src/acg-data/error.mli

@@ -26,7 +26,7 @@
 type lex_error =
   | Unstarted_comment
   | Unstarted_bracket
-  | Mismatch_parentheses
+  | Mismatch_parentheses of char
   | Unclosed_comment
   | Expect of string
   | Bad_token
@@ -39,6 +39,7 @@ type parse_error =
   | Duplicated_type of string
   | Binder_expected of string
   | Unknown_constant of string
+  | Not_def_as_infix of string
   | Unknown_constant_nor_variable of string
   | Unknown_constant_nor_type of string
   | Unknown_type of string

src/acg-data/interface.ml

@@ -43,9 +43,9 @@ sig
   (* val find_type : string -> t -> stype *)
   val find_term : string -> t -> term * stype
   val is_type : string -> t -> bool
-  val is_constant : string -> t -> bool*Abstract_syntax.syntactic_behavior option
-  val precedence : string -> t -> (float*Abstract_syntax.associativity) option
-  val new_precedence : t -> (float * t)
+  val is_constant : string -> t -> bool * Abstract_syntax.syntactic_behavior option
+  (*val precedence : string -> t -> (float*Abstract_syntax.associativity) option *)
+  val new_precedence : ?before:string -> string -> t -> (float * t)
   val type_to_string : stype -> t -> string
   val term_to_string : term -> t -> string
   val id_to_string : t -> int -> Abstract_syntax.syntactic_behavior*string

src/acg-data/interface.mli

@@ -80,20 +80,23 @@ sig
       atomic type in [s] and [false] oterwise *)
   val is_type : string -> t -> bool
     
-  (** [is_constant id s] returns [(true,Some b)] together with its
-      syntactic behaviour [b] if [id] is the name of a constant in [s]
-      and [false,None] oterwise *)
+  (** [is_constant id s] returns [(true,Some (b,pred))] together with
+      its syntactic behaviour [b] and its precedence [pred] if [id] is
+      the name of a constant in [s] and [false,None] oterwise *)
   val is_constant : string -> t -> bool * Abstract_syntax.syntactic_behavior option
 
   (** [precedence id s] returns a [Some f] where [f] is float
       indicating the precedence of the infix operator [id]. It returns
       [None] if [id] is not an infix operator. *)
-  val precedence : string -> t -> (float * Abstract_syntax.associativity) option
-
-  (** [new_precedence s] returns a pair consisting of a new precedence
-      value, higher thant any other one in the signature [s], and the
-      new signature taking this new value into account. *)
-  val new_precedence : t -> (float * t)
+  (*  val precedence : string -> t -> (float * Abstract_syntax.associativity) option *)
+
+  (** [new_precedence ?before id s] returns a pair consisting of a new
+      precedence value associated to [id], and the new signature
+      taking this new value into account. If the optional string
+      argument [before] is not provided, then [id] is given the
+      highest precedence so far. Otherwise, it is given the precedence
+      just below [before].*)
+  val new_precedence : ?before:string -> string -> t -> (float * t)
                                         
   (** [type_to_string ty sg] returns the string corresponding to a
       type [ty] of type {!Logic.Lambda.Lambda.stype}) with respect to the

src/acg-data/signature.ml

@@ -49,9 +49,10 @@ struct
 	    size:int;
 	    terms:entry Symbols.t;
 	    types:entry Symbols.t;
+            precedence: (float * string option) Symbols.t ; (* indicates the precedence and a link to the previous one *)
+            max_pred : float * string option ; (* indicates the greatest precedence and a link to the previous one *)
 	    ids:entry Id.t;
 	    is_2nd_order:bool;
-            precedence:float;
 	    extension_timestamp:float;
 	    definition_timestamp:float}
 
@@ -98,7 +99,8 @@ struct
      types=Symbols.empty;
      ids=Id.empty;
      is_2nd_order=true;
-     precedence = 0.;
+     precedence = Symbols.empty;
+     max_pred = 0., None ;
      definition_timestamp=timestamp;
      extension_timestamp=timestamp}
 
@@ -288,23 +290,56 @@ struct
     | _ -> false
     | exception Symbols.Not_found -> false
 				       
-  let is_constant s {terms=syms} =
+  let is_constant s {terms=syms;precedence} =
     match Symbols.find s syms with
     | Term_declaration (_,_,behavior,_) -> true,Some behavior
     | Term_definition (_,_,behavior,_,_) -> true,Some behavior
     | _ -> false,None
     | exception Symbols.Not_found -> false,None
 
-  let precedence s {terms=syms} =
-    match Symbols.find s syms with
-    | Term_declaration (_,_,Infix f,_) -> Some f
-    | Term_definition (_,_,Infix f,_,_) -> Some f
-    | _ -> None
+  let precedence s {precedence} =
+    match Symbols.find s precedence with
+    | f,_ -> Some f
     | exception Symbols.Not_found -> None
 
-  let new_precedence sg =
-    let p = sg.precedence +. 1. in
-    p,{sg with precedence = p}
+  let new_precedence ?before id sg =
+    match before, sg.max_pred with
+    | None, (f, None) ->
+       let p = f +. 1. in
+       p, {sg with
+            max_pred = p, Some id;
+            precedence = Symbols.add id (p,None) sg.precedence}
+    | None, (f, (Some _ as max)) ->
+       let p = f +. 1. in
+       p, {sg with
+            max_pred = p, Some id;
+            precedence = Symbols.add id (p,max) sg.precedence}
+    | Some upper_bound, (f, None) ->
+       (* Strange to give an upper bound when there is no max. Behaves
+          like introducing the first element *)
+       let p = f +. 1. in
+       p, {sg with
+            max_pred = p, Some id;
+            precedence = Symbols.add id (p,None) sg.precedence}
+    | Some upper_bound, _ ->
+       (match Symbols.find upper_bound sg.precedence with
+        | f_up, None ->
+           let f_down = 0. in
+           let p =  (f_up +. f_down)/. 2. in
+           let new_pred =
+             Symbols.add ~overwrite:true upper_bound
+                         (f_up,Some id)
+                         (Symbols.add id (p,None) sg.precedence) in
+             p, {sg with precedence = new_pred}
+        | f_up, Some lower_bound ->
+           let f_down,_ = Symbols.find lower_bound sg.precedence in
+           let p =  (f_up +. f_down)/. 2. in
+           let new_pred =
+             Symbols.add upper_bound
+                         (f_up,Some id)
+                         (Symbols.add id (p,Some lower_bound) sg.precedence) in
+           p, {sg with precedence = new_pred}
+        | exception Not_found -> failwith "Bug: Shouldn't happen")
 			                     
   let add_warnings _ sg = sg
 			   
@@ -430,10 +465,10 @@ module Table = Table.Make_table(struct let b = 10 end)
 
     exception Conflict
     let empty = IntMap.empty
-    let add ?(override=false) k v t = 
+    let add ?(overwrite=false) k v t = 
     try 
     let _ = IntMap.find k t in
-    if override then IntMap.add k v t else raise Conflict
+    if overwrite then IntMap.add k v t else raise Conflict
     with
     | Not_found -> IntMap.add k v t
 

src/data/test-fix.acg

+signature Integer =
+    int : type;
+    infix [Right] + : int -> int -> int ;
+    infix [Left, < +] - : int -> int -> int ;
+    infix [Right] * : int -> int -> int ;
+    infix [NonAssoc] / : int -> int -> int;
+    infix @ : int -> int -> int ;
+    prefix | : int -> int ;
+    prefix ! : int -> int ;
+    a, b, c, d : int;
+    x, y, z : int -> int;
+end
+    
+	
\ No newline at end of file

src/grammars/TODO.parser_bugs

@@ -2,14 +2,14 @@
 
 * DONE Add an optional ";" before the "end" keyword
 * DONE Change lexers to avoid problems with keywords
-* TODO Add precedence values and management in the signature
+* DONE Add precedence values and management in the signature
 * TODO Add (+) notation style to prevent the infix use of +
-* TODO Add syntactic extensions to handle associativity and precedence of infix operators
+* DONE Add syntactic extensions to handle associativity and precedence of infix operators
 * TODO Add error (and warning) messages management to the Error module, and make a difference between "real" parsing errors and errors resulting from evaluating the parsing against some environment. The latter can be output all together (may be some limit to be set)
 * DONE Move from dypgen to menhir in scripts
-* TODO change README and INSTALL files:
+* DONE change README and INSTALL files:
 + [X] to indicate new dependencies (menhir, logs...)
-+ [ ] to document syntax extensions for infix operators, precedence of the latter over application. Highest precedence for prefix operators
-* TODO What about lexicon composition when one lexicon at least is non-linear?
++ [X] to document syntax extensions for infix operators, precedence of the latter over application. Highest precedence for prefix operators
+* DONE What about lexicon composition when one lexicon at least is non-linear?
 * TODO Add debug flag (+ flag for log sources?)
 * TODO Change command line parsing to use Cmd

src/grammars/data_lexer.mll

@@ -25,19 +25,34 @@
 
   let loc lexbuf = Lexing.lexeme_start_p lexbuf,Lexing.lexeme_end_p lexbuf
 
+  type brackets =
+    | Round
+    | Square
+    | Curly
+
   let brackets = ref []
 
-  let add_bracket loc = brackets:=loc::!brackets
+  let kind_to_char = function
+    | Round -> '('
+    | Square -> '['
+    | Curly -> '{'
+                 
+  let add_bracket br loc =
+    brackets:=(loc,br)::!brackets
 
-  let remove_bracket l = match !brackets with
+  let remove_bracket br l =
+    match !brackets with
     | [] -> raise (Error.Error (Error.Lexer_error (Error.Unstarted_bracket, l)))
-    | _::tl -> brackets := tl
+    | (_,k)::tl when k = br -> brackets := tl
+    | (l,k)::_ ->
+       raise (Error.Error (Error.Lexer_error (Error.Mismatch_parentheses (kind_to_char k),l)))
 
   let check_brackets () =
     match !brackets with
       | [] -> ()
-      | (p1,p2)::__ -> let () = brackets := [] in 
-	  raise (Error.Error (Error.Lexer_error (Error.Mismatch_parentheses,(p1,p2))))
+      | (loc,c)::_ ->
+         let () = brackets := [] in 
+	 raise (Error.Error (Error.Lexer_error (Error.Mismatch_parentheses (kind_to_char c),loc)))
                 
   type context =
     | NoContext
@@ -61,7 +76,7 @@ let letter = ['a'-'z' 'A'-'Z'  '
 let digit = ['0'-'9']
 let string = (letter|digit|'_')*'\''*
   
-let symbol = ['|' '!' '"' '#' '$' '%' '&' '\'' '*' '+' '-' '/' '<' '>' '?' '@' '[' '\\' ']' '^' '`' '{' '}' '~' ]
+let symbol = ['|' '!' '"' '#' '$' '%' '&' '\'' '*' '+' '-' '/' '<' '>' '?' '@' '\\' '^' '`'  '~' ]
 let keyword = ("end" | "type" | "prefix" | "infix" | "binder" | "lambda" | "Lambda")
 
 rule lexer =
@@ -118,16 +133,24 @@ rule lexer =
 	       let () = check_brackets () in
 		 Data_parser.COLON(loc lexbuf)}
       | [','] {
-	       let () = check_brackets () in
+            (*	       let () = check_brackets () in *)
 		 Data_parser.COMMA(loc lexbuf)}
       | ['('] {
 	       let l = loc lexbuf in
-	       let () = add_bracket l in
+	       let () = add_bracket Round l in
 		 Data_parser.LPAREN l}
       | [')'] {
 	       let brac_loc = loc lexbuf in
-	       let () = remove_bracket brac_loc in
+	       let () = remove_bracket Round brac_loc in
 		 Data_parser.RPAREN brac_loc}
+      | ['['] {
+	       let l = loc lexbuf in
+	       let () = add_bracket Square l in
+		 Data_parser.LSQBRACKET l}
+      | [']'] {
+	       let brac_loc = loc lexbuf in
+	       let () = remove_bracket Square brac_loc in
+		 Data_parser.RSQBRACKET brac_loc}
       | ['.'] {
 		 Data_parser.DOT(loc lexbuf)}
       | "end" {

src/grammars/dune

@@ -9,9 +9,8 @@
  (modules term_parser_test))
 
 (menhir
-; (flags (--explain --table --compile-errors /home/pogodall/work/dev/ACGtk/src/grammars/data_parser.messages))
  (merge_into data_parser)
- (flags (--explain --table))
+ (flags (--explain --table --strict))
  (modules file_parser sig_parser lex_parser type_parser term_parser))
 
 

src/grammars/messages.ml

@@ -44,95 +44,109 @@ let message =
         "A type expression is expected.\n"
     | 77 ->
         "An equality symbol '=' is expected.\n"
-    | 124 | 78 ->
+    | 141 | 78 ->
         "A signature entry (type declaration, type definition, term declaration, or term definition) is expected.\n"
     | 75 ->
         "A declaration of a signature (keyword 'signature') or of a lexicon (keyword 'lexicon' or 'nl_lexicon') is expected.\n"
-    | 133 ->
+    | 150 ->
         "An identifier (the name of a new lexicon) is expected.\n"
-    | 134 ->
+    | 151 ->
         "A left parenthesis '(' is expected.\n"
-    | 136 ->
+    | 153 ->
         "A right parenthesis ')' is expected.\n"
-    | 137 ->
+    | 154 ->
         "A colon ':' is expected.\n"
-    | 138 ->
+    | 155 ->
         "An identifier (the name of a signature) is expected.\n"
-    | 139 ->
+    | 156 ->
         "An equality symbol '=' is expected.\n"
-    | 141 ->
+    | 158 ->
         "A semi-colon ';' or the 'end' keyword are expected.\n"
-    | 147 ->
+    | 164 ->
         "An identifier (the name of a new lexicon) is expected\n"
-    | 148 ->
+    | 165 ->
         "A left parenthesis '(' is expected.\n"
-    | 149 ->
+    | 166 ->
         "An identifier (the name of a signature) is expected.\n"
-    | 150 ->
+    | 167 ->
         "A right parenthesis ')' is expected.\n"
-    | 151 ->
+    | 168 ->
         "A expression in the form of \": <identifier> =\" where the identifier is the name of a signature is expected.\n"
-    | 152 | 135 | 76 ->
+    | 169 | 152 | 76 ->
         "An identifier (the name of a signature) is expected.\n"
-    | 153 ->
+    | 170 ->
         "An equality symbold '=' is expected.\n"
-    | 154 | 142 | 140 ->
+    | 171 | 159 | 157 ->
         "A lexicon entry of the form \"<term> := <term>;\" or \"<type> := <type>\" is expected.\n"
-    | 157 | 156 ->
+    | 174 | 173 ->
         "An expression representing the composition of lexicons is expected.\n"
-    | 162 ->
+    | 179 ->
         "The composition operator '<<' or a right parenthesis ')' is expected.\n"
-    | 159 | 166 ->
+    | 176 | 183 ->
         "The composition operator '<<' is expected.\n"
-    | 160 ->
+    | 177 ->
         "An identifier (the name of a lexicon), or an expression representing the composition of lexicons is expected.\n"
-    | 172 ->
+    | 189 ->
         "An identifier or a keyword ('infix', 'prefix', or 'binder') is expected.\n"
-    | 87 | 79 ->
+    | 79 ->
         "A symbol is expected.\n"
-    | 88 | 80 ->
-        "A typing judgmenet in the form of \": <type>;\" or a defintion in the form of \"= <term>: <type>;\" is expected.\n"
-    | 89 | 81 ->
+    | 95 ->
+        "An associativity specification (one of the keywords 'Left', 'Right', or 'NonAssoc') or a precedence specification in the form of \"< <sym>\" where \"<sym>\" is an other infix symbol are expected.\n"
+    | 99 ->
+        "A right square bracket ']' or a comma \",\" followed by a precedence specification in the form of \"< <sym>\" where \"<sym>\" is an other infix symbol are expected.\n"
+    | 98 ->
+        "An associativity specification (one of the keywords 'Left', 'Right', or 'NonAssoc') is expected.\n"
+    | 100 ->
+        "A precedence specification in the form of \"< <sym>\" where \"<sym>\" is an other infix symbol is expected.\n"
+    | 97 ->
+        "A right square bracket ']' or a comma ',' followed by an associativity specification (one of the keywords 'Left', 'Right', or 'NonAssoc') are expected.\n"
+    | 96 ->
+        "An identifier is expected.\n"
+    | 87 | 104 ->
+        "A symbol or a declaration of associativity an precedence property are expected.\n"
+    | 88 | 80 | 105 ->
+        "A typing judgement in the form of \": <type>;\" or a defintion in the form of \"= <term>: <type>;\" is expected.\n"
+    | 89 | 81 | 106 ->
         "A typing judgment in the form \"<term> : <type>;\" is expected.\n"
-    | 90 | 82 ->