Solve shift/reduce conflict in the lexer

lexer.mll

@@ -3,11 +3,14 @@
   exception Unexpected_char of char
 }
 
+let id = [ 'a'-'z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* in
+
 rule token = parse
     | [ ' ' '\t' ] { token lexbuf }
     | '\n' { token lexbuf }
-    | '.'([ 'a'-'z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* as s)"<=" { UPDATE (s) }
-    | '.'([ 'a'-'z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* as s) { SELECT (s) }
+    | '.'(id as s)"<=" { UPDATE (s) }
+    | '.'(id as s) { SELECT (s) }
+    | '.'(is as s)":=" { FUPD(s) }
     | '[' { LBRACK }
     | ']' { RBRACK }
     | ':' { COLUMN }
@@ -17,7 +20,6 @@ rule token = parse
     | "ς" { SIGMA }
     | '=' { EQUAL }
     | "::=" { DEF }
-    | ":=" { FUPD }
     | '.' { DOT }
     | "->" { ARR }
     | "λ" { LAMBDA }
@@ -25,7 +27,7 @@ rule token = parse
     | "let" { VAR (Parsing.rhs_start_pos 1) }
     | "check" { CHECK (Parsing.rhs_start_pos 1) }
     | "norm" { NORM (Parsing.rhs_start_pos 1) }
-    | [ 'a'-'z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* as s { ID (s) }
+    | id as s { ID (s) }
     | [ 'A'-'Z' ] ['a'-'z' 'A'-'Z' '_' '0'-'9']* as s { CID (s) }
     | _ as c { raise (Unexpected_char c) }
     | eof { raise End_of_file }

parser.mly

@@ -20,8 +20,8 @@
     Base.labels := insert1 l' !Base.labels; l'
 %}
 
-%token <string> ID CID SELECT UPDATE
-%token LBRACK RBRACK COLUMN SEMICOLUMN LPAR RPAR SIGMA EQUAL DEF DOT FUPD
+%token <string> ID CID SELECT UPDATE FUPD
+%token LBRACK RBRACK COLUMN SEMICOLUMN LPAR RPAR SIGMA EQUAL DEF DOT
 %token LAMBDA ARR
 %token <Lexing.position> TYPE VAR CHECK NORM
 
@@ -63,7 +63,7 @@ term:   obj                               { $1 }
       | LAMBDA LPAR ID COLUMN ty RPAR obj { Abst (Id ($3), $5, $7)}
       | obj SELECT                        { Select ($1, label ($2)) }
       | obj UPDATE meth                   { Update ($1, label ($2), $3) }
-      | obj DOT ID FUPD term              { Field_update ($1, label ($3), $5) }
+      | obj FUPD term                     { Field_update ($1, label ($2), $3) }
 ;
 
 meth:   SIGMA LPAR ID COLUMN ty RPAR term { Method (Id ($3), $5, $7) }