first draft MSO lark

parsers/logic.lark

+formula : formula or formula 
+        | formula and formula 
+        | formula implies formula 
+        | formulas ssi formula 
+        | all1 formulas 
+        | all2 formulas 
+        | exists1 formulas 
+        | exists2 formulas 
+        | mod formulas 
+        | atoms
+
+or      : "OR" | "|" | "∨"
+and     : "AND | "&" | "∧"
+implies : "implies" | "->" 
+ssi     : "ssi"     | "<->"
+all1    : ("All"    | "A"  | "∀" ) vardef ":" formula
+all2    : ("All2"   | "A2" | "∀2") vardef ":" formula
+exists1 : ("Exists" | "E"  | "∃" ) vardef ":" formula
+exists2 : ("Exists2"| "E2" | "∃2") vardef ":" formula
+mod     : "Mod(" (integer",")? integer")"  var1def ":" formula
+integer : INT   -> number
+string  : CNAME -> str
+
+vardef: (identifier ",")* identifier
+identifier: string
+
+atoms   : numerical_predicates
+        | descriptive_predicates
+        | set_predicates
+
+
+constantes : max | min | emptyset | fullset
+max : "max"
+min : "min"
+emptyset : "∅" | "Empty"
+fullset  : "FULL"
+
+value : identifier | constantes | functional_operation
+
+functional_operation : value "+" integer
+                     | "letter(" value ")"
+
+numerical_predicates : value "<" value 
+                     | value "<=" value
+                     | value ">" value
+                     | value ">=" value
+                     | value "=" value
+                     | value "=" value
+                     | value "!=" value
+                     | value "+" integer "=" value
+                     | integer  "+" value "=" value
+                     | (integer | value) "=" (integer | value) "%" integer
+                     | value "%" integer
+
+descriptive_predicates : letter_predicate | word_predicate
+
+letter_predicate    : LETTER "(" value ")"
+                    | \l "(" hash ")" "(" value ")"
+                    | \l tuple "(" value ")"
+
+
+word_predicate      : LETTER+ "(" value ")"
+                    | \w "(" (Hashable | SetOfHashable)+ ")"
+                    | \W "(" (Hashable | SetOfHashable)+ ")"
+
+set_predicates      : value ("in" | "∈") identifier
+                    | identifier ("contains" | "⊂") identifier
+                    | "Union(" (identifier ",")* identifier ")" 
+                    | identifier "∪" identifier
+                    | "Intersection(" (identifier ",")* identifier ")"
+                    | identifier "∩" identifier
+                    | "Partition(" (identifier ",")* identifier ")"
+
+%import utils.hashable
+%import utils.tuple
+        
+
+%import common.LETTER
+%import common.CNAME
+%import common.INT
+%import common.WS
+%ignore WS