Hey everyone! Yesterday, I posted about an assignment I got for parsing logical propositions. After a lot of research and trying different things, I got it to work for individual propositions: going from a string to my own custom type Proposition. However, now I am at a complete roadblock - I have almost no idea how to combine these components to work for more complex propositions. I am not even sure whether they are suitable to be combined and work together. You will the code and the screenshot of my current output below, any advice / ways for approaching this would be greatly appreciated!

```
type Proposition
= A
| B
| C
| And Proposition Proposition
| Or Proposition Proposition
| Implies Proposition Proposition
| Not Proposition
| Equal Proposition Proposition
andParser : Parser Proposition
andParser =
oneOf
[ succeed A
|. keyword "A"
, succeed B
|. keyword "B"
, succeed C
|. keyword "C"
, succeed And
|. symbol "&"
|. spaces
|. symbol "("
|. spaces
|= lazy (\_ -> andParser)
|. spaces
|. symbol ","
|. spaces
|= lazy (\_ -> andParser)
|. spaces
|. symbol ")"
]
orParser : Parser Proposition
orParser =
oneOf
[ succeed A
|. keyword "A"
, succeed B
|. keyword "B"
, succeed C
|. keyword "C"
, succeed Or
|. symbol "|"
|. spaces
|. symbol "("
|. spaces
|= lazy (\_ -> orParser)
|. spaces
|. symbol ","
|. spaces
|= lazy (\_ -> orParser)
|. spaces
|. symbol ")"
]
implParser : Parser Proposition
implParser =
oneOf
[ succeed A
|. keyword "A"
, succeed B
|. keyword "B"
, succeed C
|. keyword "C"
, succeed Implies
|. symbol ">"
|. spaces
|. symbol "("
|. spaces
|= lazy (\_ -> implParser)
|. spaces
|. symbol ","
|. spaces
|= lazy (\_ -> implParser)
|. spaces
|. symbol ")"
]
equalParser : Parser Proposition
equalParser =
oneOf
[ succeed A
|. keyword "A"
, succeed B
|. keyword "B"
, succeed C
|. keyword "C"
, succeed Equal
|. symbol "="
|. spaces
|. symbol "("
|. spaces
|= lazy (\_ -> equalParser)
|. spaces
|. symbol ","
|. spaces
|= lazy (\_ -> equalParser)
|. spaces
|. symbol ")"
]
notParser : Parser Proposition
notParser =
oneOf
[ succeed A
|. keyword "A"
, succeed B
|. keyword "B"
, succeed C
|. keyword "C"
, succeed Not
|. symbol "N"
|. symbol "("
|. spaces
|= lazy (\_ -> notParser)
|. spaces
|. symbol ")"
]
my_results: List String
my_results =
[ "and parser test ____& (A , B)______",
pr <| Parser.run andParser "& (A , C)",
"or parser test ____ | (A , B) ______",
pr <| Parser.run orParser "| (A , B)",
"implies parser test ____ > (A , B) ______",
pr <| Parser.run implParser "> (A , B)",
"equal parser test ____ = (A , B) ______",
pr <| Parser.run equalParser "= (A , B)",
"equal parser test ____ N ( A ) ______",
pr <| Parser.run notParser "N(B)",
"parsing & ( N (B) ) C",
pr <| Parser.run andParser "& ( A, N(B) ) "
]
```