How to parse a boolean expression - parsing

Question

I'm pretty new to F#, and I'm trying to use recursion to solve a problem.
The function receives a string, and returns a bool. The string gets parsed, and evaluated. This is bool logic, so
(T|F) returns true
(T&(T&T)) returns true
((T|T)&(T&F)) returns false
(F) = returns false
My idea was that every time I found a ), replace the part of the string from the previous ( to that ) with the result of the Comparison match. Doing this over and over until only T or F remains, to return true or false.
EDIT:
I expect it to take the string, and keep swapping out what is in between the ( and ) with the result of the comparison until it comes down to a T or F. What is happening, is an error about an incomplete structured construct. The error is in the for loop.
As I am so new to this language, I'm not sure what I'm doing wrong. Do you see it?
let ComparisonSolver (comp:string) =
let mutable trim = comp
trim <- trim.Replace("(", "")
trim <- trim.Replace(")", "")
match trim with
| "T" -> "T"
| "F" -> "F"
| "!T" -> "F"
| "!F" -> "T"
| "T&T" -> "T"
| "F&F" -> "T"
| "T&F" -> "F"
| "F&T" -> "F"
| "T|T" -> "T"
| "F|F" -> "F"
| "T|F" -> "T"
| "F|T" -> "T"
| _ -> ""
let rec BoolParser arg =
let mutable args = arg
if String.length arg = 1 then
match arg with
| "T" -> true
| "F" -> false
else
let mutable ParseStart = 0
let endRange = String.length args
for letter in [0 .. endRange]
if args.[letter] = "(" then
ParseStart <- letter
else if args.[letter] = ")" then
args <- args.Replace(args.[ParseStart .. letter], ComparisonSolver args.[ParseStart .. letter])
BoolParser args
let result = BoolParser "(T)&(F)"

Answer 1

There are a few things you need to correct.
for letter in [0 .. endRange] is missing a do at the end of it - it should be for letter in [0 .. endRange] do
The if comparisons in the for loop are comparing chars with strings. You need to replace "(" and ")" with '(' and ')'
for letter in [0 .. endRange] will go out of range: In F# the array construct [x..y] will go from x to y inclusive. It's a bit like in C# if you had for (int i = 0; i <= array.Length; i++). In F# you can also declare loops like this: for i = 0 to endRange - 1 do.
for letter in [0 .. endRange] will go out of range again: It's going from 0 to endrange, which is the length of args. But args is getting shortened in the for loop, so it will eventually try to get a character from args that's out of range.
Now, the problem with the if..then..else statements, which is what I think you were looking at from the beginning.
if args.[letter] = '(' then
ParseStart <- letter
else if args.[letter] = ')' then
args <- args.Replace(args.[ParseStart .. letter], ComparisonSolver args.[ParseStart .. letter])
BoolParser args
Let's take the code within the two branches as two separate functions.
The first does ParseStart <- letter, which assigns letter to ParseStart. This function returns unit, which is F# equivalent of void.
The second does:
args <- args.Replace(args.[ParseStart .. letter], ComparisonSolver args.[ParseStart .. letter])
BoolParser args
This function returns a bool.
Now when you put them together in an if..then..else statement you have in one branch that results a unit and in the other in a bool. In this case it doesn't know which one to return, so it shows an "expression was expected to have type" error.
I strongly suspect that you wanted to call BoolParser args from outside
the for/if loop. But it's been indented so that F# treats it as part of the else if statement.

Answer 2

There are many ways to parse a boolean expression. It might be a good idea to look at the excellent library FParsec.
http://www.quanttec.com/fparsec/
Another way to implement parsers in F# is to use Active Patterns which can make for readable code
https://learn.microsoft.com/en-us/dotnet/fsharp/language-reference/active-patterns
It's hard to provide good error reporting through Active Patterns but perhaps you can find some inpiration from the following example:
let next s i = struct (s, i) |> Some
// Skips whitespace characters
let (|SkipWhitespace|_|) struct (s, i) =
let rec loop j =
if j < String.length s && s.[j] = ' ' then
loop (j + 1)
else
next s j
loop i
// Matches a specific character: ch
let (|Char|_|) ch struct (s, i) =
if i < String.length s && s.[i] = ch then
next s (i + 1)
else
None
// Matches a specific character: ch
// and skips trailing whitespaces
let (|Token|_|) ch =
function
| Char ch (SkipWhitespace ps) -> Some ps
| _ -> None
// Parses the boolean expressions
let parse s =
let rec term =
function
| Token 'T' ps -> Some (true, ps)
| Token 'F' ps -> Some (false, ps)
| Token '(' (Parse (v, Token ')' ps)) -> Some (v, ps)
| _ -> None
and opReducer p ch reducer =
let (|P|_|) ps = p ps
let rec loop l =
function
| Token ch (P (r, ps)) -> loop (reducer l r) ps
| Token ch _ -> None
| ps -> Some (l, ps)
function
| P (l, ps) -> loop l ps
| _ -> None
and andExpression ps = opReducer term '&' (&&) ps
and orExpression ps = opReducer andExpression '|' (||) ps
and parse ps = orExpression ps
and (|Parse|_|) ps = parse ps
match (struct (s, 0)) with
| SkipWhitespace (Parse (v, _)) -> Some v
| _ -> None
module Tests =
// FsCheck allows us to get better confidence in that the parser actually works
open FsCheck
type Whitespace =
| Space
type Ws = Ws of (Whitespace [])*(Whitespace [])
type Expression =
| Term of Ws*bool
| And of Expression*Ws*Expression
| Or of Expression*Ws*Expression
override x.ToString () =
let orPrio = 1
let andPrio = 2
let sb = System.Text.StringBuilder 16
let ch c = sb.Append (c : char) |> ignore
let token (Ws (l, r)) c =
sb.Append (' ', l.Length) |> ignore
sb.Append (c : char) |> ignore
sb.Append (' ', r.Length) |> ignore
let enclose p1 p2 f =
if p1 > p2 then ch '('; f (); ch ')'
else f ()
let rec loop prio =
function
| Term (ws, v) -> token ws (if v then 'T' else 'F')
| And (l, ws, r) -> enclose prio andPrio <| fun () -> loop andPrio l; token ws '&' ;loop andPrio r
| Or (l, ws, r) -> enclose prio orPrio <| fun () -> loop orPrio l ; token ws '|' ;loop orPrio r
loop andPrio x
sb.ToString ()
member x.ToBool () =
let rec loop =
function
| Term (_, v) -> v
| And (l, _, r) -> loop l && loop r
| Or (l, _, r) -> loop l || loop r
loop x
type Properties() =
static member ``Parsing expression shall succeed`` (expr : Expression) =
let expected = expr.ToBool () |> Some
let str = expr.ToString ()
let actual = str |> parse
expected = actual
let fscheck () =
let config = { Config.Quick with MaxTest = 1000; MaxRejected = 1000 }
Check.All<Properties> config