BuildAllFormulasInterpritations

    let BuildAllFormulasInterpritations formulaCalcList =
        let vars =
            formulaCalcList
            |> List.filter (function
                | Formula.Var (_) -> true
                | _ -> false)

        let data = List.init vars.Length (fun _ -> [ true; false ])
        cartList data

There are only two steps to calculate all possible interpretations for a formula in the propositional logic.

1. Filter out all non-variable elements.
2. Build a cartesian product for a list length of (1.) with the possible values as a parameter.

P.S. to expand the function for a modal logic the function to retrieve possible combinations for a input set from fun _ -> [ true; false ] to fun _ -> [ true; semitrue; false; semifalse ]

Example

Input:

    [0]: Var "P"
    [1]: Var "Q"
    [2]: Var "R"
    [3]: Var "S"
    [4]: Neg (Var "S")
    [5]: Conj (Var "P", Var "Q")
    [6]: Bic (Var "R", Neg (Var "S"))
    [7]: Impl (Conj (Var "P", Var "Q"), Bic (Var ..., ...))
    _FullList: {SharpLogic.Formula.Formula[8]}

Output:

    [0]: Length = 4
    [1]: Length = 4
    [2]: Length = 4
    [3]: Length = 4
    [4]: Length = 4
    [5]: Length = 4
    [6]: Length = 4
    [7]: Length = 4
    [8]: Length = 4
    [9]: Length = 4
    [10]: Length = 4
    [11]: Length = 4
    [12]: Length = 4
    [13]: Length = 4
    [14]: Length = 4
    [15]: Length = 4
    _FullList: {Microsoft.FSharp.Collections.FSharpList<bool>[16]}

each element is

Length = 4
    [0]: true
    [1]: true
    [2]: true
    [3]: true
    _FullList: {bool[4]}

with all possible combinations according to cartesian product 2^n

Usage

let formulaInterpritations = BuildAllFormulasInterpritations formulas