Starting with NAND only...

logicGates.fs

type LogicGate =
    | ON
    | OFF
    | NAND of LogicGate * LogicGate
    | NOT  of LogicGate
    | AND  of LogicGate * LogicGate
    | OR   of LogicGate * LogicGate
    | NOR  of LogicGate * LogicGate
    | XOR  of LogicGate * LogicGate
    | XNOR of LogicGate * LogicGate

let rec evaluate input =
    match input with
    | ON         -> true
    | OFF        -> false
    | NAND(a, b) -> not (evaluate a && evaluate b)
    | NOT(a)     -> evaluate (NAND(a, a))
    | AND(a, b)  -> evaluate (NOT(NAND(a, b)))
    | OR(a, b)   -> evaluate (NAND(NOT(a), NOT(b)))
    | NOR(a, b)  -> evaluate (NOT(OR(a, b)))
    | XOR(a, b)  -> evaluate (AND(NAND(a, b), OR(a, b)))
    | XNOR(a, b) -> evaluate (NOT(XOR(a, b)))

[
    NAND(OFF, OFF);
    NAND(OFF, ON);
    NAND(ON,  OFF);
    NAND(ON,  ON)
] |> List.map (fun x -> printfn (evaluate x))