// NuGet package is available.
#r "nuget: TypeInferencer"

open TypeInferencer

// `let id = fun x -> x in id id`
let expr =
    ELet("id",
        EAbs("x", EVar "x"),
        EApp(EVar "id", EVar "id"))

// Type environment (is empty)
let env = TypeEnv []

// Do inferring with `Algorithm W` (top-down)
let actual = infer TopDown env expr

// `a -> a`
System.Diagnostics.Debug.Assert(
    match actual with
    | TFun(TVar n1, TVar n2) when n1 = n2 -> true
    | _ -> false
)

// Pretty printing
printfn "Expression: %s" (show expr)
printfn "Actual: %s" (show actual)

Expression: let id = fun x -> x in id id
Actual: a3 -> a3

type public Lit =
    | LInt of value:int32
    | LBool of value:bool

type public Exp =
    | EVar of name:string
    | ELit of literal:Lit
    | EApp of func:Exp * arg:Exp
    | EAbs of name:string * expr:Exp
    | ELet of name:string * expr:Exp * body:Exp
    | EFix of func:string * name:string * expr:Exp

type public Type =
    | TVar of name:string
    | TInt
    | TBool
    | TFun of parameterType:Type * resultType:Type

type public InferAlgorithm =
    | TopDown
    | BottomUp

[<AutoOpen>]
module public Inferencer =
    let infer: InferAlgorithm -> TypeEnv -> Exp -> Type