let binary = function '*' -> (*) | '+' -> (+) | _ -> (-)
let appendOp ((ll, lrs), rs) v = function
    | '*' as op -> (v, (binary op, ll)::lrs), rs
    | op -> (v, []), (binary op, (ll, lrs))::rs
 
let evalOp eval (x, xs) = List.foldBack (fun ((@), l) r -> eval l @ r) xs (eval x)
let eval = evalOp <| evalOp id
let literal x = (x, []), []
let replaceHead v ((_, lrs), rs) = (v, lrs), rs
 
let step (expr, view, op) = function
    | '=' ->  let view = eval expr in literal view, view, Some '='
    | c when '0' <= c && c <= '9' ->
        let d = int c - int '0'
        match op with
        | Some '=' -> literal d, d, None
        | Some op -> appendOp expr d op, d, None
        | None ->
            let view = view * 10 + d
            replaceHead view expr, view, None
 
    | op -> expr, (eval expr), Some op
 
let calc = Seq.fold step (literal 0, 0, None) >> fun (_,v,_) -> string v
 
let (=>) src exp = 
    let act = calc src
    let msg = if act = exp then "ok" else "error" 
    printfn "%s { src = %A, exp = %A, act = %A }" msg src exp act
 
// お題：電卓を実装する
// 引数はボタン入力履歴で、戻り値は現在の表示
// ボタンは 0123456789-+*= のみ
"5" => "5"
"5+" => "5"
"5+3" => "3"
"5+3=" => "8"
 
"5*-3=" => "2" // 最後に入力した演算子が有効
"5-3+" => "2" // 途中結果を表示する
"5-3*2=" => "-1" // -+ よりも * が優先される
 
// 初期値は 0
"" => "0"
"-10=" => "-10"
"*10=" => "0"
 
"4+3=2=" => "2" // = の次に数値が入力された場合、途中結果は捨てる
"4+3=*2=" => "14" // * よりも = が優先される

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