(*
//
// Course: BU CAS CS 520
// Instructor: Hongwei Xi (hwxi AT cs DOT bu DOT edu)
// This file is for Assignment 3, BU CAS CS 520, Fall, 2010
//
*)

(* ****** ****** *)

datatype Utm = (* for untyped alpha-normal forms *)
  | UTMind of int
  | UTMvar of string
  | UTMlam of Utm
  | UTMapp of (Utm, Utm)
  | UTMlet of (Utm, Utm)
  | UTMfix of Utm
  | UTMint of int
  | UTMbool of bool
  | UTMstr of string
  | UTMopr of (string, Utmlst)
  | UTMif of (Utm, Utm, Utm)
// end of [Utm]

where Utmlst = list0 Utm

datatype Val =
  | VALint of int
  | VALbool of bool
  | VALstr of string
  | VALvoid of ()
  | VALclo of (Utm, Env) // for representing closures
  | VALfix of (Utm, Env) // for handling fix // fix f(x).e => lam x.e[f->fix...]
// end of [Val]

where Env = list0 (Val)

(* ****** ****** *)
//
// As an example, the following term defines a function that
// doubles its argument (which represents an integer), that is
// lam x. x + x:
// UTMlam (UTMopr ("+", cons (UTMind 1, cons (UTMind 1, nil))))
//
// As another example, the following term represents fix f(x). f(x):
// UTMfix (UTMapp (UTMind(2), UTMind(1)))
//
(* ****** ****** *)
//
// 10 points
// Please construct a term [TALLY] which represents the tally
// function presented in class
//
(*
// concrete syntax:
TALLY = fix f(x). if x > 0 then x + f(x-1) else 0
*)
val TALLY : Utm

(* ****** ****** *)
//
// 10 points
// Please construct a term [ISPRIME] which represents a function
// that checks whether a given natural number is a prime.
//
val ISPRIME : Utm

(* ****** ****** *)
//
// 40 points
// Please implement a function [utmeval] which evaluates a term
// to a value according to the call-by-value semantics
//
fun utmeval (u: Utm): Val

(* ****** ****** *)

(* end of [utmeval.sats] *)