(* calc1.ml: original calculator from Week7, enhanced with Booleans and Immutable Pairs *) type term = Intconstant of int | Multiplication of (term * term) | Addition of (term * term) | Variable of char | Let of (char * term * term) | Iszero of term | If of (term * term * term) | Makepair of (term * term) | First of term ;; type expressed_value = Int of int | Bool of bool | Pair of expressed_value * expressed_value;; type bound_value = expressed_value;; type assignment = (char * bound_value) list;; let rec eval (t : term) (g : assignment) = match t with Intconstant x -> Int x | Multiplication (t1, t2) -> (* we don't handle cases where the subterms don't evaluate to Ints *) let Int i1 = eval t1 g in let Int i2 = eval t2 g (* Multiplication (t1, t2) should evaluate to an Int *) in Int (i1 * i2) | Addition (t1, t2) -> let Int i1 = eval t1 g in let Int i2 = eval t2 g in Int (i1 + i2) | Variable (var) -> (* we don't handle cases where g doesn't bind var to any value *) List.assoc var g | Let (var_to_bind, t2, t3) -> (* evaluate t3 under a new assignment where var_to_bind has been bound to the result of evaluating t2 under the current assignment *) let value2 = eval t2 g in let g' = (var_to_bind, value2) :: g in eval t3 g' | Iszero (t1) -> (* we don't handle cases where t1 doesn't evaluate to an Int *) let Int i1 = eval t1 g (* Iszero t1 should evaluate to a Bool *) in Bool (i1 = 0) | If (t1, t2, t3) -> (* we don't handle cases where t1 doesn't evaluate to a boolean *) let Bool b1 = eval t1 g in if b1 then eval t2 g else eval t3 g | Makepair (t1, t2) -> let value1 = eval t1 g in let value2 = eval t2 g in Pair (value1, value2) | First (t1) -> (* we don't handle cases where t1 doesn't evaluate to a Pair *) let Pair (value1, value2) = eval t1 g in value1 ;;