implementing a Type checker for AST -- 2

In Java, write a type-checker for the language specified by the CFG below, with initial variable E: E → INT  |  ID  |  (E BINOP E) | E COMP E  |  BLOCK  |  ID := E | if E then BLOCK else BLOCK | while E do BLOCK | repeat BLOCK until E BLOCK → { ENE } ENE → E  |  E; ENE COMP → ==  |  <  |  >  |  <=  |  >= BINOP → +  |  −  |  *  |  / ID → (an identifier) INT → (an integer) The type-checker is not responsible for constructing an AST for an expression as above, but may take it as input. It is also not responsible for checking that variables are well-defined where they occur: it is allowed to assume that any variable it encounters is well-defined, and has type Int. Your type-checker should assign types as follows: It should assign Int to any identifier, integer, or arithmetic expression on values of type Int; It should assign Bool to any comparison between values of type Int; It should assign Unit to any if statement or any loop, or to any assignment to an identifier; It should assign to any BLOCK, the type of the last expression within that BLOCK. The type-checker should produce a String as output, containing the value "Int", "Bool", or "Unit", as appropriate. The type-checker should throw a TCException if it encounters any of the following: an expression which either involves comparisons / operations / assignments in which one arguments does not have type Int; a conditional / loop with a condition which is not of type Bool; a conditional / loop with a BLOCK expression which is not of type Unit. In the tests that it will be checks against, it should always terminate correctly or throw a TCException; in particular, it should not simply abort if it encounters some other problem.