compiler in while language using WIDE IDE

1- Let s : N ! N? be the successor function on natural numbers defined as follows: s(n) = n + 1. Note that s does always terminate. Let the following WHILE program P be given: read X Y:= cons nil X write Y Define an encoding c such that [[P]]WHILE implements s via c. Explain what conditions your c needs to fulfill and show that those conditions actually hold (Note that this is quite easy in this case). 2- Let W0 be the following sublanguage of WHILE: W0 contains all WHILE programs that use variable 0 as output variable. Write a compiler [login to view URL] from WHILE to W0. This compiler takes a WHILE program (in list notation) as input and returns a WHILE program (in list notation) that behaves identically but uses variable 0 as output variable. [Note that this is an extremely simple compiler which does not require complex tree traversal.] 3- Write a compiler [login to view URL] which translates WHILE programs into I-programs, ie WHILE programs that only use one variable, namely var 0. Your program should call the following auxiliary functions: While2l [login to view URL] , Number [login to view URL] , and [login to view URL] which is attached. Your compiler only needs to traverse commands (once you hit an expression you can call While2l [login to view URL]). Your compiler should not have more than about 70 lines of code (not counting comments). Note that such non-trivial programs which call other non-trivial programs may take some time in WIDE to compile (on my old machine about a minute or so). Don’t forget to test your compiler on several input programs. Add comments to your program where useful.