The current K LAMBDA semantics of mu $($in Lesson $8)$ is based on substitution, and then letrec is defined as a derived operation using mu$.$ Give mu a different semantics, as a derived construct by translation into other LAMBDA constructs, like we defined letrec in Lesson $7.$ To test it$,$ use the same definition of letrec in terms of mu $($from Lesson $8)$ and write $3$ recursive programs, like the provided factorial$-$letrec.lambda. Note: See the mu$-$derived exercise in the nightly built for details and test programs. Exercise $2(10$ points$)$: Modify the K definition of IMP to not automatically initialize variables to $0.$ Instead, declared variables should stay uninitialized until assigned a value, and the execution should get stuck when an uninitialized variable is looked up$.$ Note: See the uninitialized$-$variables exercise in the nightly built for details and test programs. Exercise $3(10$ points$)$: Mofify IMP so that the K $$followed by$$ arrow, ~$>,$ does not explicitly occur in the definition $($it currently occurs in the semantics of sequential composition$).$ Hint: make sequential composition strict$(1)$ or seqstrict, and have statements reduce to $\{\}$ instead of $.,...$ and don$$t forget to make $\{\}$ a KResult $($you may need a new syntactic category for that, which only includes $\{\}$ and is included in KResult$).$ Note: See the purely$-$syntactic exercise in the nightly built for details and test programs. Exercise $4(10$ points$)$: Define a variant of callcc, say callCC, which never returns to the current continuation unless a value is specifically passed to that continuation. Can you define them in terms of each other? Pick one of the substitution versus the environment$-$based definitions $($get extra$-$credit if you do both$).$ Note: See the callCC $($substitution$),$ from$-$call$-$CC$-$to$-$callcc $($substitution$),$ from$-$callcc$-$to$-$call$-$CC$($substitution$),$ callCC $($environment$),$ from$-$call$-$CC$-$to$-$callcc $($environment$),$ and from$-$callcc$-$to$-$call$-$CC $($environment$)$ exercises in the nightly built for details and test programs. Exercise $5(10$ points$)$: The current halt; statement of IMP$++$ only halts the current thread. Define an abort; statement which halts the entire program.