Multiplexer

Write a function of type:

mux2 : bool -> bool -> bool -> bool

such that mux2 s0 a b equals to a if s0 is true, otherwise it equals to b.

Try with different implementation styles, using:

the built-in logical connectives not, &&, ||;
conditional expressions;
pattern matching.

Then, write a function of type:

mux4 : bool -> bool -> bool -> bool -> bool -> bool -> bool

such that mux4 s1 s0 a0 a1 a2 a3 equals to ai if s1 s0 is the binary encoding of i.

The function mux4 must pass the following unit tests:

assert(mux4 false false false true false true = false);;
assert(mux4 false true false true false true = true);;
assert(mux4 true false false true false true = false);;
assert(mux4 true true false true false true = true);;

In the implementation of mux4, try to reuse mux2.