(programming required) In the programming language ML (see Figure 5.34 for more), write a program to translate an arbitrary statement of propositional logic into a logically equivalent statement that...

(programming required) In the programming language ML (see Figure 5.34 for more), write a program to translate an arbitrary statement of propositional logic into a logically equivalent statement that has the following special form. (In other words, implement the proof of Exercises 5.94 and 5.95 as a recursive function.)

1.| is the only logical connective

2. ↓ is the only logical connective

Exercises 5.94

Recall Example 5.18, in which we defined a well-formed formula (a “wff”) of propositional logic as a variable; the negation (¬) of a wff; or the conjunction/disjunction/implication (∧, ∨, and ⇒) of two wffs. Assuming we allow the corresponding new connective in the following exercises as part of a wff, give a proof using structural induction (see Example 5.21 for an example) that any wff is logically equivalent to one using only . .