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• a boolean constant true or false;
• a symbol S;
• (list 'not X) where X is a bool-SchemeExp ;
• (list op X Y) where op is 'and , 'or , or 'implies where X and Y are {{bool-SchemeExp}}sSchemeExps;
• (list 'if X Y Z) where X, Y, and Z are {{bool-SchemeExp}}sSchemeExps.

The provided functions parse and unparse have the following signatures.

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We suggest simply traversing the tree using the structural recursion template for type boolExp and converting all structures (other than if}}s) to the corresponding {{if structures.

Write an inductive data definition and template for boolean formulas in if form, naming this type ifExp. (Note: make-If is the only constructor, other than variables and constants, for ifExp.

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