Sheet10 - McMaster University Department of Computing and...

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McMaster University Department of Computing and Software Dr. W. Kahl COMP SCI 1FC3 Exercise Sheet 10 COMP SCI 1FC3 — Mathematics for Computing 27 March 2009 Exercise 10.1 — Syntax Trees for Propositional Logic The assignment generator for Assignment 1 used (a variant of) the following Haskell datatype to represent formulae of propositional logic (see also textbook section 4.3 p. 301and p. 305): data PropForm = Var String | FF | TT | Negation PropForm | Conjunction PropForm PropForm | Disjunction PropForm PropForm | Implication PropForm PropForm | Biimplication PropForm PropForm | ExclusiveOr PropForm PropForm deriving ( Eq , Ord ) (a) Define Haskell values f1 , f2 , f3 , f4 :: PropForm representing the formulae F T ”, “ p p ”, “ p q p q ”, and “ p ∧ ¬ q ↔ ¬( p q ) ”. (b) Implement the function subformulae :: PropForm -> [ PropForm ] which computes all subformulae of its argument. For example, the subformulae of “ p q p ” are “ p ”, “ q ”, “ p q ”, and “ p q p ”.
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