-- | data type definition of WFF: well formed formula
data Wff = Var String
| Not Wff
| And Wff Wff
| Or Wff Wff
| Imply Wff Wff
-- | Negation norm form nnf function
-- precondition: φ is implication free
-- postcondition: NNF (φ) computes a NNF for φ
nnf :: Wff -> Wff
nnf (Var p) = Var p
nnf (Not (Not p)) = (nnf p)
nnf (And p q) = And (nnf p) (nnf q)
nnf (Or p q) = Or (nnf p) (nnf q)
nnf (Not (And p q)) = Or (nnf(Not p)) (nnf(Not q))
nnf (Not (Or p q)) = And (nnf(Not p)) (nnf(Not q))
测试用例:¬( p ∨ Q )
(*** Exception:: Non-exhaustive patterns in function nnf
但是,如果我将nnf (Not p) = Not (nnf p)
添加到该函数中,它将显示
Pattern match(es) are overlapped
In an equation for ‘nnf’:
nnf (Not (Not p)) = ...
nnf (Not (And p q)) = ...
nnf (Not (Or p q)) = ...
我想知道我做错了什么?
答案 0 :(得分:2)
您只是将线路插入错误的位置。 nnf (Not p) = ...
是一个否定的全能。如果您稍后添加其他处理更具体否定的条款,例如Not (And p q)
,则它们可能不再触发。
包罗万象的条款需要最后,即
nnf (Var p) = Var p
nnf (Not (Not p)) = (nnf p)
nnf (And p q) = And (nnf p) (nnf q)
nnf (Or p q) = Or (nnf p) (nnf q)
nnf (Not (And p q)) = Or (nnf $ Not p) (nnf $ Not q)
nnf (Not (Or p q)) = And (nnf $ Not p) (nnf $ Not q)
nnf (Not p) = Not $ nnf p