我试图用变量范围表示公式,例如,公式或变量和常量:
R(a,b) -> Q [Q takes formulae as substitutions]
R(x,b) v P(b) [x takes constants or variables as substitutions]
公式上的函数具有类约束,用于指定正在考虑的变量类型。例如,术语,变量和替换类可能具有以下结构:
class Var b where ...
class (Var b) => Term b a | b -> a where ...
class (Term b a) => Subst s b a | b a -> s where ...
有许多算法处理句法术语操作,对变量类型的参数化术语类型将是有益的。例如,考虑对具有不同变量类型的某些术语类型的公式的通用统一算法:
unify :: (Subst s b a) => a -> a -> s b a
unify (P -> F(a,b)) ((Q v R) -> F(a,b)) = {P\(Q v R)} -- formulae
unify (P(x,f(a,b))) (P(g(c),f(y,b))) = {x\g(c),y\a} -- variables and constants
表示此类变量变量的最佳方式是什么?我已经尝试了各种方法,但尚未确定令人满意的解决方案。
答案 0 :(得分:4)
如果你说下面简单的术语和公式表示出了什么问题,也许你的问题会更清楚?有一百万种方法可以做这种事情(由{-LANGUAGE GADTs-}
扩展的可能性很大)
{-#LANGUAGE TypeOperators#-}
data Term v c = Var v
| Const c deriving (Show, Eq, Ord)
data Formula p v c = Atom p
| Term v c := Term v c
| Formula p v c :-> Formula p v c
| Not (Formula p v c)
| Subst v (Term v c) (Formula p v c)
| Inst p (Formula p v c) (Formula p v c)
deriving (Show, Eq, Ord)
update f v c v' = case v == v' of True -> c; False -> f v'
one = Const (1:: Int)
zero = Const (0 :: Int)
x = Var 'x'
y = Var 'y'
p = Atom 'p'
q = Atom 'q'
absurd = one := zero
brouwer p = (((p :-> absurd) :-> absurd) :-> absurd) :-> (p :-> absurd)
ref :: (v -> c) -> Term v c -> c
ref i (Var v) = i v
ref i (Const c) = c
eval :: (Eq c , Eq v , Eq p) => (v -> c) -> (p -> Bool) -> Formula p v c -> Bool
eval i j (Atom p) = j p
eval i j (p := q) = ref i p == ref i q
eval i j (p :-> q) = not ( eval i j p) || eval i j q
eval i j (Not p) = not (eval i j p)
eval i j q@(Subst v t p) = eval (update i v (ref i t)) j q
eval i j q@(Inst p r s) = eval i (update j p (eval i j r)) s