let rec eval t =
try let t' = eval1 t
in eval t'
with NoRuleApplies -> t
Where eval1 is a single step evaluation of the abstract syntax tree, and NoRuleApplies is an exception that's raised if there are no rules that can reduce the _expression_. Now, there's a footnote that it isn't good style in ML. It seems even less natural in Haskell, at least to me, but I still don't know the language that well.
The natural equivalent to what Pierce has in ML is something along the lines of
data ArithExpr
= TmTrue
| TmFalse
| TmIfExpr ArithExpr ArithExpr ArithExpr
| TmZero
| TmSucc ArithExpr
| TmPred ArithExpr
| TmIsZero ArithExpr
deriving (Show, Eq)
eval1 :: ArithExpr -> ArithExpr
eval1 (TmIfExpr TmTrue t _) = t
eval1 (TmIfExpr TmFalse _ t) = t
eval1 (TmIfExpr t1 t2 t3) =
let t1' = eval1 t1
in TmIfExpr t1' t2 t3
-- and so on
But, how to terminate the recursion in the full eval?
I'm considering changing eval1 to be ArithExpr->Maybe ArithExpr
If the _expression_ is reducible, then I return Just t, and if it's not reducible, then Nothing
It makes eval1 a bit more complicated, and not as straightforward translation from the type system being described, though.
e.g reducing If looks more like
eval1 (TmIfExpr t1 t2 t3) =
let t1' = eval1 t1
in case t1' of
{ Just t1'' -> Just $ TmIfExpr t1'' t2 t3
; Nothing -> Nothing
}
and eval then looks like
eval t =
let t' = eval1 t
in case t' of
{ Just t'' -> eval t''
; Nothing -> t'
}
I'm looking for some suggestions on the direction to proceed.
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