Past exam of the computer science course of the University of Oxford / 2015 / Principles of programming languages / 1 / d / Solution 2026-10-31
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There is one undifferentiated exception, so use the two alternatives of the Haskell algebraic data type Maybe: Just x succeeds and Nothing fails. A suitable exception monad transformer is:
type ExT m a = m (Maybe a)

result :: Monad m => a -> ExT m a
result x = resultM (Just x)

bind :: Monad m => ExT m a -> (a -> ExT m b) -> ExT m b
bind p f = bindM p (\r -> case r of
  Nothing -> resultM Nothing
  Just x  -> f x)

orelse :: Monad m => ExT m a -> ExT m a -> ExT m a
orelse p q = bindM p (\r -> case r of
  Nothing -> q
  Just x  -> resultM (Just x))

failure :: Monad m => ExT m a
failure = resultM Nothing
The distinction between bindM and bind matters. The handler must inspect the failed alternative using the base computational monad; the transformed bind would propagate failure without running that inspection. The alternative computation q runs only after p returns Nothing; any effects already performed by the base computational monad remain subject to that base's semantics.
Left identity follows by selecting Just x. Right identity follows because either alternative is passed back to resultM. For associativity, base associativity exposes the first alternative: Nothing propagates through both remaining steps; Just x runs f x, with its Nothing and Just alternatives treated identically on both sides. Thus this representation also satisfies the monad laws.
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State monad transformer 2026-10-31
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A state monad layered over a base computational monad. An unsuccessful base computation may return no final program state; this matters when combining it with an exception monad transformer.
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