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# Monad comprehensions

## Translation rules

Variables : x and y Expressions : e, f and g Patterns : w Qualifiers : p, q and r

The main translation rule for monad comprehensions.

[ e | q ] = [| q |] >>= (return . (\q_v -> e))

`(.)_v`

rules. Note that `_v`

is a postfix rule application.

(w <- e)_v = w (let w = d)_v = w (g)_v = () (p , q)_v = (p_v,q_v) (p | v)_v = (p_v,q_v) (q, then f)_v = q_v (q, then f by e)_v = q_v (q, then group by e using f)_v = q_v (q, then group using f)_v = q_v

`[|.|]`

rules.

[| w <- e |] = e [| let w = d |] = return d [| g |] = guard g [| p, q |] = ([| p |] >>= (return . (\p_v -> [| q |] >>= (return . (\q_v -> (p_v,q_v)))))) >>= id [| p | q |] = mzip [| p |] [| q |] [| q, then f |] = f [| q |] [| q, then f by e |] = f (\q_v -> e) [| q |] [| q, then group by e using f |] = (f (\q_v -> e) [| q |]) >>= (return . (unzip q_v)) [| q, then group using f |] = (f [| q |]) >>= (return . (unzip q_v))

`unzip (.)`

rules. Note that `unzip`

is a desugaring rule (i.e., not a function to be included in the generated code).

unzip () = id unzip x = id unzip (w1,w2) = \e -> ((unzip w1) (e >>= (return .(\(x,y) -> x))), (unzip w2) (e >>= (return . (\(x,y) -> y))))