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unit x = Cons x Nil;
append l1 l2 = case l1 of {
Nil -> l2;
Cons x l1' -> Cons x (append l1' l2)
};
gradient e = gradient' (Num 1) e output;
gradient' adj e r = case e of {
Var x -> r (unit (x, unit adj));
Num a -> r Nil;
Add e1 e2 -> gradient' adj e1
(\m1 -> gradient' adj e2
(\m2 -> r (combine m1 m2)));
Mul e1 e2 -> gradient' (Mul adj e2) e1
(\m1 -> gradient' (Mul adj e1) e2
(\m2 -> r (combine m1 m2)))
};
combine m1 m2 = case m1 of {
Nil -> m2;
Cons (x, l) m1' -> combine m1' (insert x l m2)
};
insert x l m = case m of {
Nil -> unit (x, l);
Cons (y, l') m' -> case eq x y of {
True -> Cons (y, append l l') m';
False -> Cons (y, l') (insert x l m')
}
};
eq x y = case x of {
A -> case y of { A -> True; _ -> False };
B -> case y of { B -> True; _ -> False };
C -> case y of { C -> True; _ -> False }
};
expr = gradient (Mul (Add (Var A) (Num 2)) (Mul (Num 3) (Var B)));
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