Both `alternative` and `monad` implement `applicative`. However,
their default implementations for `seq_right` and `seq_left` are
different. The `alternative` implementation uses the inefficient default
version for `seq_right` available at `applicative`:
```
(seq_right := λ α β a b, const α id <$> a <*> b)
```
instead of the more efficient
```
(seq_right := λ α β x y, x >>= λ _, y)
```
defined at `monad` using the `bind` operator.
This commit makes sure the `applicative` instances for `reader_t`,
`state_t`, `option` and `parsec_t` use the efficient version.
I found the problem when inspecting the generated code for:
```
def symbol (s : string) : parsec' unit :=
(str s *> whitespace) <?> ("'" ++ s ++ "'")
```
@kha, `eqn_compiler.lemmas` is false by default.
I will keep them disabled until I remove the inductive compiler.
I'm building the new inductive datatype module (to replace the inductive
compiler), and the lemmas will fail to be proved in the next commits
until the transition is complete.
(Type u) is the old (Type (u+1))
(PType u) is the old (Type u)
Type* is the old (Type (_+1))
PType* is the old Type*
The stdlib can be compiled, but we still have > 70 broken tests
See discussion at #1341
