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doc: clarify ac canonical forms
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fblanqui committed Oct 30, 2024
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Expand Up @@ -128,14 +128,14 @@ the system with additional information on its properties and behavior.
for every canonical term of the form ``f t u``, we have ``t ≤ u``,
where ```` is a total ordering on terms left unspecified.

If a symbol ``f`` is ``associative left`` then there is no
canonical term of the form ``f t (f u v)`` and thus every
canonical term headed by ``f`` is of the form ``f … (f (f t₁ t₂)
t₃) … tₙ``. If a symbol ``f`` is ``associative`` or ``associative
right`` then there is no canonical term of the form ``f (f t u)
v`` and thus every canonical term headed by ``f`` is of the form
``f t₁ (f t₂ (f t₃ … tₙ) … )``. Moreover, in both cases, if ``f``
is also ``commutative`` then we have ``t₁ ≤ t₂ ≤ … ≤ tₙ``.
If a symbol ``f`` is ``commutative`` and ``associative left`` then
there is no canonical term of the form ``f t (f u v)`` and thus
every canonical term headed by ``f`` is of the form ``f … (f (f t₁
t₂) t₃) … tₙ``. If a symbol ``f`` is ``commutative`` and
``associative`` or ``associative right`` then there is no
canonical term of the form ``f (f t u) v`` and thus every
canonical term headed by ``f`` is of the form ``f t₁ (f t₂ (f t₃ …
tₙ) … )``. Moreover, in both cases, we have ``t₁ ≤ t₂ ≤ … ≤ tₙ``.

- **Exposition modifiers** define how a symbol can be used outside the
module where it is defined. By default, the symbol can be used
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