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Doc: clarify ac canonical forms #1147

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Oct 30, 2024
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2 changes: 1 addition & 1 deletion .github/workflows/main.yml
Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,7 @@ jobs:
strategy:
fail-fast: false
matrix:
ocaml-version: [5.2.0, 5.1.1, 5.0.0, 4.14.1, 4.13.1, 4.12.1, 4.11.2, 4.10.2, 4.09.1, 4.08.1]
ocaml-version: [5.2.0, 5.1.1, 5.0.0, 4.14.2, 4.13.1, 4.12.1, 4.11.2, 4.10.2, 4.09.1, 4.08.1]
runs-on: ubuntu-latest
steps:
- name: checking out lambdapi repo ...
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16 changes: 8 additions & 8 deletions doc/commands.rst
Original file line number Diff line number Diff line change
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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