Skip to content

Commit

Permalink
Fix some pandoc conversion errors
Browse files Browse the repository at this point in the history
  • Loading branch information
edwinb committed Mar 23, 2015
1 parent dadfc86 commit 142f92f
Showing 1 changed file with 10 additions and 10 deletions.
20 changes: 10 additions & 10 deletions docs/proofs/patterns.rst
Original file line number Diff line number Diff line change
Expand Up @@ -42,7 +42,7 @@ well-typed inputs. This is important for proofs, since it provides a
guarantee that the proof is valid in *all* cases, not just those for
which it happens to be well-defined.

To create a template definition for the proof, press ``\backslashd`` the
To create a template definition for the proof, press ``\d`` the
equivalent in your editor of choice) on the line with the type
declaration. You should see:

Expand All @@ -54,7 +54,7 @@ declaration. You should see:
To prove this by induction on ``n``, as we sketched in Section
[sect:induction], we begin with a case split on ``n`` (press
``\backslashc`` with the cursor over the ``n`` in the definition.) You
``\c`` with the cursor over the ``n`` in the definition.) You
should see:

.. code-block:: idris
Expand All @@ -67,7 +67,7 @@ should see:
If we inspect the types of the newly created metavariables,
``plus_commutes_rhs_1`` and ``plus_commutes_rhs_2``, we see that the
type of each reflects that ``n`` has been refined to ``Z`` and ``S k``
in each respective case. Pressing ``\backslasht`` over
in each respective case. Pressing ``\t`` over
``plus_commutes_rhs_1`` shows:

.. code-block:: idris
Expand Down Expand Up @@ -100,7 +100,7 @@ Base Case
---------

We can create a separate lemma for the base case interactively, by
pressing ``\backslashl`` with the cursor over ``plus_commutes_Z``. This
pressing ``\l`` with the cursor over ``plus_commutes_Z``. This
yields:

.. code-block:: idris
Expand All @@ -122,7 +122,7 @@ specific value for its *second argument* (in fact, the left hand side of
the equality has been reduced from ``plus 0 m``.) Again, we can prove
this by induction, this time on ``m``.

First, create a template definition with ``\backslashd``:
First, create a template definition with ``\d``:

.. code-block:: idris
Expand All @@ -137,7 +137,7 @@ implciit, we will need to bring ``m`` into scope manually:
plus_commutes_Z : m = plus m 0
plus_commutes_Z {m} = ?plus_commutes_Z_rhs
Now, case split on ``m`` with ``\backslashc``:
Now, case split on ``m`` with ``\c``:

.. code-block:: idris
Expand All @@ -154,7 +154,7 @@ which is easily proved by reflection:
plus_commutes_Z_rhs_1 : 0 = 0
For such trivial proofs, we can let write the proof automatically by
pressing ``\backslasho`` with the cursor over ``plus_commutes_Z_rhs_1``.
pressing ``\o`` with the cursor over ``plus_commutes_Z_rhs_1``.
This yields:

.. code-block:: idris
Expand Down Expand Up @@ -260,7 +260,7 @@ In this case, inspecting the type of the hole gives:
--------------------------------------
plus_commutes_Z_rhs_2 : S k = S k
Either way, we can use proof search (``\backslasho``) to complete the
Either way, we can use proof search (``\o``) to complete the
proof, giving:

.. code-block:: idris
Expand Down Expand Up @@ -320,15 +320,15 @@ The good news is that ``m`` and ``k`` now appear in the correct order.
However, we still have to show that the successor symbol ``S`` can be
moved to the front in the right hand side of this equality. This
remaining lemma takes a similar form to the ``plus_commutes_Z``; we
begin by making a new top level lemma with ``\backslashl``. This gives:
begin by making a new top level lemma with ``\l``. This gives:

.. code-block:: idris
plus_commutes_S : (k : Nat) -> (m : Nat) -> S (plus m k) = plus m (S k)
Unlike the previous case, ``k`` and ``m`` are not made implicit because
we cannot in general infer arguments to a function from its result.
Again, we make a template definition with ``\backslashd``:
Again, we make a template definition with ``\d``:

.. code-block:: idris
Expand Down

0 comments on commit 142f92f

Please sign in to comment.