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That's most of it now - just missing a section on multiplicities, and a section on the differences from Idris 1. Ideally, there should also be a much more gentle introduction (basically doing the same as the first 3 chapters of TypeDD in Idris). But that's for some other time...
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8.0 KiB
ReStructuredText
257 lines
8.0 KiB
ReStructuredText
.. _sect-interactive:
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*******************
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Interactive Editing
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*******************
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By now, we have seen several examples of how Idris’ dependent type
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system can give extra confidence in a function’s correctness by giving
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a more precise description of its intended behaviour in its *type*. We
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have also seen an example of how the type system can help with embedded DSL
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development by allowing a programmer to describe the type system of an
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object language. However, precise types give us more than verification
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of programs — we can also use the type system to help write programs which
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are *correct by construction*, interactively.
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The Idris REPL provides several commands for inspecting and
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modifying parts of programs, based on their types, such as case
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splitting on a pattern variable, inspecting the type of a
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hole, and even a basic proof search mechanism. In this
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section, we explain how these features can be exploited by a text
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editor, and specifically how to do so in `Vim
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<https://github.com/edwinb/idris2-vim>`_. An interactive mode
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for `Emacs <https://github.com/idris-hackers/idris-mode>`_ is also
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available (though not yet updated for Idris 2).
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Editing at the REPL
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===================
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The REPL provides a number of commands, which we will describe
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shortly, which generate new program fragments based on the currently
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loaded module. These take the general form:
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::
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:command [line number] [name]
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That is, each command acts on a specific source line, at a specific
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name, and outputs a new program fragment. Each command has an
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alternative form, which *updates* the source file in-place:
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::
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:command! [line number] [name]
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It is also possible to invoke Idris in a mode which runs a REPL command,
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displays the result, then exits, using ``idris2 --client``. For example:
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::
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$ idris2 --client ':t plus'
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Prelude.plus : Nat -> Nat -> Nat
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$ idris2 --client '2+2'
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4
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A text editor can take advantage of this, along with the editing
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commands, in order to provide interactive editing support.
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Editing Commands
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================
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:addclause
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----------
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The ``:addclause n f`` command, abbreviated ``:ac n f``, creates a
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template definition for the function named ``f`` declared on line
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``n``. For example, if the code beginning on line 94 contains:
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.. code-block:: idris
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vzipWith : (a -> b -> c) ->
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Vect n a -> Vect n b -> Vect n c
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then ``:ac 94 vzipWith`` will give:
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.. code-block:: idris
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vzipWith f xs ys = ?vzipWith_rhs
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The names are chosen according to hints which may be given by a
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programmer, and then made unique by the machine by adding a digit if
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necessary. Hints can be given as follows:
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.. code-block:: idris
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%name Vect xs, ys, zs, ws
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This declares that any names generated for types in the ``Vect`` family
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should be chosen in the order ``xs``, ``ys``, ``zs``, ``ws``.
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:casesplit
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----------
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The ``:casesplit n x`` command, abbreviated ``:cs n x``, splits the
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pattern variable ``x`` on line ``n`` into the various pattern forms it
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may take, removing any cases which are impossible due to unification
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errors. For example, if the code beginning on line 94 is:
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.. code-block:: idris
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vzipWith : (a -> b -> c) ->
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Vect n a -> Vect n b -> Vect n c
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vzipWith f xs ys = ?vzipWith_rhs
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then ``:cs 96 xs`` will give:
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.. code-block:: idris
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vzipWith f [] ys = ?vzipWith_rhs_1
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vzipWith f (x :: xs) ys = ?vzipWith_rhs_2
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That is, the pattern variable ``xs`` has been split into the two
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possible cases ``[]`` and ``x :: xs``. Again, the names are chosen
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according to the same heuristic. If we update the file (using
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``:cs!``) then case split on ``ys`` on the same line, we get:
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.. code-block:: idris
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vzipWith f [] [] = ?vzipWith_rhs_3
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That is, the pattern variable ``ys`` has been split into one case
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``[]``, Idris having noticed that the other possible case ``y ::
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ys`` would lead to a unification error.
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:addmissing
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-----------
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The ``:addmissing n f`` command, abbreviated ``:am n f``, adds the
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clauses which are required to make the function ``f`` on line ``n``
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cover all inputs. For example, if the code beginning on line 94 is:
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.. code-block:: idris
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vzipWith : (a -> b -> c) ->
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Vect n a -> Vect n b -> Vect n c
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vzipWith f [] [] = ?vzipWith_rhs_1
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then ``:am 96 vzipWith`` gives:
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.. code-block:: idris
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vzipWith f (x :: xs) (y :: ys) = ?vzipWith_rhs_2
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That is, it notices that there are no cases for empty vectors,
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generates the required clauses, and eliminates the clauses which would
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lead to unification errors.
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:proofsearch
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------------
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The ``:proofsearch n f`` command, abbreviated ``:ps n f``, attempts to
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find a value for the hole ``f`` on line ``n`` by proof search,
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trying values of local variables, recursive calls and constructors of
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the required family. Optionally, it can take a list of *hints*, which
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are functions it can try applying to solve the hole. For
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example, if the code beginning on line 94 is:
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.. code-block:: idris
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vzipWith : (a -> b -> c) ->
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Vect n a -> Vect n b -> Vect n c
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vzipWith f [] [] = ?vzipWith_rhs_1
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vzipWith f (x :: xs) (y :: ys) = ?vzipWith_rhs_2
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then ``:ps 96 vzipWith_rhs_1`` will give
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.. code-block:: idris
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[]
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This works because it is searching for a ``Vect`` of length 0, of
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which the empty vector is the only possibility. Similarly, and perhaps
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surprisingly, there is only one possibility if we try to solve ``:ps
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97 vzipWith_rhs_2``:
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.. code-block:: idris
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f x y :: vzipWith f xs ys
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This works because ``vzipWith`` has a precise enough type: The
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resulting vector has to be non-empty (a ``::``); the first element
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must have type ``c`` and the only way to get this is to apply ``f`` to
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``x`` and ``y``; finally, the tail of the vector can only be built
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recursively.
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:makewith
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---------
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The ``:makewith n f`` command, abbreviated ``:mw n f``, adds a
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``with`` to a pattern clause. For example, recall ``parity``. If line
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10 is:
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.. code-block:: idris
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parity (S k) = ?parity_rhs
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then ``:mw 10 parity`` will give:
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.. code-block:: idris
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parity (S k) with (_)
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parity (S k) | with_pat = ?parity_rhs
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If we then fill in the placeholder ``_`` with ``parity k`` and case
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split on ``with_pat`` using ``:cs 11 with_pat`` we get the following
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patterns:
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.. code-block:: idris
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parity (S (plus n n)) | even = ?parity_rhs_1
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parity (S (S (plus n n))) | odd = ?parity_rhs_2
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Note that case splitting has normalised the patterns here (giving
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``plus`` rather than ``+``). In any case, we see that using
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interactive editing significantly simplifies the implementation of
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dependent pattern matching by showing a programmer exactly what the
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valid patterns are.
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Interactive Editing in Vim
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==========================
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The editor mode for Vim provides syntax highlighting, indentation and
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interactive editing support using the commands described above.
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Interactive editing is achieved using the following editor commands,
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each of which update the buffer directly:
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- ``\a`` adds a template definition for the name declared on the
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current line (using ``:addclause``).
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- ``\c`` case splits the variable at the cursor (using
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``:casesplit``).
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- ``\m`` adds the missing cases for the name at the cursor (using
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``:addmissing``).
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- ``\w`` adds a ``with`` clause (using ``:makewith``).
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- ``\s`` invokes a proof search to solve the hole under the
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cursor (using ``:proofsearch``).
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There are also commands to invoke the type checker and evaluator:
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- ``\t`` displays the type of the (globally visible) name under the
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cursor. In the case of a hole, this displays the context
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and the expected type.
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- ``\e`` prompts for an expression to evaluate.
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- ``\r`` reloads and type checks the buffer.
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Corresponding commands are also available in the Emacs mode. Support
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for other editors can be added in a relatively straightforward manner
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by using ``idris2 -–client``.
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More sophisticated support can be added by using the IDE protocol (yet to
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be documented for Idris 2, but which mostly extends to protocol documented for
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`Idris 1 <http://docs.idris-lang.org/en/latest/reference/ide-protocol.html>`_.
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