Linear types
============
.. extension:: LinearTypes
:shortdesc: Enable linear types.
:since: 9.0.1
Enable the linear arrow ``a %1 -> b`` and the multiplicity-polymorphic arrow
``a %m -> b``.
**This extension is currently considered experimental, expect bugs,
warts, and bad error messages; everything down to the syntax is
subject to change**. See, in particular,
:ref:`linear-types-limitations` below. We encourage you to experiment
with this extension and report issues in the GHC bug tracker `the GHC
bug tracker `__, adding the
tag ``LinearTypes``.
A function ``f`` is linear if: when its result is consumed *exactly
once*, then its argument is consumed *exactly once*. Intuitively, it
means that in every branch of the definition of ``f``, its argument
``x`` must be used exactly once. Which can be done by
* Returning ``x`` unmodified
* Passing ``x`` to a *linear* function
* Pattern-matching on ``x`` and using each argument exactly once in the
same fashion.
* Calling it as a function and using the result exactly once in the same
fashion.
With ``-XLinearTypes``, you can write ``f :: a %1 -> b`` to mean that
``f`` is a linear function from ``a`` to ``b``. If
:extension:`UnicodeSyntax` is enabled, the ``%1 ->`` arrow can be
written as ``⊸``.
To allow uniform handling of linear ``a %1 -> b`` and unrestricted ``a
-> b`` functions, there is a new function type ``a %m -> b``.
Here, ``m`` is a type of new kind ``Multiplicity``. We have:
::
data Multiplicity = One | Many -- Defined in GHC.Types
type a %1 -> b = a %One -> b
type a -> b = a %Many -> b
(See :ref:`promotion`).
We say that a variable whose multiplicity constraint is ``Many`` is
*unrestricted*.
The multiplicity-polymorphic arrow ``a %m -> b`` is available in a prefix
version as ``GHC.Exts.FUN m a b``, which can be applied
partially. See, however :ref:`linear-types-limitations`.
Linear and multiplicity-polymorphic arrows are *always declared*,
never inferred. That is, if you don't give an appropriate type
signature to a function, it will be inferred as being a regular
function of type ``a -> b``.
Data types
----------
By default, all fields in algebraic data types are linear (even if
``-XLinearTypes`` is not turned on). Given
::
data T1 a = MkT1 a
the value ``MkT1 x`` can be constructed and deconstructed in a linear context:
::
construct :: a %1 -> T1 a
construct x = MkT1 x
deconstruct :: T1 a %1 -> a
deconstruct (MkT1 x) = x -- must consume `x` exactly once
When used as a value, ``MkT1`` is given a multiplicity-polymorphic
type: ``MkT1 :: forall {m} a. a %m -> T1 a``. This makes it possible
to use ``MkT1`` in higher order functions. The additional multiplicity
argument ``m`` is marked as inferred (see
:ref:`inferred-vs-specified`), so that there is no conflict with
visible type application. When displaying types, unless
``-XLinearTypes`` is enabled, multiplicity polymorphic functions are
printed as regular functions (see :ref:`printing-linear-types`);
therefore constructors appear to have regular function types.
::
mkList :: [a] -> [MkT1 a]
mkList xs = map MkT1 xs
Hence the linearity of type constructors is invisible when
``-XLinearTypes`` is off.
Whether a data constructor field is linear or not can be customized using the GADT syntax. Given
::
data T2 a b c where
MkT2 :: a -> b %1 -> c %1 -> T2 a b -- Note unrestricted arrow in the first argument
the value ``MkT2 x y z`` can be constructed only if ``x`` is
unrestricted. On the other hand, a linear function which is matching
on ``MkT2 x y z`` must consume ``y`` and ``z`` exactly once, but there
is no restriction on ``x``.
If :extension:`LinearTypes` is disabled, all fields are considered to be linear
fields, including GADT fields defined with the ``->`` arrow.
In a ``newtype`` declaration, the field must be linear. Attempting to
write an unrestricted newtype constructor with GADT syntax results in
an error.
.. _printing-linear-types:
Printing multiplicity-polymorphic types
---------------------------------------
If :extension:`LinearTypes` is disabled, multiplicity variables in types are defaulted
to ``Many`` when printing, in the same manner as described in :ref:`printing-levity-polymorphic-types`.
In other words, without :extension:`LinearTypes`, multiplicity-polymorphic functions
``a %m -> b`` are printed as normal Haskell2010 functions ``a -> b``. This allows
existing libraries to be generalized to linear types in a backwards-compatible
manner; the general types are visible only if the user has enabled
:extension:`LinearTypes`.
(Note that a library can declare a linear function in the contravariant position,
i.e. take a linear function as an argument. In this case, linearity cannot be
hidden; it is an essential part of the exposed interface.)
.. _linear-types-limitations:
Limitations
-----------
Linear types are still considered experimental and come with several
limitations. If you have read the full design in the proposal (see
:ref:`linear-types-references` below), here is a run down of the
missing pieces.
- Multiplicity polymorphism is incomplete and experimental. You may
have success using it, or you may not. Expect it to be really unreliable.
- There is currently no support for multiplicity annotations such as
``x :: a %p``, ``\(x :: a %p) -> ...``.
- All ``case``, ``let`` and ``where`` statements consume their
right-hand side, or scrutiny, ``Many`` times. That is, the following
will not type check:
::
g :: A %1 -> (A, B)
h :: A %1 -> B %1 -> C
f :: A %1 -> C
f x =
case g x of
(y, z) -> h y z
This can be worked around by defining extra functions which are
specified to be linear, such as:
::
g :: A %1 -> (A, B)
h :: A %1 -> B %1 -> C
f :: A %1 -> C
f x = f' (g x)
where
f' :: (A, B) %1 -> C
f' (y, z) = h y z
- There is no support for linear pattern synonyms.
- ``@``-patterns and view patterns are not linear.
- The projection function for a record with a single linear field should be
multiplicity-polymorphic; currently it's unrestricted.
- Attempting to use of linear types in Template Haskell will probably
not work.
.. _linear-types-references:
Design and further reading
--------------------------
* The design for this extension is described in details in the `Linear
types proposal
`__
* This extension has been originally conceived of in the paper `Linear
Haskell: practical linearity in a higher-order polymorphic language
`__
(POPL 2018)
* There is a `wiki page dedicated to the linear types extension `__