diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,49 +1,55 @@
-# Revision history for finitary
-
-## 2.0.0.0 -- 2020-05-05
-
-* Support GHC 8.10
-* Remove support for GHCs older than 8.6
-* Remove dependency on ``coercible-utils``
-* ``previous`` and ``next`` now return ``Maybe``s
-* Better tests
-* Better documentation
-
-## 1.2.0.0 -- 2019-10-17
-
-* Remove ``nextSkipping`` and ``previousSkipping`` as unnecessary.
-* Add (and note) support for GHC 8.2.2.
-* Remove MTL dependency.
-* Remove ``enumerate*`` class methods.
-* Add ``inhabitants``, ``inhabitantsFrom``, ``inhabitantsTo``,
-  ``inhabitantsFromTo``.
-
-## 1.1.0.0 -- 2019-09-21
-
-* Repair a disagreement between ``Ord`` and ``Finitary`` derivations via
-  ``Generic`` (thanks jle`!).
-* Fix serious bug with ``next`` and ``previous``.
-
-## 1.0.0.1 -- 2019-09-17
-
-* Fix README (no code changes).
-
-## 1.0.0.0 -- 2019-09-17
-
-* Rewritten documentation to be more clear, and state more laws.
-* Added ``nextSkipping`` and ``previousSkipping`` methods to allow 'skipping
-  over' some elements when enumerating in a more efficient manner.
-* Added ``Eq a`` as a constraint for ``Finitary a`` instances (as without it,
-  the laws don't make much sense).
-* Fixed numerous typoes and unclear statements.
-* Stated that ``Finitary`` must be order-preserving relative any instances with
-  ``Ord`` instances; existing instances modified to follow this law.
-* Added more tests.
-* Fixed odd issue with some element cardinalities and lengths for sized
-  ``Vector`` instances.
-* Tightened bounds to be more conservative.
-* Support GHC 8.8.
-
-## 0.1.0.0 -- 2019-09-10
-
-* First version. Released on an unsuspecting world.
+# Revision history for finitary
+
+## 2.1.0.1 -- 2021-02-09
+
+* Fix incorrect instance for `Finite a => Finite ( Down a )`
+* Add cabal flags to give the option of removing dependencies on `vector` and `bitvec`
+* Ensure GHC 9.0 compatibility
+
+## 2.0.0.0 -- 2020-05-05
+
+* Support GHC 8.10
+* Remove support for GHCs older than 8.6
+* Remove dependency on ``coercible-utils``
+* ``previous`` and ``next`` now return ``Maybe``s
+* Better tests
+* Better documentation
+
+## 1.2.0.0 -- 2019-10-17
+
+* Remove ``nextSkipping`` and ``previousSkipping`` as unnecessary.
+* Add (and note) support for GHC 8.2.2.
+* Remove MTL dependency.
+* Remove ``enumerate*`` class methods.
+* Add ``inhabitants``, ``inhabitantsFrom``, ``inhabitantsTo``,
+  ``inhabitantsFromTo``.
+
+## 1.1.0.0 -- 2019-09-21
+
+* Repair a disagreement between ``Ord`` and ``Finitary`` derivations via
+  ``Generic`` (thanks jle`!).
+* Fix serious bug with ``next`` and ``previous``.
+
+## 1.0.0.1 -- 2019-09-17
+
+* Fix README (no code changes).
+
+## 1.0.0.0 -- 2019-09-17
+
+* Rewritten documentation to be more clear, and state more laws.
+* Added ``nextSkipping`` and ``previousSkipping`` methods to allow 'skipping
+  over' some elements when enumerating in a more efficient manner.
+* Added ``Eq a`` as a constraint for ``Finitary a`` instances (as without it,
+  the laws don't make much sense).
+* Fixed numerous typoes and unclear statements.
+* Stated that ``Finitary`` must be order-preserving relative any instances with
+  ``Ord`` instances; existing instances modified to follow this law.
+* Added more tests.
+* Fixed odd issue with some element cardinalities and lengths for sized
+  ``Vector`` instances.
+* Tightened bounds to be more conservative.
+* Support GHC 8.8.
+
+## 0.1.0.0 -- 2019-09-10
+
+* First version. Released on an unsuspecting world.
diff --git a/LICENSE.md b/LICENSE.md
--- a/LICENSE.md
+++ b/LICENSE.md
@@ -1,675 +1,675 @@
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-A patent license is "discriminatory" if it does not include within the
-scope of its coverage, prohibits the exercise of, or is conditioned on
-the non-exercise of one or more of the rights that are specifically
-granted under this License. You may not convey a covered work if you
-are a party to an arrangement with a third party that is in the
-business of distributing software, under which you make payment to the
-third party based on the extent of your activity of conveying the
-work, and under which the third party grants, to any of the parties
-who would receive the covered work from you, a discriminatory patent
-license (a) in connection with copies of the covered work conveyed by
-you (or copies made from those copies), or (b) primarily for and in
-connection with specific products or compilations that contain the
-covered work, unless you entered into that arrangement, or that patent
-license was granted, prior to 28 March 2007.
-
-Nothing in this License shall be construed as excluding or limiting
-any implied license or other defenses to infringement that may
-otherwise be available to you under applicable patent law.
-
-#### 12. No Surrender of Others' Freedom.
-
-If conditions are imposed on you (whether by court order, agreement or
-otherwise) that contradict the conditions of this License, they do not
-excuse you from the conditions of this License. If you cannot convey a
-covered work so as to satisfy simultaneously your obligations under
-this License and any other pertinent obligations, then as a
-consequence you may not convey it at all. For example, if you agree to
-terms that obligate you to collect a royalty for further conveying
-from those to whom you convey the Program, the only way you could
-satisfy both those terms and this License would be to refrain entirely
-from conveying the Program.
-
-#### 13. Use with the GNU Affero General Public License.
-
-Notwithstanding any other provision of this License, you have
-permission to link or combine any covered work with a work licensed
-under version 3 of the GNU Affero General Public License into a single
-combined work, and to convey the resulting work. The terms of this
-License will continue to apply to the part which is the covered work,
-but the special requirements of the GNU Affero General Public License,
-section 13, concerning interaction through a network will apply to the
-combination as such.
-
-#### 14. Revised Versions of this License.
-
-The Free Software Foundation may publish revised and/or new versions
-of the GNU General Public License from time to time. Such new versions
-will be similar in spirit to the present version, but may differ in
-detail to address new problems or concerns.
-
-Each version is given a distinguishing version number. If the Program
-specifies that a certain numbered version of the GNU General Public
-License "or any later version" applies to it, you have the option of
-following the terms and conditions either of that numbered version or
-of any later version published by the Free Software Foundation. If the
-Program does not specify a version number of the GNU General Public
-License, you may choose any version ever published by the Free
-Software Foundation.
-
-If the Program specifies that a proxy can decide which future versions
-of the GNU General Public License can be used, that proxy's public
-statement of acceptance of a version permanently authorizes you to
-choose that version for the Program.
-
-Later license versions may give you additional or different
-permissions. However, no additional obligations are imposed on any
-author or copyright holder as a result of your choosing to follow a
-later version.
-
-#### 15. Disclaimer of Warranty.
-
-THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
-APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
-HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT
-WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT
-LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND
-PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE
-DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR
-CORRECTION.
-
-#### 16. Limitation of Liability.
-
-IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR
-CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
-INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES
-ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT
-NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
-LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM
-TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER
-PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
-
-#### 17. Interpretation of Sections 15 and 16.
-
-If the disclaimer of warranty and limitation of liability provided
-above cannot be given local legal effect according to their terms,
-reviewing courts shall apply local law that most closely approximates
-an absolute waiver of all civil liability in connection with the
-Program, unless a warranty or assumption of liability accompanies a
-copy of the Program in return for a fee.
-
-END OF TERMS AND CONDITIONS
-
-### How to Apply These Terms to Your New Programs
-
-If you develop a new program, and you want it to be of the greatest
-possible use to the public, the best way to achieve this is to make it
-free software which everyone can redistribute and change under these
-terms.
-
-To do so, attach the following notices to the program. It is safest to
-attach them to the start of each source file to most effectively state
-the exclusion of warranty; and each file should have at least the
-"copyright" line and a pointer to where the full notice is found.
-
-        <one line to give the program's name and a brief idea of what it does.>
-        Copyright (C) <year>  <name of author>
-
-        This program is free software: you can redistribute it and/or modify
-        it under the terms of the GNU General Public License as published by
-        the Free Software Foundation, either version 3 of the License, or
-        (at your option) any later version.
-
-        This program is distributed in the hope that it will be useful,
-        but WITHOUT ANY WARRANTY; without even the implied warranty of
-        MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-        GNU General Public License for more details.
-
-        You should have received a copy of the GNU General Public License
-        along with this program.  If not, see <https://www.gnu.org/licenses/>.
-
-Also add information on how to contact you by electronic and paper
-mail.
-
-If the program does terminal interaction, make it output a short
-notice like this when it starts in an interactive mode:
-
-        <program>  Copyright (C) <year>  <name of author>
-        This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
-        This is free software, and you are welcome to redistribute it
-        under certain conditions; type `show c' for details.
-
-The hypothetical commands \`show w' and \`show c' should show the
-appropriate parts of the General Public License. Of course, your
-program's commands might be different; for a GUI interface, you would
-use an "about box".
-
-You should also get your employer (if you work as a programmer) or
-school, if any, to sign a "copyright disclaimer" for the program, if
-necessary. For more information on this, and how to apply and follow
-the GNU GPL, see <https://www.gnu.org/licenses/>.
-
-The GNU General Public License does not permit incorporating your
-program into proprietary programs. If your program is a subroutine
-library, you may consider it more useful to permit linking proprietary
-applications with the library. If this is what you want to do, use the
-GNU Lesser General Public License instead of this License. But first,
-please read <https://www.gnu.org/licenses/why-not-lgpl.html>.
+### GNU GENERAL PUBLIC LICENSE
+
+Version 3, 29 June 2007
+
+Copyright (C) 2007 Free Software Foundation, Inc.
+<https://fsf.org/>
+
+Everyone is permitted to copy and distribute verbatim copies of this
+license document, but changing it is not allowed.
+
+### Preamble
+
+The GNU General Public License is a free, copyleft license for
+software and other kinds of works.
+
+The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works. By contrast,
+the GNU General Public License is intended to guarantee your freedom
+to share and change all versions of a program--to make sure it remains
+free software for all its users. We, the Free Software Foundation, use
+the GNU General Public License for most of our software; it applies
+also to any other work released this way by its authors. You can apply
+it to your programs, too.
+
+When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+To protect your rights, we need to prevent others from denying you
+these rights or asking you to surrender the rights. Therefore, you
+have certain responsibilities if you distribute copies of the
+software, or if you modify it: responsibilities to respect the freedom
+of others.
+
+For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must pass on to the recipients the same
+freedoms that you received. You must make sure that they, too, receive
+or can get the source code. And you must show them these terms so they
+know their rights.
+
+Developers that use the GNU GPL protect your rights with two steps:
+(1) assert copyright on the software, and (2) offer you this License
+giving you legal permission to copy, distribute and/or modify it.
+
+For the developers' and authors' protection, the GPL clearly explains
+that there is no warranty for this free software. For both users' and
+authors' sake, the GPL requires that modified versions be marked as
+changed, so that their problems will not be attributed erroneously to
+authors of previous versions.
+
+Some devices are designed to deny users access to install or run
+modified versions of the software inside them, although the
+manufacturer can do so. This is fundamentally incompatible with the
+aim of protecting users' freedom to change the software. The
+systematic pattern of such abuse occurs in the area of products for
+individuals to use, which is precisely where it is most unacceptable.
+Therefore, we have designed this version of the GPL to prohibit the
+practice for those products. If such problems arise substantially in
+other domains, we stand ready to extend this provision to those
+domains in future versions of the GPL, as needed to protect the
+freedom of users.
+
+Finally, every program is threatened constantly by software patents.
+States should not allow patents to restrict development and use of
+software on general-purpose computers, but in those that do, we wish
+to avoid the special danger that patents applied to a free program
+could make it effectively proprietary. To prevent this, the GPL
+assures that patents cannot be used to render the program non-free.
+
+The precise terms and conditions for copying, distribution and
+modification follow.
+
+### TERMS AND CONDITIONS
+
+#### 0. Definitions.
+
+"This License" refers to version 3 of the GNU General Public License.
+
+"Copyright" also means copyright-like laws that apply to other kinds
+of works, such as semiconductor masks.
+
+"The Program" refers to any copyrightable work licensed under this
+License. Each licensee is addressed as "you". "Licensees" and
+"recipients" may be individuals or organizations.
+
+To "modify" a work means to copy from or adapt all or part of the work
+in a fashion requiring copyright permission, other than the making of
+an exact copy. The resulting work is called a "modified version" of
+the earlier work or a work "based on" the earlier work.
+
+A "covered work" means either the unmodified Program or a work based
+on the Program.
+
+To "propagate" a work means to do anything with it that, without
+permission, would make you directly or secondarily liable for
+infringement under applicable copyright law, except executing it on a
+computer or modifying a private copy. Propagation includes copying,
+distribution (with or without modification), making available to the
+public, and in some countries other activities as well.
+
+To "convey" a work means any kind of propagation that enables other
+parties to make or receive copies. Mere interaction with a user
+through a computer network, with no transfer of a copy, is not
+conveying.
+
+An interactive user interface displays "Appropriate Legal Notices" to
+the extent that it includes a convenient and prominently visible
+feature that (1) displays an appropriate copyright notice, and (2)
+tells the user that there is no warranty for the work (except to the
+extent that warranties are provided), that licensees may convey the
+work under this License, and how to view a copy of this License. If
+the interface presents a list of user commands or options, such as a
+menu, a prominent item in the list meets this criterion.
+
+#### 1. Source Code.
+
+The "source code" for a work means the preferred form of the work for
+making modifications to it. "Object code" means any non-source form of
+a work.
+
+A "Standard Interface" means an interface that either is an official
+standard defined by a recognized standards body, or, in the case of
+interfaces specified for a particular programming language, one that
+is widely used among developers working in that language.
+
+The "System Libraries" of an executable work include anything, other
+than the work as a whole, that (a) is included in the normal form of
+packaging a Major Component, but which is not part of that Major
+Component, and (b) serves only to enable use of the work with that
+Major Component, or to implement a Standard Interface for which an
+implementation is available to the public in source code form. A
+"Major Component", in this context, means a major essential component
+(kernel, window system, and so on) of the specific operating system
+(if any) on which the executable work runs, or a compiler used to
+produce the work, or an object code interpreter used to run it.
+
+The "Corresponding Source" for a work in object code form means all
+the source code needed to generate, install, and (for an executable
+work) run the object code and to modify the work, including scripts to
+control those activities. However, it does not include the work's
+System Libraries, or general-purpose tools or generally available free
+programs which are used unmodified in performing those activities but
+which are not part of the work. For example, Corresponding Source
+includes interface definition files associated with source files for
+the work, and the source code for shared libraries and dynamically
+linked subprograms that the work is specifically designed to require,
+such as by intimate data communication or control flow between those
+subprograms and other parts of the work.
+
+The Corresponding Source need not include anything that users can
+regenerate automatically from other parts of the Corresponding Source.
+
+The Corresponding Source for a work in source code form is that same
+work.
+
+#### 2. Basic Permissions.
+
+All rights granted under this License are granted for the term of
+copyright on the Program, and are irrevocable provided the stated
+conditions are met. This License explicitly affirms your unlimited
+permission to run the unmodified Program. The output from running a
+covered work is covered by this License only if the output, given its
+content, constitutes a covered work. This License acknowledges your
+rights of fair use or other equivalent, as provided by copyright law.
+
+You may make, run and propagate covered works that you do not convey,
+without conditions so long as your license otherwise remains in force.
+You may convey covered works to others for the sole purpose of having
+them make modifications exclusively for you, or provide you with
+facilities for running those works, provided that you comply with the
+terms of this License in conveying all material for which you do not
+control copyright. Those thus making or running the covered works for
+you must do so exclusively on your behalf, under your direction and
+control, on terms that prohibit them from making any copies of your
+copyrighted material outside their relationship with you.
+
+Conveying under any other circumstances is permitted solely under the
+conditions stated below. Sublicensing is not allowed; section 10 makes
+it unnecessary.
+
+#### 3. Protecting Users' Legal Rights From Anti-Circumvention Law.
+
+No covered work shall be deemed part of an effective technological
+measure under any applicable law fulfilling obligations under article
+11 of the WIPO copyright treaty adopted on 20 December 1996, or
+similar laws prohibiting or restricting circumvention of such
+measures.
+
+When you convey a covered work, you waive any legal power to forbid
+circumvention of technological measures to the extent such
+circumvention is effected by exercising rights under this License with
+respect to the covered work, and you disclaim any intention to limit
+operation or modification of the work as a means of enforcing, against
+the work's users, your or third parties' legal rights to forbid
+circumvention of technological measures.
+
+#### 4. Conveying Verbatim Copies.
+
+You may convey verbatim copies of the Program's source code as you
+receive it, in any medium, provided that you conspicuously and
+appropriately publish on each copy an appropriate copyright notice;
+keep intact all notices stating that this License and any
+non-permissive terms added in accord with section 7 apply to the code;
+keep intact all notices of the absence of any warranty; and give all
+recipients a copy of this License along with the Program.
+
+You may charge any price or no price for each copy that you convey,
+and you may offer support or warranty protection for a fee.
+
+#### 5. Conveying Modified Source Versions.
+
+You may convey a work based on the Program, or the modifications to
+produce it from the Program, in the form of source code under the
+terms of section 4, provided that you also meet all of these
+conditions:
+
+-   a) The work must carry prominent notices stating that you modified
+    it, and giving a relevant date.
+-   b) The work must carry prominent notices stating that it is
+    released under this License and any conditions added under
+    section 7. This requirement modifies the requirement in section 4
+    to "keep intact all notices".
+-   c) You must license the entire work, as a whole, under this
+    License to anyone who comes into possession of a copy. This
+    License will therefore apply, along with any applicable section 7
+    additional terms, to the whole of the work, and all its parts,
+    regardless of how they are packaged. This License gives no
+    permission to license the work in any other way, but it does not
+    invalidate such permission if you have separately received it.
+-   d) If the work has interactive user interfaces, each must display
+    Appropriate Legal Notices; however, if the Program has interactive
+    interfaces that do not display Appropriate Legal Notices, your
+    work need not make them do so.
+
+A compilation of a covered work with other separate and independent
+works, which are not by their nature extensions of the covered work,
+and which are not combined with it such as to form a larger program,
+in or on a volume of a storage or distribution medium, is called an
+"aggregate" if the compilation and its resulting copyright are not
+used to limit the access or legal rights of the compilation's users
+beyond what the individual works permit. Inclusion of a covered work
+in an aggregate does not cause this License to apply to the other
+parts of the aggregate.
+
+#### 6. Conveying Non-Source Forms.
+
+You may convey a covered work in object code form under the terms of
+sections 4 and 5, provided that you also convey the machine-readable
+Corresponding Source under the terms of this License, in one of these
+ways:
+
+-   a) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by the
+    Corresponding Source fixed on a durable physical medium
+    customarily used for software interchange.
+-   b) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by a
+    written offer, valid for at least three years and valid for as
+    long as you offer spare parts or customer support for that product
+    model, to give anyone who possesses the object code either (1) a
+    copy of the Corresponding Source for all the software in the
+    product that is covered by this License, on a durable physical
+    medium customarily used for software interchange, for a price no
+    more than your reasonable cost of physically performing this
+    conveying of source, or (2) access to copy the Corresponding
+    Source from a network server at no charge.
+-   c) Convey individual copies of the object code with a copy of the
+    written offer to provide the Corresponding Source. This
+    alternative is allowed only occasionally and noncommercially, and
+    only if you received the object code with such an offer, in accord
+    with subsection 6b.
+-   d) Convey the object code by offering access from a designated
+    place (gratis or for a charge), and offer equivalent access to the
+    Corresponding Source in the same way through the same place at no
+    further charge. You need not require recipients to copy the
+    Corresponding Source along with the object code. If the place to
+    copy the object code is a network server, the Corresponding Source
+    may be on a different server (operated by you or a third party)
+    that supports equivalent copying facilities, provided you maintain
+    clear directions next to the object code saying where to find the
+    Corresponding Source. Regardless of what server hosts the
+    Corresponding Source, you remain obligated to ensure that it is
+    available for as long as needed to satisfy these requirements.
+-   e) Convey the object code using peer-to-peer transmission,
+    provided you inform other peers where the object code and
+    Corresponding Source of the work are being offered to the general
+    public at no charge under subsection 6d.
+
+A separable portion of the object code, whose source code is excluded
+from the Corresponding Source as a System Library, need not be
+included in conveying the object code work.
+
+A "User Product" is either (1) a "consumer product", which means any
+tangible personal property which is normally used for personal,
+family, or household purposes, or (2) anything designed or sold for
+incorporation into a dwelling. In determining whether a product is a
+consumer product, doubtful cases shall be resolved in favor of
+coverage. For a particular product received by a particular user,
+"normally used" refers to a typical or common use of that class of
+product, regardless of the status of the particular user or of the way
+in which the particular user actually uses, or expects or is expected
+to use, the product. A product is a consumer product regardless of
+whether the product has substantial commercial, industrial or
+non-consumer uses, unless such uses represent the only significant
+mode of use of the product.
+
+"Installation Information" for a User Product means any methods,
+procedures, authorization keys, or other information required to
+install and execute modified versions of a covered work in that User
+Product from a modified version of its Corresponding Source. The
+information must suffice to ensure that the continued functioning of
+the modified object code is in no case prevented or interfered with
+solely because modification has been made.
+
+If you convey an object code work under this section in, or with, or
+specifically for use in, a User Product, and the conveying occurs as
+part of a transaction in which the right of possession and use of the
+User Product is transferred to the recipient in perpetuity or for a
+fixed term (regardless of how the transaction is characterized), the
+Corresponding Source conveyed under this section must be accompanied
+by the Installation Information. But this requirement does not apply
+if neither you nor any third party retains the ability to install
+modified object code on the User Product (for example, the work has
+been installed in ROM).
+
+The requirement to provide Installation Information does not include a
+requirement to continue to provide support service, warranty, or
+updates for a work that has been modified or installed by the
+recipient, or for the User Product in which it has been modified or
+installed. Access to a network may be denied when the modification
+itself materially and adversely affects the operation of the network
+or violates the rules and protocols for communication across the
+network.
+
+Corresponding Source conveyed, and Installation Information provided,
+in accord with this section must be in a format that is publicly
+documented (and with an implementation available to the public in
+source code form), and must require no special password or key for
+unpacking, reading or copying.
+
+#### 7. Additional Terms.
+
+"Additional permissions" are terms that supplement the terms of this
+License by making exceptions from one or more of its conditions.
+Additional permissions that are applicable to the entire Program shall
+be treated as though they were included in this License, to the extent
+that they are valid under applicable law. If additional permissions
+apply only to part of the Program, that part may be used separately
+under those permissions, but the entire Program remains governed by
+this License without regard to the additional permissions.
+
+When you convey a copy of a covered work, you may at your option
+remove any additional permissions from that copy, or from any part of
+it. (Additional permissions may be written to require their own
+removal in certain cases when you modify the work.) You may place
+additional permissions on material, added by you to a covered work,
+for which you have or can give appropriate copyright permission.
+
+Notwithstanding any other provision of this License, for material you
+add to a covered work, you may (if authorized by the copyright holders
+of that material) supplement the terms of this License with terms:
+
+-   a) Disclaiming warranty or limiting liability differently from the
+    terms of sections 15 and 16 of this License; or
+-   b) Requiring preservation of specified reasonable legal notices or
+    author attributions in that material or in the Appropriate Legal
+    Notices displayed by works containing it; or
+-   c) Prohibiting misrepresentation of the origin of that material,
+    or requiring that modified versions of such material be marked in
+    reasonable ways as different from the original version; or
+-   d) Limiting the use for publicity purposes of names of licensors
+    or authors of the material; or
+-   e) Declining to grant rights under trademark law for use of some
+    trade names, trademarks, or service marks; or
+-   f) Requiring indemnification of licensors and authors of that
+    material by anyone who conveys the material (or modified versions
+    of it) with contractual assumptions of liability to the recipient,
+    for any liability that these contractual assumptions directly
+    impose on those licensors and authors.
+
+All other non-permissive additional terms are considered "further
+restrictions" within the meaning of section 10. If the Program as you
+received it, or any part of it, contains a notice stating that it is
+governed by this License along with a term that is a further
+restriction, you may remove that term. If a license document contains
+a further restriction but permits relicensing or conveying under this
+License, you may add to a covered work material governed by the terms
+of that license document, provided that the further restriction does
+not survive such relicensing or conveying.
+
+If you add terms to a covered work in accord with this section, you
+must place, in the relevant source files, a statement of the
+additional terms that apply to those files, or a notice indicating
+where to find the applicable terms.
+
+Additional terms, permissive or non-permissive, may be stated in the
+form of a separately written license, or stated as exceptions; the
+above requirements apply either way.
+
+#### 8. Termination.
+
+You may not propagate or modify a covered work except as expressly
+provided under this License. Any attempt otherwise to propagate or
+modify it is void, and will automatically terminate your rights under
+this License (including any patent licenses granted under the third
+paragraph of section 11).
+
+However, if you cease all violation of this License, then your license
+from a particular copyright holder is reinstated (a) provisionally,
+unless and until the copyright holder explicitly and finally
+terminates your license, and (b) permanently, if the copyright holder
+fails to notify you of the violation by some reasonable means prior to
+60 days after the cessation.
+
+Moreover, your license from a particular copyright holder is
+reinstated permanently if the copyright holder notifies you of the
+violation by some reasonable means, this is the first time you have
+received notice of violation of this License (for any work) from that
+copyright holder, and you cure the violation prior to 30 days after
+your receipt of the notice.
+
+Termination of your rights under this section does not terminate the
+licenses of parties who have received copies or rights from you under
+this License. If your rights have been terminated and not permanently
+reinstated, you do not qualify to receive new licenses for the same
+material under section 10.
+
+#### 9. Acceptance Not Required for Having Copies.
+
+You are not required to accept this License in order to receive or run
+a copy of the Program. Ancillary propagation of a covered work
+occurring solely as a consequence of using peer-to-peer transmission
+to receive a copy likewise does not require acceptance. However,
+nothing other than this License grants you permission to propagate or
+modify any covered work. These actions infringe copyright if you do
+not accept this License. Therefore, by modifying or propagating a
+covered work, you indicate your acceptance of this License to do so.
+
+#### 10. Automatic Licensing of Downstream Recipients.
+
+Each time you convey a covered work, the recipient automatically
+receives a license from the original licensors, to run, modify and
+propagate that work, subject to this License. You are not responsible
+for enforcing compliance by third parties with this License.
+
+An "entity transaction" is a transaction transferring control of an
+organization, or substantially all assets of one, or subdividing an
+organization, or merging organizations. If propagation of a covered
+work results from an entity transaction, each party to that
+transaction who receives a copy of the work also receives whatever
+licenses to the work the party's predecessor in interest had or could
+give under the previous paragraph, plus a right to possession of the
+Corresponding Source of the work from the predecessor in interest, if
+the predecessor has it or can get it with reasonable efforts.
+
+You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License. For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+#### 11. Patents.
+
+A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based. The
+work thus licensed is called the contributor's "contributor version".
+
+A contributor's "essential patent claims" are all patent claims owned
+or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version. For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement). To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients. "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+A patent license is "discriminatory" if it does not include within the
+scope of its coverage, prohibits the exercise of, or is conditioned on
+the non-exercise of one or more of the rights that are specifically
+granted under this License. You may not convey a covered work if you
+are a party to an arrangement with a third party that is in the
+business of distributing software, under which you make payment to the
+third party based on the extent of your activity of conveying the
+work, and under which the third party grants, to any of the parties
+who would receive the covered work from you, a discriminatory patent
+license (a) in connection with copies of the covered work conveyed by
+you (or copies made from those copies), or (b) primarily for and in
+connection with specific products or compilations that contain the
+covered work, unless you entered into that arrangement, or that patent
+license was granted, prior to 28 March 2007.
+
+Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+#### 12. No Surrender of Others' Freedom.
+
+If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License. If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under
+this License and any other pertinent obligations, then as a
+consequence you may not convey it at all. For example, if you agree to
+terms that obligate you to collect a royalty for further conveying
+from those to whom you convey the Program, the only way you could
+satisfy both those terms and this License would be to refrain entirely
+from conveying the Program.
+
+#### 13. Use with the GNU Affero General Public License.
+
+Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU Affero General Public License into a single
+combined work, and to convey the resulting work. The terms of this
+License will continue to apply to the part which is the covered work,
+but the special requirements of the GNU Affero General Public License,
+section 13, concerning interaction through a network will apply to the
+combination as such.
+
+#### 14. Revised Versions of this License.
+
+The Free Software Foundation may publish revised and/or new versions
+of the GNU General Public License from time to time. Such new versions
+will be similar in spirit to the present version, but may differ in
+detail to address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies that a certain numbered version of the GNU General Public
+License "or any later version" applies to it, you have the option of
+following the terms and conditions either of that numbered version or
+of any later version published by the Free Software Foundation. If the
+Program does not specify a version number of the GNU General Public
+License, you may choose any version ever published by the Free
+Software Foundation.
+
+If the Program specifies that a proxy can decide which future versions
+of the GNU General Public License can be used, that proxy's public
+statement of acceptance of a version permanently authorizes you to
+choose that version for the Program.
+
+Later license versions may give you additional or different
+permissions. However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+#### 15. Disclaimer of Warranty.
+
+THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT
+WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND
+PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE
+DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR
+CORRECTION.
+
+#### 16. Limitation of Liability.
+
+IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR
+CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES
+ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT
+NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
+LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM
+TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER
+PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
+
+#### 17. Interpretation of Sections 15 and 16.
+
+If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+END OF TERMS AND CONDITIONS
+
+### How to Apply These Terms to Your New Programs
+
+If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these
+terms.
+
+To do so, attach the following notices to the program. It is safest to
+attach them to the start of each source file to most effectively state
+the exclusion of warranty; and each file should have at least the
+"copyright" line and a pointer to where the full notice is found.
+
+        <one line to give the program's name and a brief idea of what it does.>
+        Copyright (C) <year>  <name of author>
+
+        This program is free software: you can redistribute it and/or modify
+        it under the terms of the GNU General Public License as published by
+        the Free Software Foundation, either version 3 of the License, or
+        (at your option) any later version.
+
+        This program is distributed in the hope that it will be useful,
+        but WITHOUT ANY WARRANTY; without even the implied warranty of
+        MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+        GNU General Public License for more details.
+
+        You should have received a copy of the GNU General Public License
+        along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper
+mail.
+
+If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+        <program>  Copyright (C) <year>  <name of author>
+        This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+        This is free software, and you are welcome to redistribute it
+        under certain conditions; type `show c' for details.
+
+The hypothetical commands \`show w' and \`show c' should show the
+appropriate parts of the General Public License. Of course, your
+program's commands might be different; for a GUI interface, you would
+use an "about box".
+
+You should also get your employer (if you work as a programmer) or
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. For more information on this, and how to apply and follow
+the GNU GPL, see <https://www.gnu.org/licenses/>.
+
+The GNU General Public License does not permit incorporating your
+program into proprietary programs. If your program is a subroutine
+library, you may consider it more useful to permit linking proprietary
+applications with the library. If this is what you want to do, use the
+GNU Lesser General Public License instead of this License. But first,
+please read <https://www.gnu.org/licenses/why-not-lgpl.html>.
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,152 +1,148 @@
-# ``finitary``
-
-## What's all this about?
-
-``finitary`` allows us to specify that a type is _finite_ (that is, contains
-finitely many inhabitants which are not ``_|_``), and have confirmation of this
-fact by GHC. Additionally, it offers a ``Generics``-based auto-derivation
-interface for this, as well as multiple helper functions that are enabled by all
-this machinery.
-
-### Why is this a big deal?
-
-Consider ``Enum``. It's not difficult to see that ``Enum`` has issues:
-
-#### It's partial all over the place
-
-What will this code do?
-
-```haskell
-toEnum 3 :: Bool
-```
-
-The answer is 'a runtime error'. How about this?
-
-```haskell
-succ True
-```
-
-The answer, again, is 'a runtime error'. Many of the methods provided by ``Enum``
-are partial like this, because many types that happen to be ``Enum`` instances
-have cardinalities (much) smaller than ``Int``, which necessitates leaving some
-``Int`` values 'out'.
-
-The converse is not much better: on some platforms, ``Int`` has _smaller_
-cardinality than some types with ``Enum`` instances in ``base``. For example, on 
-a platform where ``Int`` is 32 bits wide, the ``Word64`` instance will definitely 
-cause problems, as it's 'too big'.
-
-#### It gives us almost no information
-
-An ``Enum`` instance says that a type can be munged to and from an ``Int``...
-somehow. While ``base`` and the Haskell Report certainly provide some limits 
-on its behaviour, a lot of questions remain unanswered, including:
-
-* How many inhabitants does this type have?
-* What are the 'safe' values of ``Int`` I can feed to ``toEnum``?
-* For any ``x``, is ``toEnum . (+ 1) . fromEnum $ x`` safe (in that it'll give
-  us a value instead of blowing up)?
-
-#### We don't have a (default) way to auto-derive it
-
-Quoting ``base``:
-
-> Instances of ``Enum`` may be derived for any enumeration type (types whose
-> constructors have no fields).
-
-But what if your type has fields, especially when they're instances of ``Enum``? 
-Unfortunately, no auto-derivation for you. While this stance makes some sense, 
-it's still rather inconvenient.
-
-## OK, so what are you offering instead?
-
-The core of ``finitary`` is the ``Finitary`` type class. If we have an instance
-of ``Finitary`` for some type ``a``, we have a witness to an isomorphism between
-``a`` and some ``(KnownNat n) => Finite n``. More precisely, we (together with GHC)
-know:
-
-* That ``a`` has finitely-many non-``_|_`` inhabitants
-* The value of ``n``, which is the _cardinality_ of ``a`` (how many inhabitants we have exactly)
-* Two functions to 'witness' the isomorphism, namely ``fromFinite :: Finite n ->
-  a`` and ``toFinite :: a -> Finite n``
-
-### How does ``Finitary`` solve the issues behind ``Enum``?
-
-#### Everything is total, forever
-
-There is no way to call ``fromFinite`` or ``toFinite`` with an 'inappropriate'
-argument. We always know - if you give me a ``Finite n``, I will give you back a
-(unique) ``a``, guaranteed.
-
-#### We learn a lot from a type having a ``Finitary`` instance
-
-Aside from cardinality, we also inherently get the ability to:
-
-* Have a 'starting' and 'ending' value (assuming the cardinality of the type
-  isn't zero); and
-* Get the 'next' or 'previous' value, or report that it doesn't exist.
-
-All of this is safe, total and can be relied upon. Check out the documentation
-for more details - all of this functionality is provided. We also have functions
-to help enumerate values of ``Finitary`` types.
-
-#### But what about auto-derivation?
-
-We have you covered. If you want to auto-derive an instance of
-``Finitary`` for your type, you absolutely can, using the power of
-``GHC.Generics``:
-
-```haskell
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE DeriveAnyClass #-}
-{-# LANGUAGE DeriveGeneric #-}
-{-# LANGUAGE DerivingStrategies #-}
-
-import Data.Finitary (Finitary)
-import Data.Vector.Sized (Vector)
-import Data.Word (Word8)
-import GHC.Generics (Generic)
-
-data Foo = Bar | Baz (Word8, Word8) | Quux (Vector 4 Bool)
-  deriving stock (Eq, Generic)
-  deriving anyclass (Finitary) 
-```
-
-Furthermore, GHC will even calculate the cardinality for you. To assist in this,
-we have provided as many instances of ``Finitary`` for 'base' types as possible - 
-see the documentation for full details.
-
-### That all seems rather cool - what else can I do with this?
-
-Knowing that a type has finite cardinality is usable for many things - all of
-which we plan to provide. Some examples (with links once we have working, tested
-code) include:
-
-* [Automatic derivation of instances][1]
-* Type-safe refinement
-* Random generation and stream sampling
-* Efficient sets, allowing operations like complements and a ``Monoid`` under
-  intersection
-* Efficient maps
-* Various clever ``lens`` tricks
-
-If there's something else interesting you think can be done with this, let us
-know: it might make it onto this list, and into code.
-
-## What will this work on?
-
-Currently, we support the lates three versions of GHC. This, as current, is:
-
-* 8.6.5
-* 8.8.3
-* 8.10.1
-
-So far, the tests have all been on x86_64 GNU/Linux. If you have results on
-other platforms or architectures, please let us know too!
-
-## License
-
-This library is under the GNU General Public License, version 3 or later (SPDX
-code ``GPL-3.0-or-later``). For more details, see the ``LICENSE.md`` file.
-
-[1]: https://notabug.org/koz.ross/finitary-derive
+# ``finitary``
+
+## What's all this about?
+
+``finitary`` allows us to specify that a type is _finite_ (that is, contains
+finitely many inhabitants which are not ``_|_``), and have confirmation of this
+fact by GHC. Additionally, it offers a ``Generics``-based auto-derivation
+interface for this, as well as multiple helper functions that are enabled by all
+this machinery.
+
+### Why is this a big deal?
+
+Consider ``Enum``. It's not difficult to see that ``Enum`` has issues:
+
+#### It's partial all over the place
+
+What will this code do?
+
+```haskell
+toEnum 3 :: Bool
+```
+
+The answer is 'a runtime error'. How about this?
+
+```haskell
+succ True
+```
+
+The answer, again, is 'a runtime error'. Many of the methods provided by ``Enum``
+are partial like this, because many types that happen to be ``Enum`` instances
+have cardinalities (much) smaller than ``Int``, which necessitates leaving some
+``Int`` values 'out'.
+
+The converse is not much better: on some platforms, ``Int`` has _smaller_
+cardinality than some types with ``Enum`` instances in ``base``. For example, on 
+a platform where ``Int`` is 32 bits wide, the ``Word64`` instance will definitely 
+cause problems, as it's 'too big'.
+
+#### It gives us almost no information
+
+An ``Enum`` instance says that a type can be munged to and from an ``Int``...
+somehow. While ``base`` and the Haskell Report certainly provide some limits 
+on its behaviour, a lot of questions remain unanswered, including:
+
+* How many inhabitants does this type have?
+* What are the 'safe' values of ``Int`` I can feed to ``toEnum``?
+* For any ``x``, is ``toEnum . (+ 1) . fromEnum $ x`` safe (in that it'll give
+  us a value instead of blowing up)?
+
+#### We don't have a (default) way to auto-derive it
+
+Quoting ``base``:
+
+> Instances of ``Enum`` may be derived for any enumeration type (types whose
+> constructors have no fields).
+
+But what if your type has fields, especially when they're instances of ``Enum``? 
+Unfortunately, no auto-derivation for you. While this stance makes some sense, 
+it's still rather inconvenient.
+
+## OK, so what are you offering instead?
+
+The core of ``finitary`` is the ``Finitary`` type class. If we have an instance
+of ``Finitary`` for some type ``a``, we have a witness to an isomorphism between
+``a`` and some ``(KnownNat n) => Finite n``. More precisely, we (together with GHC)
+know:
+
+* That ``a`` has finitely-many non-``_|_`` inhabitants
+* The value of ``n``, which is the _cardinality_ of ``a`` (how many inhabitants we have exactly)
+* Two functions to 'witness' the isomorphism, namely ``fromFinite :: Finite n ->
+  a`` and ``toFinite :: a -> Finite n``
+
+### How does ``Finitary`` solve the issues behind ``Enum``?
+
+#### Everything is total, forever
+
+There is no way to call ``fromFinite`` or ``toFinite`` with an 'inappropriate'
+argument. We always know - if you give me a ``Finite n``, I will give you back a
+(unique) ``a``, guaranteed.
+
+#### We learn a lot from a type having a ``Finitary`` instance
+
+Aside from cardinality, we also inherently get the ability to:
+
+* Have a 'starting' and 'ending' value (assuming the cardinality of the type
+  isn't zero); and
+* Get the 'next' or 'previous' value, or report that it doesn't exist.
+
+All of this is safe, total and can be relied upon. Check out the documentation
+for more details - all of this functionality is provided. We also have functions
+to help enumerate values of ``Finitary`` types.
+
+#### But what about auto-derivation?
+
+We have you covered. If you want to auto-derive an instance of
+``Finitary`` for your type, you absolutely can, using the power of
+``GHC.Generics``:
+
+```haskell
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DeriveAnyClass #-}
+{-# LANGUAGE DeriveGeneric #-}
+{-# LANGUAGE DerivingStrategies #-}
+
+import Data.Finitary (Finitary)
+import Data.Vector.Sized (Vector)
+import Data.Word (Word8)
+import GHC.Generics (Generic)
+
+data Foo = Bar | Baz (Word8, Word8) | Quux (Vector 4 Bool)
+  deriving stock (Eq, Generic)
+  deriving anyclass (Finitary) 
+```
+
+Furthermore, GHC will even calculate the cardinality for you. To assist in this,
+we have provided as many instances of ``Finitary`` for 'base' types as possible - 
+see the documentation for full details.
+
+### That all seems rather cool - what else can I do with this?
+
+Knowing that a type has finite cardinality is usable for many things - all of
+which we plan to provide. Some examples (with links once we have working, tested
+code) include:
+
+* [Automatic derivation of instances][1]
+* Type-safe refinement
+* Random generation and stream sampling
+* Efficient sets, allowing operations like complements and a ``Monoid`` under
+  intersection
+* Efficient maps
+* Various clever ``lens`` tricks
+
+If there's something else interesting you think can be done with this, let us
+know: it might make it onto this list, and into code.
+
+## What will this work on?
+
+Currently, we support GHC versions ranging from 8.6 to 9.0.
+
+The library has been tested on x86_64, GNU/Linux and Windows.
+If you have results on other platforms or architectures, please let us know too!
+
+## License
+
+This library is under the GNU General Public License, version 3 or later (SPDX
+code ``GPL-3.0-or-later``). For more details, see the ``LICENSE.md`` file.
+
+[1]: https://notabug.org/sheaf/finitary-derive
diff --git a/Setup.hs b/Setup.hs
--- a/Setup.hs
+++ b/Setup.hs
@@ -1,3 +1,3 @@
-import Distribution.Simple
-
-main = defaultMain
+import Distribution.Simple
+
+main = defaultMain
diff --git a/finitary.cabal b/finitary.cabal
--- a/finitary.cabal
+++ b/finitary.cabal
@@ -1,81 +1,98 @@
-cabal-version:      2.2
-name:               finitary
-version:            2.0.0.0
-synopsis:           A better, more type-safe Enum.
-description:
-  Provides a type class witnessing that a type has
-  finitely-many inhabitants, as well as its cardinality.
-  Also provides an auto-deriving framework using GHC
-  Generics, together with a range of instances for existing
-  types.
-
-homepage:           https://notabug.org/koz.ross/finitary
-bug-reports:        https://notabug.org/koz.ross/finitary/issues
-license:            GPL-3.0-or-later
-license-file:       LICENSE.md
-author:             Koz Ross
-maintainer:         koz.ross@retro-freedom.nz
-copyright:          (C) Koz Ross 2019-2020
-category:           Data
-build-type:         Simple
-tested-with:        GHC ==8.6.5 || ==8.8.3 || ==8.10.1
-extra-source-files:
-  CHANGELOG.md
-  README.md
-  LICENSE.md
-
-source-repository head
-  type:     git
-  location: git://notabug.org/koz.ross/finitary.git
-
-library
-  exposed-modules:  Data.Finitary
-  other-modules:    Data.Finitary.TH
-  build-depends:
-    , base                       >=4.12     && <5
-    , bitvec                     ^>=1.0.3.0
-    , finite-typelits            ^>=0.1.4.2
-    , ghc-typelits-knownnat      ^>=0.7.2
-    , ghc-typelits-natnormalise  ^>=0.7.2
-    , primitive                  ^>=0.7.0.1
-    , template-haskell           >=2.14.0.0 && <3.0.0.0
-    , typelits-witnesses         ^>=0.4.0.0
-    , vector                     ^>=0.12.1.2
-    , vector-sized               ^>=1.4.1.0
-
-  hs-source-dirs:   src
-  ghc-options:
-    -Wall -Wcompat -Wincomplete-record-updates
-    -Wincomplete-uni-patterns -Wredundant-constraints
-
-  default-language: Haskell2010
-
-test-suite tests
-  type:             exitcode-stdio-1.0
-  main-is:          Main.hs
-  other-modules:
-    Data.Finitary
-    Data.Finitary.TH
-
-  build-depends:
-    , base
-    , bitvec
-    , finite-typelits
-    , ghc-typelits-knownnat
-    , ghc-typelits-natnormalise
-    , hedgehog                   ^>=1.0.2
-    , hspec                      ^>=2.7.1
-    , hspec-hedgehog             ^>=0.0.1.2
-    , primitive
-    , template-haskell
-    , typelits-witnesses
-    , vector
-    , vector-sized
-
-  hs-source-dirs:   test src
-  ghc-options:
-    -Wall -Wcompat -Wincomplete-record-updates
-    -Wincomplete-uni-patterns -Wredundant-constraints -O2 -threaded
-    -with-rtsopts=-N
-
-  default-language: Haskell2010
+cabal-version:      2.2
+name:               finitary
+version:            2.1.0.1
+synopsis:           A better, more type-safe Enum.
+description:
+  Provides a type class witnessing that a type has
+  finitely-many inhabitants, as well as its cardinality.
+  Also provides an auto-deriving framework using GHC
+  Generics, together with a range of instances for existing
+  types.
+
+homepage:           https://notabug.org/sheaf/finitary
+bug-reports:        https://notabug.org/sheaf/finitary/issues
+license:            GPL-3.0-or-later
+license-file:       LICENSE.md
+author:             Koz Ross
+maintainer:         Sam Derbyshire
+copyright:          (C) Koz Ross 2019-2020
+category:           Data
+build-type:         Simple
+tested-with:        GHC ==8.6.5 || ==8.8.3 || ==8.10.1 || == 9.0.1
+extra-source-files:
+  CHANGELOG.md
+  README.md
+  LICENSE.md
+
+flag bitvec
+  description: Include 'bitvec' instances
+  default: True
+  manual: False
+
+flag vector
+  description: Include 'vector' instances
+  default: True
+  manual: False
+
+source-repository head
+  type:     git
+  location: git://notabug.org/sheaf/finitary.git
+
+library
+  exposed-modules:  Data.Finitary
+  other-modules:    Data.Finitary.TH
+  build-depends:
+    , base                       >=4.12     && <5
+    , finite-typelits            ^>=0.1.4.2
+    , ghc-typelits-knownnat      ^>=0.7.2
+    , ghc-typelits-natnormalise  ^>=0.7.2
+    , template-haskell           >=2.14.0.0 && <3.0.0.0
+    , typelits-witnesses         ^>=0.4.0.0
+
+  if flag(bitvec)
+    cpp-options:
+      -DBITVEC
+    build-depends:
+      , bitvec                   >=1.0.3.0 && < 1.2
+  if flag(vector)
+    cpp-options:
+      -DVECTOR
+    build-depends:
+      , primitive                ^>=0.7.0.1
+      , vector                   ^>=0.12.1.2
+      , vector-sized             ^>=1.4.1.0
+
+  hs-source-dirs:   src
+  ghc-options:
+    -Wall -Wcompat -Wincomplete-record-updates
+    -Wincomplete-uni-patterns -Wredundant-constraints
+
+  default-language: Haskell2010
+
+test-suite tests
+  type:             exitcode-stdio-1.0
+  main-is:          Main.hs
+
+  build-depends:
+    , base
+    , bitvec
+    , finite-typelits
+    , finitary
+    , ghc-typelits-knownnat
+    , ghc-typelits-natnormalise
+    , hedgehog                   ^>=1.0.2
+    , hspec                      ^>=2.7.1
+    , hspec-hedgehog             ^>=0.0.1.2
+    , primitive
+    , template-haskell
+    , typelits-witnesses
+    , vector
+    , vector-sized
+
+  hs-source-dirs:   test
+  ghc-options:
+    -Wall -Wcompat -Wincomplete-record-updates
+    -Wincomplete-uni-patterns -Wredundant-constraints -O2 -threaded
+    -with-rtsopts=-N
+
+  default-language: Haskell2010
diff --git a/src/Data/Finitary.hs b/src/Data/Finitary.hs
--- a/src/Data/Finitary.hs
+++ b/src/Data/Finitary.hs
@@ -1,690 +1,702 @@
-{-# LANGUAGE AllowAmbiguousTypes #-}
-{-# LANGUAGE ConstrainedClassMethods #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE DefaultSignatures #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE TemplateHaskell #-}
-{-# LANGUAGE Trustworthy #-}
-{-# LANGUAGE TypeApplications #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE NoStarIsType #-}
-{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
-{-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-}
-
-{-
- - Copyright (C) 2019-2020  Koz Ross <koz.ross@retro-freedom.nz>
- -
- - This program is free software: you can redistribute it and/or modify
- - it under the terms of the GNU General Public License as published by
- - the Free Software Foundation, either version 3 of the License, or
- - (at your option) any later version.
- -
- - This program is distributed in the hope that it will be useful,
- - but WITHOUT ANY WARRANTY; without even the implied warranty of
- - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- - GNU General Public License for more details.
- -
- - You should have received a copy of the GNU General Public License
- - along with this program.  If not, see <http://www.gnu.org/licenses/>.
- -}
-
--- |
--- Module:        Data.Finitary
--- Description:   A type class witnessing that a type has finite cardinality.
--- Copyright:     (C) Koz Ross, 2019-2020
--- License:       GPL version 3.0 or later
--- Maintainer:    koz.ross@retro-freedom.nz
--- Stability:     Experimental
--- Portability:   GHC only
---
--- This package provides the 'Finitary' type class, a range of useful
--- \'base\' instances for commonly-used finitary types, and some helper
--- functions for enumerating values of types with 'Finitary' instances.
---
--- For your own types, there are three possible ways to define an instance of
--- 'Finitary':
---
--- __Via 'Generic'__
---
--- If your data type implements 'Generic' (and is finitary), you can
--- automatically derive your instance:
---
--- > {-# LANGUAGE DeriveAnyClass #-}
--- > {-# LANGUAGE DeriveGeneric #-}
--- > {-# LANGUAGE DerivingStrategies #-}
--- >
--- > import Data.Finitary (Finitary)
--- > import Data.Word (Word8, Word16)
--- > import GHC.Generics (Generic)
--- >
--- > data Foo = Bar | Baz (Word8, Word8) | Quux Word16
--- >    deriving stock (Eq, Generic)
--- >    deriving anyclass (Finitary)
---
--- This is the easiest method, and also the safest, as GHC will automatically
--- determine the cardinality of @Foo@, as well as defining law-abiding methods.
--- It may be somewhat slower than a \'hand-rolled\' method in some cases.
---
--- __By defining only 'Cardinality', 'fromFinite' and 'toFinite'__
---
--- If you want a manually-defined instance, but don't wish to define every
--- method, only 'fromFinite' and 'toFinite' are needed, along with
--- 'Cardinality'. 'Cardinality' in particular must be defined with care, as
--- otherwise, you may end up with inconstructable values or indexes that don't
--- correspond to anything.
---
--- __By defining everything__
---
--- For maximum control, you can define all the methods. Ensure you follow all
--- the laws!
-module Data.Finitary
-  ( Finitary (..),
-
-    -- * Enumeration functions
-    inhabitants,
-    inhabitantsFrom,
-    inhabitantsTo,
-    inhabitantsFromTo,
-  )
-where
-
-import Control.Applicative (Alternative (..), Const)
-import Control.Monad (forM_, join)
-import Control.Monad.Primitive (PrimMonad (..))
-import Control.Monad.ST (ST, runST)
-import Data.Bifunctor (bimap, first)
-import qualified Data.Bit as B
-import qualified Data.Bit.ThreadSafe as BTS
-import Data.Bool (bool)
-import Data.Finitary.TH
-import Data.Finite
-  ( Finite,
-    combineProduct,
-    finites,
-    separateProduct,
-    separateSum,
-    shiftN,
-    weakenN,
-  )
-import Data.Functor.Identity (Identity)
-import Data.Int (Int16, Int32, Int64, Int8)
-import Data.Kind (Type)
-import Data.List.NonEmpty (NonEmpty (..))
-import qualified Data.List.NonEmpty as NE
-import Data.Ord (Down (..))
-import Data.Proxy (Proxy (..))
-import Data.Semigroup (All, Any, Dual, First, Last, Max, Min, Product, Sum)
-import Data.Type.Equality ((:~:) (..))
-import qualified Data.Vector.Generic as VG
-import qualified Data.Vector.Generic.Mutable as VGM
-import qualified Data.Vector.Generic.Mutable.Sized as VGMS
-import qualified Data.Vector.Generic.Sized as VGS
-import qualified Data.Vector.Mutable.Sized as VMS
-import qualified Data.Vector.Sized as VS
-import qualified Data.Vector.Storable.Mutable.Sized as VSMS
-import qualified Data.Vector.Storable.Sized as VSS
-import qualified Data.Vector.Unboxed.Mutable.Sized as VUMS
-import qualified Data.Vector.Unboxed.Sized as VUS
-import Data.Void (Void)
-import Data.Word (Word16, Word32, Word64, Word8)
-import Foreign.Storable (Storable)
-import GHC.Generics
-  ( (:*:) (..),
-    (:+:) (..),
-    Generic,
-    K1 (..),
-    M1 (..),
-    Rep,
-    U1 (..),
-    V1,
-    from,
-    to,
-  )
-import GHC.TypeLits.Compare (isLE)
-import GHC.TypeNats
-import Numeric.Natural (Natural)
-
--- | Witnesses an isomorphism between @a@ and some @(KnownNat n) => Finite n@.
--- Effectively, a lawful instance of this shows that @a@ has exactly @n@
--- (non-@_|_@) inhabitants, and that we have a bijection with 'fromFinite' and
--- 'toFinite' as each \'direction\'.
---
--- For any type @a@ with an instance of @Finitary@, for every non-@_|_@ @x :: a@, we have
--- a unique /index/ @i :: Finite n@. We will also refer to any such @x@ as an
--- /inhabitant/ of @a@. We can convert inhabitants to indexes using @toFinite@,
--- and also convert indexes to inhabitants with @fromFinite@.
---
--- __Laws__
---
--- The main laws state that 'fromFinite' should be a bijection, with 'toFinite' as
--- its inverse, and 'Cardinality' must be a truthful representation of the
--- cardinality of the type. Thus:
---
---    * \[\texttt{fromFinite} \circ \texttt{toFinite} = \texttt{toFinite} \circ
--- \texttt{fromFinite} = \texttt{id}\]
---    * \[\forall x, y :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \; \texttt{fromFinite} \; x = \texttt{fromFinite} \; y
--- \rightarrow x = y\]
---    * \[\forall x :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \; \exists y :: a \mid \texttt{fromFinite} \; x
--- = y\]
---
--- Furthermore, 'fromFinite' should be _order-preserving_. Namely, if @a@ is an
--- instance of @Ord@, we must have:
---
---    * \[\forall i, j :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \;
---    \texttt{fromFinite} \; i \leq \texttt{fromFinite} \; j \rightarrow i \leq j \]
---
--- Lastly, if you define any of the other methods, these laws must hold:
---
---    * \[ a \neq \emptyset \rightarrow \texttt{start} :: a = \texttt{fromFinite} \; \texttt{minBound} \]
---    * \[ a \neq \emptyset \rightarrow \texttt{end} :: a = \texttt{fromFinite} \; \texttt{maxBound} \]
---    * \[ \forall x :: a \; \texttt{end} :: a \neq x \rightarrow \texttt{next} \; x =
--- (\texttt{fromFinite} \circ + 1 \circ \texttt{toFinite}) \; x \]
---    * \[ \forall x :: a \; \texttt{start} :: a \neq x \rightarrow \texttt{previous} \; x =
--- (\texttt{fromFinite} \circ - 1 \circ \texttt{toFinite}) \; x \]
---
--- Together with the fact that @Finite n@ is well-ordered whenever @KnownNat n@
--- holds, a law-abiding @Finitary@ instance for a type @a@ defines a constructive
--- [well-order](https://en.wikipedia.org/wiki/Well-order), witnessed by
--- 'toFinite' and 'fromFinite', which agrees with the @Ord@ instance for @a@, if
--- any.
---
--- We /strongly/ suggest that @fromFinite@ and @toFinite@ should have
--- time complexity \(\Theta(1)\), or, if that's not possible, \(O(\texttt{Cardinality} \; a)\).
--- The latter is the case for instances generated using
--- @Generics@-based derivation, but not for \'basic\' types; thus, these
--- functions for your derived types will only be as slow as their \'structure\',
--- rather than their \'contents\', provided the contents are of these \'basic\'
--- types.
-class (Eq a, KnownNat (Cardinality a)) => Finitary (a :: Type) where
-  -- | How many (non-@_|_@) inhabitants @a@ has, as a typelevel natural number.
-  type Cardinality a :: Nat
-
-  type Cardinality a = GCardinality (Rep a)
-
-  -- | Converts an index into its corresponding inhabitant.
-  fromFinite :: Finite (Cardinality a) -> a
-  default fromFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => Finite (Cardinality a) -> a
-  fromFinite = to . gFromFinite
-
-  -- | Converts an inhabitant to its corresponding index.
-  toFinite :: a -> Finite (Cardinality a)
-  default toFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => a -> Finite (Cardinality a)
-  toFinite = gToFinite . from
-
-  -- | The first inhabitant, by index, assuming @a@ has any inhabitants.
-  start :: (1 <= Cardinality a) => a
-  start = fromFinite minBound
-
-  -- | The last inhabitant, by index, assuming @a@ has any inhabitants.
-  end :: (1 <= Cardinality a) => a
-  end = fromFinite maxBound
-
-  -- | @previous x@ gives the inhabitant whose index precedes the index of @x@,
-  -- or 'empty' if no such index exists.
-  previous :: a -> Maybe a
-  previous = fmap fromFinite . guarded (/= maxBound) . dec . toFinite
-
-  -- | @next x@ gives the inhabitant whose index follows the index of @x@, or
-  -- 'empty' if no such index exists.
-  next :: a -> Maybe a
-  next = fmap fromFinite . guarded (/= minBound) . inc . toFinite
-
-class (KnownNat (GCardinality a)) => GFinitary (a :: Type -> Type) where
-  type GCardinality a :: Nat
-  gFromFinite :: Finite (GCardinality a) -> a x
-  gToFinite :: a x -> Finite (GCardinality a)
-
-instance GFinitary V1 where
-  type GCardinality V1 = 0
-  {-# INLINE gFromFinite #-}
-  gFromFinite = const undefined
-  {-# INLINE gToFinite #-}
-  gToFinite = const undefined
-
-instance GFinitary U1 where
-  type GCardinality U1 = 1
-  {-# INLINE gFromFinite #-}
-  gFromFinite = const U1
-  {-# INLINE gToFinite #-}
-  gToFinite = const 0
-
-instance (Finitary a) => GFinitary (K1 _1 a) where
-  type GCardinality (K1 _1 a) = Cardinality a
-  {-# INLINE gFromFinite #-}
-  gFromFinite = K1 . fromFinite
-  {-# INLINE gToFinite #-}
-  gToFinite = toFinite . unK1
-
-instance (GFinitary a, GFinitary b) => GFinitary (a :+: b) where
-  type GCardinality (a :+: b) = GCardinality a + GCardinality b
-  {-# INLINE gFromFinite #-}
-  gFromFinite = either (L1 . gFromFinite) (R1 . gFromFinite) . separateSum
-  {-# INLINE gToFinite #-}
-  gToFinite (L1 x) = weakenN . gToFinite $ x
-  gToFinite (R1 x) = shiftN . gToFinite $ x
-
-instance (GFinitary a, GFinitary b) => GFinitary (a :*: b) where
-  type GCardinality (a :*: b) = GCardinality a * GCardinality b
-  {-# INLINE gFromFinite #-}
-  gFromFinite i =
-    let (x, y) = separateProduct' i
-     in gFromFinite x :*: gFromFinite y
-  {-# INLINE gToFinite #-}
-  gToFinite (x :*: y) = combineProduct' @(GCardinality a) @(GCardinality b) (weakenN . gToFinite $ x, weakenN . gToFinite $ y)
-
-instance (GFinitary a) => GFinitary (M1 _x _y a) where
-  type GCardinality (M1 _x _y a) = GCardinality a
-  {-# INLINE gFromFinite #-}
-  gFromFinite = M1 . gFromFinite
-  {-# INLINE gToFinite #-}
-  gToFinite = gToFinite . unM1
-
--- * Instances
--- Basic types
-
-instance Finitary Void
-
-instance Finitary ()
-
-instance Finitary (Proxy a)
-
-instance Finitary Bool
-
-instance Finitary Any
-
-instance Finitary All
-
-instance Finitary B.Bit where
-  type Cardinality B.Bit = 2
-  {-# INLINE fromFinite #-}
-  fromFinite = B.Bit . toEnum . fromEnum
-  {-# INLINE toFinite #-}
-  toFinite = toEnum . fromEnum . B.unBit
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (== minBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (== maxBound)
-
-instance Finitary BTS.Bit where
-  type Cardinality BTS.Bit = 2
-  {-# INLINE fromFinite #-}
-  fromFinite = BTS.Bit . toEnum . fromEnum
-  {-# INLINE toFinite #-}
-  toFinite = toEnum . fromEnum . BTS.unBit
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (== minBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (== maxBound)
-
-instance Finitary Ordering
-
--- | 'Char' has one inhabitant per Unicode code point.
-instance Finitary Char where
-  type Cardinality Char = $(charCardinality)
-  {-# INLINE fromFinite #-}
-  fromFinite = toEnum . fromEnum
-  {-# INLINE toFinite #-}
-  toFinite = toEnum . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (/= maxBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (/= minBound)
-
-instance Finitary Word8 where
-  type Cardinality Word8 = $(cardinalityOf @Word8)
-  {-# INLINE fromFinite #-}
-  fromFinite = toEnum . fromEnum
-  {-# INLINE toFinite #-}
-  toFinite = toEnum . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (/= maxBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (/= minBound)
-
-instance Finitary Word16 where
-  type Cardinality Word16 = $(cardinalityOf @Word16)
-  {-# INLINE fromFinite #-}
-  fromFinite = toEnum . fromEnum
-  {-# INLINE toFinite #-}
-  toFinite = toEnum . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (/= maxBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (/= minBound)
-
-instance Finitary Word32 where
-  type Cardinality Word32 = $(cardinalityOf @Word32)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
-instance Finitary Word64 where
-  type Cardinality Word64 = $(cardinalityOf @Word64)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
-instance Finitary Int8 where
-  type Cardinality Int8 = $(cardinalityOf @Int8)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral . subtract 128 . fromIntegral @_ @Int16
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral . (+ 128) . fromIntegral @_ @Int16
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (/= maxBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (/= minBound)
-
-instance Finitary Int16 where
-  type Cardinality Int16 = $(cardinalityOf @Int16)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral . subtract 32768 . fromIntegral @_ @Int32
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral . (+ 32768) . fromIntegral @_ @Int32
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = fmap succ . guarded (/= maxBound)
-  {-# INLINE previous #-}
-  previous = fmap pred . guarded (/= minBound)
-
-instance Finitary Int32 where
-  type Cardinality Int32 = $(cardinalityOf @Int32)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral @_ @Int32 . subtract $(adjustmentOf @Int32) . fromIntegral @_ @Integer
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral . (+ $(adjustmentOf @Int32)) . fromIntegral @_ @Integer . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
-instance Finitary Int64 where
-  type Cardinality Int64 = $(cardinalityOf @Int64)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral @_ @Int64 . subtract $(adjustmentOf @Int64) . fromIntegral @_ @Integer
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral . (+ $(adjustmentOf @Int64)) . fromIntegral @_ @Integer . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
--- Variable-width instances
-
--- | 'Int' has a finite number of inhabitants, varying by platform. This
--- instance will determine this when the library is built.
-instance Finitary Int where
-  type Cardinality Int = $(cardinalityOf @Int)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral @_ @Int . subtract $(adjustmentOf @Int) . fromIntegral @_ @Integer
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral . (+ $(adjustmentOf @Int)) . fromIntegral @_ @Integer . fromEnum
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
--- | 'Word' has a finite number of inhabitants, varying by platform. This
--- instance will determine this when the library is built.
-instance Finitary Word where
-  type Cardinality Word = $(cardinalityOf @Word)
-  {-# INLINE fromFinite #-}
-  fromFinite = fromIntegral
-  {-# INLINE toFinite #-}
-  toFinite = fromIntegral
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
--- | Since any type is isomorphic to itself, it follows that a \'valid\' @Finite
--- n@ (meaning that @n@ is a 'KnownNat') has finite cardinality.
-instance (KnownNat n) => Finitary (Finite n) where
-  type Cardinality (Finite n) = n
-  {-# INLINE fromFinite #-}
-  fromFinite = id
-  {-# INLINE toFinite #-}
-  toFinite = id
-  {-# INLINE start #-}
-  start = minBound
-  {-# INLINE end #-}
-  end = maxBound
-  {-# INLINE next #-}
-  next = guarded (== minBound) . inc
-  {-# INLINE previous #-}
-  previous = guarded (== maxBound) . dec
-
--- | @Maybe a@ introduces one additional inhabitant (namely, 'Nothing') to @a@.
-instance (Finitary a) => Finitary (Maybe a)
-
--- | The sum of two finite types will also be finite, with a cardinality equal
--- to the sum of their cardinalities.
-instance (Finitary a, Finitary b) => Finitary (Either a b)
-
--- | The product of two finite types will also be finite, with a cardinality
--- equal to the product of their cardinalities.
-instance (Finitary a, Finitary b) => Finitary (a, b)
-
-instance (Finitary a, Finitary b, Finitary c) => Finitary (a, b, c)
-
-instance (Finitary a, Finitary b, Finitary c, Finitary d) => Finitary (a, b, c, d)
-
-instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e) => Finitary (a, b, c, d, e)
-
-instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e, Finitary f) => Finitary (a, b, c, d, e, f)
-
-instance (Finitary a) => Finitary (Const a b)
-
--- | For any @newtype@-esque thing over a type with a @Finitary@ instance, we
--- can just \'inherit\' the behaviour of @a@.
-instance (Finitary a) => Finitary (Sum a)
-
-instance (Finitary a) => Finitary (Product a)
-
-instance (Finitary a) => Finitary (Dual a)
-
-instance (Finitary a) => Finitary (Last a)
-
-instance (Finitary a) => Finitary (First a)
-
-instance (Finitary a) => Finitary (Identity a)
-
-instance (Finitary a) => Finitary (Max a)
-
-instance (Finitary a) => Finitary (Min a)
-
--- | Despite the @newtype@-esque nature of @Down@, due to the requirement that
--- 'fromFinite' is order-preserving, the instance for @Down a@ reverses the
--- indexing.
-instance (Finitary a) => Finitary (Down a) where
-  type Cardinality (Down a) = Cardinality a
-  {-# INLINE fromFinite #-}
-  fromFinite = Down . fromFinite . opp @a
-  {-# INLINE toFinite #-}
-  toFinite (Down x) = opp @a . toFinite $ x
-
--- | A fixed-length vector over a type @a@ with an instance of @Finitary@ can be
--- thought of as a fixed-length word over an alphabet of size @Cardinality a@.
--- Since there are only finitely-many of these, we can index them in lex order,
--- with the ordering determined by the @Finitary a@ instance (thus, the
--- \'first\' such @Vector@ is the one where each element is @start :: a@, and
--- the \'last\' is the one where each element is @end :: a@).
-instance (Finitary a, KnownNat n) => Finitary (VS.Vector n a) where
-  type Cardinality (VS.Vector n a) = Cardinality a ^ n
-  {-# INLINE fromFinite #-}
-  fromFinite i = runST (go i)
-    where
-      go :: Finite (Cardinality (VS.Vector n a)) -> ST s (VS.Vector n a)
-      go ix = do
-        v <- VMS.new
-        unroll v ix
-        VS.unsafeFreeze v
-  {-# INLINE toFinite #-}
-  toFinite = roll
-
-instance (Finitary a, VUMS.Unbox a, KnownNat n) => Finitary (VUS.Vector n a) where
-  type Cardinality (VUS.Vector n a) = Cardinality a ^ n
-  {-# INLINE fromFinite #-}
-  fromFinite i = runST (go i)
-    where
-      go :: Finite (Cardinality (VUS.Vector n a)) -> ST s (VUS.Vector n a)
-      go ix = do
-        v <- VUMS.new
-        unroll v ix
-        VUS.unsafeFreeze v
-  {-# INLINE toFinite #-}
-  toFinite = roll
-
-instance (Finitary a, Storable a, KnownNat n) => Finitary (VSS.Vector n a) where
-  type Cardinality (VSS.Vector n a) = Cardinality a ^ n
-  {-# INLINE fromFinite #-}
-  fromFinite i = runST (go i)
-    where
-      go :: Finite (Cardinality (VSS.Vector n a)) -> ST s (VSS.Vector n a)
-      go ix = do
-        v <- VSMS.new
-        unroll v ix
-        VSS.unsafeFreeze v
-  {-# INLINE toFinite #-}
-  toFinite = roll
-
--- * Enumeration helpers
-
--- | Produce every inhabitant of @a@, in ascending order of indexes.
--- If you want descending order, use @Down a@ instead.
-{-# INLINE inhabitants #-}
-inhabitants :: forall (a :: Type). (Finitary a) => [a]
-inhabitants = fromFinite <$> finites
-
--- | Produce every inhabitant of @a@, starting with the argument, in ascending
--- order of indexes.
--- If you want descending order, use @Down a@ instead.
-{-# INLINE inhabitantsFrom #-}
-inhabitantsFrom :: forall (a :: Type). (Finitary a) => a -> NonEmpty a
-inhabitantsFrom x = x :| concatMap @Maybe (fmap fromFinite . enumFrom . toFinite) (next x)
-
--- | Produce every inhabitant of @a@, up to and including the argument, in
--- ascending order of indexes.
--- If you want descending order, use @Down a@ instead.
-{-# INLINE inhabitantsTo #-}
-inhabitantsTo :: forall (a :: Type). (Finitary a) => a -> NonEmpty a
-inhabitantsTo x = NE.fromList (fromFinite <$> [0 .. toFinite x])
-
--- | Produce every inhabitant of @a@, starting with the first argument, up to
--- the second argument, in ascending order of indexes. @inhabitantsFromTo x y@
--- will produce the empty list if @toFinite x > toFinite y@.
--- If you want descending order, use @Down a@ instead.
-{-# INLINE inhabitantsFromTo #-}
-inhabitantsFromTo :: forall (a :: Type). (Finitary a) => a -> a -> [a]
-inhabitantsFromTo lo hi = fromFinite <$> [toFinite lo .. toFinite hi]
-
--- Helpers
-
-{-# INLINE combineProduct' #-}
-combineProduct' :: forall n m. (KnownNat n, KnownNat m) => (Finite n, Finite m) -> Finite (n * m)
-combineProduct' = fromIntegral . uncurry (+) . first ((natVal $ Proxy @m) *) . bimap @_ @_ @Natural @_ @Natural fromIntegral fromIntegral
-
-{-# INLINE separateProduct' #-}
-separateProduct' :: forall n m. (KnownNat n, KnownNat m) => Finite (n * m) -> (Finite n, Finite m)
-separateProduct' = bimap (fromIntegral . (\x -> fromIntegral x `div` natVal @m Proxy)) (fromIntegral . (\x -> fromIntegral x `mod` natVal @m Proxy)) . join (,)
-
-unroll :: forall a m v n. (Finitary a, PrimMonad m, KnownNat n, VGM.MVector v a) => VGMS.MVector v n (PrimState m) a -> Finite (Cardinality a ^ n) -> m ()
-unroll v acc =
-  forM_ @_ @_ @_ @()
-    (isLE (Proxy @1) (Proxy @n))
-    ( \Refl -> do
-        let (d, r) = separateProduct @(Cardinality a ^ (n -1)) @(Cardinality a) acc
-        let x = fromFinite r
-        VGMS.write v 0 x
-        unroll (VGMS.tail v) d
-    )
-
-roll :: forall a v n. (Finitary a, VG.Vector v a, KnownNat n) => VGS.Vector v n a -> Finite (Cardinality a ^ n)
-roll v = case isLE (Proxy @1) (Proxy @n) of
-  Nothing -> 0
-  Just Refl ->
-    let (h, t) = (VGS.head v, VGS.tail v)
-     in combineProduct (roll t, toFinite h)
-
-{-# INLINE inc #-}
-inc :: (Num a) => a -> a
-inc = (+ 1)
-
-{-# INLINE dec #-}
-dec :: (Num a) => a -> a
-dec = subtract 1
-
-{-# INLINE guarded #-}
-guarded :: forall (a :: Type) (f :: Type -> Type). (Alternative f) => (a -> Bool) -> a -> f a
-guarded p x = bool empty (pure x) (p x)
-
-{-# INLINE opp #-}
-opp :: forall a. (KnownNat (Cardinality a)) => Finite (Cardinality a) -> Finite (Cardinality a)
-opp = fromIntegral @_ @(Finite (Cardinality a)) . (`mod` n) . (* (n - 1)) . inc . fromIntegral @_ @Natural
-  where
-    n = natVal @(Cardinality a) Proxy
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE ConstrainedClassMethods #-}
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DefaultSignatures #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TemplateHaskell #-}
+{-# LANGUAGE Trustworthy #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE NoStarIsType #-}
+{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
+{-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-}
+
+{-
+ - Copyright (C) 2019-2020  Koz Ross <koz.ross@retro-freedom.nz>
+ -
+ - This program is free software: you can redistribute it and/or modify
+ - it under the terms of the GNU General Public License as published by
+ - the Free Software Foundation, either version 3 of the License, or
+ - (at your option) any later version.
+ -
+ - This program is distributed in the hope that it will be useful,
+ - but WITHOUT ANY WARRANTY; without even the implied warranty of
+ - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ - GNU General Public License for more details.
+ -
+ - You should have received a copy of the GNU General Public License
+ - along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ -}
+
+-- |
+-- Module:        Data.Finitary
+-- Description:   A type class witnessing that a type has finite cardinality.
+-- Copyright:     (C) Koz Ross, 2019-2020
+-- License:       GPL version 3.0 or later
+-- Stability:     Experimental
+-- Portability:   GHC only
+--
+-- This package provides the 'Finitary' type class, a range of useful
+-- \'base\' instances for commonly-used finitary types, and some helper
+-- functions for enumerating values of types with 'Finitary' instances.
+--
+-- For your own types, there are three possible ways to define an instance of
+-- 'Finitary':
+--
+-- __Via 'Generic'__
+--
+-- If your data type implements 'Generic' (and is finitary), you can
+-- automatically derive your instance:
+--
+-- > {-# LANGUAGE DeriveAnyClass #-}
+-- > {-# LANGUAGE DeriveGeneric #-}
+-- > {-# LANGUAGE DerivingStrategies #-}
+-- >
+-- > import Data.Finitary (Finitary)
+-- > import Data.Word (Word8, Word16)
+-- > import GHC.Generics (Generic)
+-- >
+-- > data Foo = Bar | Baz (Word8, Word8) | Quux Word16
+-- >    deriving stock (Eq, Generic)
+-- >    deriving anyclass (Finitary)
+--
+-- This is the easiest method, and also the safest, as GHC will automatically
+-- determine the cardinality of @Foo@, as well as defining law-abiding methods.
+-- It may be somewhat slower than a \'hand-rolled\' method in some cases.
+--
+-- __By defining only 'Cardinality', 'fromFinite' and 'toFinite'__
+--
+-- If you want a manually-defined instance, but don't wish to define every
+-- method, only 'fromFinite' and 'toFinite' are needed, along with
+-- 'Cardinality'. 'Cardinality' in particular must be defined with care, as
+-- otherwise, you may end up with inconstructable values or indexes that don't
+-- correspond to anything.
+--
+-- __By defining everything__
+--
+-- For maximum control, you can define all the methods. Ensure you follow all
+-- the laws!
+module Data.Finitary
+  ( Finitary (..),
+
+    -- * Enumeration functions
+    inhabitants,
+    inhabitantsFrom,
+    inhabitantsTo,
+    inhabitantsFromTo,
+  )
+where
+
+import Control.Applicative (Alternative (..), Const)
+import Control.Monad (join)
+import Data.Bifunctor (bimap, first)
+import Data.Bool (bool)
+import Data.Finitary.TH
+import Data.Finite
+  ( Finite,
+    finites,
+    separateSum,
+    shiftN,
+    weakenN,
+  )
+import Data.Functor.Identity (Identity)
+import Data.Int (Int16, Int32, Int64, Int8)
+import Data.Kind (Type)
+import Data.List.NonEmpty (NonEmpty (..))
+import qualified Data.List.NonEmpty as NE
+import Data.Ord (Down (..))
+import Data.Proxy (Proxy (..))
+import Data.Semigroup (All, Any, Dual, First, Last, Max, Min, Product, Sum)
+import Data.Void (Void)
+import Data.Word (Word16, Word32, Word64, Word8)
+import GHC.Generics
+  ( (:*:) (..),
+    (:+:) (..),
+    Generic,
+    K1 (..),
+    M1 (..),
+    Rep,
+    U1 (..),
+    V1,
+    from,
+    to,
+  )
+
+import GHC.TypeNats
+import Numeric.Natural (Natural)
+
+#ifdef BITVEC
+import qualified Data.Bit as B
+import qualified Data.Bit.ThreadSafe as BTS
+#endif
+
+#ifdef VECTOR
+import Control.Monad (forM_)
+import Control.Monad.Primitive (PrimMonad (..))
+import Control.Monad.ST (ST, runST)
+import Data.Finite
+  ( combineProduct,
+    separateProduct,
+  )
+import Data.Type.Equality ((:~:) (..))
+import qualified Data.Vector.Generic as VG
+import qualified Data.Vector.Generic.Mutable as VGM
+import qualified Data.Vector.Generic.Mutable.Sized as VGMS
+import qualified Data.Vector.Generic.Sized as VGS
+import qualified Data.Vector.Mutable.Sized as VMS
+import qualified Data.Vector.Sized as VS
+import qualified Data.Vector.Storable.Mutable.Sized as VSMS
+import qualified Data.Vector.Storable.Sized as VSS
+import qualified Data.Vector.Unboxed.Mutable.Sized as VUMS
+import qualified Data.Vector.Unboxed.Sized as VUS
+import Foreign.Storable (Storable)
+import GHC.TypeLits.Compare (isLE)
+#endif
+
+-- | Witnesses an isomorphism between @a@ and some @(KnownNat n) => Finite n@.
+-- Effectively, a lawful instance of this shows that @a@ has exactly @n@
+-- (non-@_|_@) inhabitants, and that we have a bijection with 'fromFinite' and
+-- 'toFinite' as each \'direction\'.
+--
+-- For any type @a@ with an instance of @Finitary@, for every non-@_|_@ @x :: a@, we have
+-- a unique /index/ @i :: Finite n@. We will also refer to any such @x@ as an
+-- /inhabitant/ of @a@. We can convert inhabitants to indexes using @toFinite@,
+-- and also convert indexes to inhabitants with @fromFinite@.
+--
+-- __Laws__
+--
+-- The main laws state that 'fromFinite' should be a bijection, with 'toFinite' as
+-- its inverse, and 'Cardinality' must be a truthful representation of the
+-- cardinality of the type. Thus:
+--
+--    * \[\texttt{fromFinite} \circ \texttt{toFinite} = \texttt{toFinite} \circ
+-- \texttt{fromFinite} = \texttt{id}\]
+--    * \[\forall x, y :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \; \texttt{fromFinite} \; x = \texttt{fromFinite} \; y
+-- \rightarrow x = y\]
+--    * \[\forall x :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \; \exists y :: a \mid \texttt{fromFinite} \; x
+-- = y\]
+--
+-- Furthermore, 'fromFinite' should be _order-preserving_. Namely, if @a@ is an
+-- instance of @Ord@, we must have:
+--
+--    * \[\forall i, j :: \texttt{Finite} \; (\texttt{Cardinality} \; a) \;
+--    \texttt{fromFinite} \; i \leq \texttt{fromFinite} \; j \rightarrow i \leq j \]
+--
+-- Lastly, if you define any of the other methods, these laws must hold:
+--
+--    * \[ a \neq \emptyset \rightarrow \texttt{start} :: a = \texttt{fromFinite} \; \texttt{minBound} \]
+--    * \[ a \neq \emptyset \rightarrow \texttt{end} :: a = \texttt{fromFinite} \; \texttt{maxBound} \]
+--    * \[ \forall x :: a \; \texttt{end} :: a \neq x \rightarrow \texttt{next} \; x =
+-- (\texttt{fromFinite} \circ + 1 \circ \texttt{toFinite}) \; x \]
+--    * \[ \forall x :: a \; \texttt{start} :: a \neq x \rightarrow \texttt{previous} \; x =
+-- (\texttt{fromFinite} \circ - 1 \circ \texttt{toFinite}) \; x \]
+--
+-- Together with the fact that @Finite n@ is well-ordered whenever @KnownNat n@
+-- holds, a law-abiding @Finitary@ instance for a type @a@ defines a constructive
+-- [well-order](https://en.wikipedia.org/wiki/Well-order), witnessed by
+-- 'toFinite' and 'fromFinite', which agrees with the @Ord@ instance for @a@, if
+-- any.
+--
+-- We /strongly/ suggest that @fromFinite@ and @toFinite@ should have
+-- time complexity \(\Theta(1)\), or, if that's not possible, \(O(\texttt{Cardinality} \; a)\).
+-- The latter is the case for instances generated using
+-- @Generics@-based derivation, but not for \'basic\' types; thus, these
+-- functions for your derived types will only be as slow as their \'structure\',
+-- rather than their \'contents\', provided the contents are of these \'basic\'
+-- types.
+class (Eq a, KnownNat (Cardinality a)) => Finitary (a :: Type) where
+  -- | How many (non-@_|_@) inhabitants @a@ has, as a typelevel natural number.
+  type Cardinality a :: Nat
+
+  type Cardinality a = GCardinality (Rep a)
+
+  -- | Converts an index into its corresponding inhabitant.
+  fromFinite :: Finite (Cardinality a) -> a
+  default fromFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => Finite (Cardinality a) -> a
+  fromFinite = to . gFromFinite
+
+  -- | Converts an inhabitant to its corresponding index.
+  toFinite :: a -> Finite (Cardinality a)
+  default toFinite :: (Generic a, GFinitary (Rep a), Cardinality a ~ GCardinality (Rep a)) => a -> Finite (Cardinality a)
+  toFinite = gToFinite . from
+
+  -- | The first inhabitant, by index, assuming @a@ has any inhabitants.
+  start :: (1 <= Cardinality a) => a
+  start = fromFinite minBound
+
+  -- | The last inhabitant, by index, assuming @a@ has any inhabitants.
+  end :: (1 <= Cardinality a) => a
+  end = fromFinite maxBound
+
+  -- | @previous x@ gives 'Just' the inhabitant whose index precedes the index of @x@,
+  -- or 'Nothing' if no such index exists.
+  previous :: a -> Maybe a
+  previous = fmap fromFinite . guarded (/= maxBound) . dec . toFinite
+
+  -- | @next x@ gives 'Just' the inhabitant whose index follows the index of @x@, or
+  -- 'Nothing' if no such index exists.
+  next :: a -> Maybe a
+  next = fmap fromFinite . guarded (/= minBound) . inc . toFinite
+
+class (KnownNat (GCardinality a)) => GFinitary (a :: Type -> Type) where
+  type GCardinality a :: Nat
+  gFromFinite :: Finite (GCardinality a) -> a x
+  gToFinite :: a x -> Finite (GCardinality a)
+
+instance GFinitary V1 where
+  type GCardinality V1 = 0
+  {-# INLINE gFromFinite #-}
+  gFromFinite = const undefined
+  {-# INLINE gToFinite #-}
+  gToFinite = const undefined
+
+instance GFinitary U1 where
+  type GCardinality U1 = 1
+  {-# INLINE gFromFinite #-}
+  gFromFinite = const U1
+  {-# INLINE gToFinite #-}
+  gToFinite = const 0
+
+instance (Finitary a) => GFinitary (K1 _1 a) where
+  type GCardinality (K1 _1 a) = Cardinality a
+  {-# INLINE gFromFinite #-}
+  gFromFinite = K1 . fromFinite
+  {-# INLINE gToFinite #-}
+  gToFinite = toFinite . unK1
+
+instance (GFinitary a, GFinitary b) => GFinitary (a :+: b) where
+  type GCardinality (a :+: b) = GCardinality a + GCardinality b
+  {-# INLINE gFromFinite #-}
+  gFromFinite = either (L1 . gFromFinite) (R1 . gFromFinite) . separateSum
+  {-# INLINABLE gToFinite #-}
+  gToFinite (L1 x) = weakenN . gToFinite $ x
+  gToFinite (R1 x) = shiftN . gToFinite $ x
+
+instance (GFinitary a, GFinitary b) => GFinitary (a :*: b) where
+  type GCardinality (a :*: b) = GCardinality a * GCardinality b
+  {-# INLINABLE gFromFinite #-}
+  gFromFinite i =
+    let (x, y) = separateProduct' i
+     in gFromFinite x :*: gFromFinite y
+  {-# INLINABLE gToFinite #-}
+  gToFinite (x :*: y) = combineProduct' @(GCardinality a) @(GCardinality b) (weakenN . gToFinite $ x, weakenN . gToFinite $ y)
+
+instance (GFinitary a) => GFinitary (M1 _x _y a) where
+  type GCardinality (M1 _x _y a) = GCardinality a
+  {-# INLINE gFromFinite #-}
+  gFromFinite = M1 . gFromFinite
+  {-# INLINE gToFinite #-}
+  gToFinite = gToFinite . unM1
+
+-- * Instances
+-- Basic types
+
+instance Finitary Void
+
+instance Finitary ()
+
+instance Finitary (Proxy a)
+
+instance Finitary Bool
+
+instance Finitary Any
+
+instance Finitary All
+
+#ifdef BITVEC
+instance Finitary B.Bit where
+  type Cardinality B.Bit = 2
+  {-# INLINE fromFinite #-}
+  fromFinite = B.Bit . toEnum . fromEnum
+  {-# INLINE toFinite #-}
+  toFinite = toEnum . fromEnum . B.unBit
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (== minBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (== maxBound)
+
+instance Finitary BTS.Bit where
+  type Cardinality BTS.Bit = 2
+  {-# INLINE fromFinite #-}
+  fromFinite = BTS.Bit . toEnum . fromEnum
+  {-# INLINE toFinite #-}
+  toFinite = toEnum . fromEnum . BTS.unBit
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (== minBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (== maxBound)
+#endif
+
+instance Finitary Ordering
+
+-- | 'Char' has one inhabitant per Unicode code point.
+instance Finitary Char where
+  type Cardinality Char = $(charCardinality)
+  {-# INLINE fromFinite #-}
+  fromFinite = toEnum . fromEnum
+  {-# INLINE toFinite #-}
+  toFinite = toEnum . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (/= maxBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (/= minBound)
+
+instance Finitary Word8 where
+  type Cardinality Word8 = $(cardinalityOf @Word8)
+  {-# INLINE fromFinite #-}
+  fromFinite = toEnum . fromEnum
+  {-# INLINE toFinite #-}
+  toFinite = toEnum . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (/= maxBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (/= minBound)
+
+instance Finitary Word16 where
+  type Cardinality Word16 = $(cardinalityOf @Word16)
+  {-# INLINE fromFinite #-}
+  fromFinite = toEnum . fromEnum
+  {-# INLINE toFinite #-}
+  toFinite = toEnum . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (/= maxBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (/= minBound)
+
+instance Finitary Word32 where
+  type Cardinality Word32 = $(cardinalityOf @Word32)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+instance Finitary Word64 where
+  type Cardinality Word64 = $(cardinalityOf @Word64)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+instance Finitary Int8 where
+  type Cardinality Int8 = $(cardinalityOf @Int8)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral . subtract 128 . fromIntegral @_ @Int16
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral . (+ 128) . fromIntegral @_ @Int16
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (/= maxBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (/= minBound)
+
+instance Finitary Int16 where
+  type Cardinality Int16 = $(cardinalityOf @Int16)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral . subtract 32768 . fromIntegral @_ @Int32
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral . (+ 32768) . fromIntegral @_ @Int32
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = fmap succ . guarded (/= maxBound)
+  {-# INLINE previous #-}
+  previous = fmap pred . guarded (/= minBound)
+
+instance Finitary Int32 where
+  type Cardinality Int32 = $(cardinalityOf @Int32)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral @_ @Int32 . subtract $(adjustmentOf @Int32) . fromIntegral @_ @Integer
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral . (+ $(adjustmentOf @Int32)) . fromIntegral @_ @Integer . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+instance Finitary Int64 where
+  type Cardinality Int64 = $(cardinalityOf @Int64)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral @_ @Int64 . subtract $(adjustmentOf @Int64) . fromIntegral @_ @Integer
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral . (+ $(adjustmentOf @Int64)) . fromIntegral @_ @Integer . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+-- Variable-width instances
+
+-- | 'Int' has a finite number of inhabitants, varying by platform. This
+-- instance will determine this when the library is built.
+instance Finitary Int where
+  type Cardinality Int = $(cardinalityOf @Int)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral @_ @Int . subtract $(adjustmentOf @Int) . fromIntegral @_ @Integer
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral . (+ $(adjustmentOf @Int)) . fromIntegral @_ @Integer . fromEnum
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+-- | 'Word' has a finite number of inhabitants, varying by platform. This
+-- instance will determine this when the library is built.
+instance Finitary Word where
+  type Cardinality Word = $(cardinalityOf @Word)
+  {-# INLINE fromFinite #-}
+  fromFinite = fromIntegral
+  {-# INLINE toFinite #-}
+  toFinite = fromIntegral
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+-- | Since any type is isomorphic to itself, it follows that a \'valid\' @Finite
+-- n@ (meaning that @n@ is a 'KnownNat') has finite cardinality.
+instance (KnownNat n) => Finitary (Finite n) where
+  type Cardinality (Finite n) = n
+  {-# INLINE fromFinite #-}
+  fromFinite = id
+  {-# INLINE toFinite #-}
+  toFinite = id
+  {-# INLINE start #-}
+  start = minBound
+  {-# INLINE end #-}
+  end = maxBound
+  {-# INLINE next #-}
+  next = guarded (== minBound) . inc
+  {-# INLINE previous #-}
+  previous = guarded (== maxBound) . dec
+
+-- | @Maybe a@ introduces one additional inhabitant (namely, 'Nothing') to @a@.
+instance (Finitary a) => Finitary (Maybe a)
+
+-- | The sum of two finite types will also be finite, with a cardinality equal
+-- to the sum of their cardinalities.
+instance (Finitary a, Finitary b) => Finitary (Either a b)
+
+-- | The product of two finite types will also be finite, with a cardinality
+-- equal to the product of their cardinalities.
+instance (Finitary a, Finitary b) => Finitary (a, b)
+
+instance (Finitary a, Finitary b, Finitary c) => Finitary (a, b, c)
+
+instance (Finitary a, Finitary b, Finitary c, Finitary d) => Finitary (a, b, c, d)
+
+instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e) => Finitary (a, b, c, d, e)
+
+instance (Finitary a, Finitary b, Finitary c, Finitary d, Finitary e, Finitary f) => Finitary (a, b, c, d, e, f)
+
+instance (Finitary a) => Finitary (Const a b)
+
+-- | For any @newtype@-esque thing over a type with a @Finitary@ instance, we
+-- can just \'inherit\' the behaviour of @a@.
+instance (Finitary a) => Finitary (Sum a)
+
+instance (Finitary a) => Finitary (Product a)
+
+instance (Finitary a) => Finitary (Dual a)
+
+instance (Finitary a) => Finitary (Last a)
+
+instance (Finitary a) => Finitary (First a)
+
+instance (Finitary a) => Finitary (Identity a)
+
+instance (Finitary a) => Finitary (Max a)
+
+instance (Finitary a) => Finitary (Min a)
+
+-- | Despite the @newtype@-esque nature of @Down@, due to the requirement that
+-- 'fromFinite' is order-preserving, the instance for @Down a@ reverses the
+-- indexing.
+instance (Finitary a) => Finitary (Down a) where
+  type Cardinality (Down a) = Cardinality a
+  {-# INLINE fromFinite #-}
+  fromFinite = Down . fromFinite . opp @a
+  {-# INLINABLE toFinite #-}
+  toFinite (Down x) = opp @a . toFinite $ x
+
+#ifdef VECTOR
+-- | A fixed-length vector over a type @a@ with an instance of @Finitary@ can be
+-- thought of as a fixed-length word over an alphabet of size @Cardinality a@.
+-- Since there are only finitely-many of these, we can index them in lex order,
+-- with the ordering determined by the @Finitary a@ instance (thus, the
+-- \'first\' such @Vector@ is the one where each element is @start :: a@, and
+-- the \'last\' is the one where each element is @end :: a@).
+instance (Finitary a, KnownNat n) => Finitary (VS.Vector n a) where
+  type Cardinality (VS.Vector n a) = Cardinality a ^ n
+  {-# INLINABLE fromFinite #-}
+  fromFinite i = runST (go i)
+    where
+      go :: Finite (Cardinality (VS.Vector n a)) -> ST s (VS.Vector n a)
+      go ix = do
+        v <- VMS.new
+        unroll v ix
+        VS.unsafeFreeze v
+  {-# INLINE toFinite #-}
+  toFinite = roll
+
+instance (Finitary a, VUMS.Unbox a, KnownNat n) => Finitary (VUS.Vector n a) where
+  type Cardinality (VUS.Vector n a) = Cardinality a ^ n
+  {-# INLINABLE fromFinite #-}
+  fromFinite i = runST (go i)
+    where
+      go :: Finite (Cardinality (VUS.Vector n a)) -> ST s (VUS.Vector n a)
+      go ix = do
+        v <- VUMS.new
+        unroll v ix
+        VUS.unsafeFreeze v
+  {-# INLINE toFinite #-}
+  toFinite = roll
+
+instance (Finitary a, Storable a, KnownNat n) => Finitary (VSS.Vector n a) where
+  type Cardinality (VSS.Vector n a) = Cardinality a ^ n
+  {-# INLINABLE fromFinite #-}
+  fromFinite i = runST (go i)
+    where
+      go :: Finite (Cardinality (VSS.Vector n a)) -> ST s (VSS.Vector n a)
+      go ix = do
+        v <- VSMS.new
+        unroll v ix
+        VSS.unsafeFreeze v
+  {-# INLINE toFinite #-}
+  toFinite = roll
+
+unroll :: forall a m v n. (Finitary a, PrimMonad m, KnownNat n, VGM.MVector v a) => VGMS.MVector v n (PrimState m) a -> Finite (Cardinality a ^ n) -> m ()
+unroll v acc =
+  forM_ @_ @_ @_ @()
+    (isLE (Proxy @1) (Proxy @n))
+    ( \Refl -> do
+        let (d, r) = separateProduct @(Cardinality a ^ (n -1)) @(Cardinality a) acc
+        let x = fromFinite r
+        VGMS.write v 0 x
+        unroll (VGMS.tail v) d
+    )
+
+roll :: forall a v n. (Finitary a, VG.Vector v a, KnownNat n) => VGS.Vector v n a -> Finite (Cardinality a ^ n)
+roll v = case isLE (Proxy @1) (Proxy @n) of
+  Nothing -> 0
+  Just Refl ->
+    let (h, t) = (VGS.head v, VGS.tail v)
+     in combineProduct (roll t, toFinite h)
+#endif
+
+-- * Enumeration helpers
+
+-- | Produce every inhabitant of @a@, in ascending order of indexes.
+-- If you want descending order, use @Down a@ instead.
+{-# INLINE inhabitants #-}
+inhabitants :: forall (a :: Type). (Finitary a) => [a]
+inhabitants = fromFinite <$> finites
+
+-- | Produce every inhabitant of @a@, starting with the argument, in ascending
+-- order of indexes.
+-- If you want descending order, use @Down a@ instead.
+{-# INLINABLE inhabitantsFrom #-}
+inhabitantsFrom :: forall (a :: Type). (Finitary a) => a -> NonEmpty a
+inhabitantsFrom x = x :| concatMap @Maybe (fmap fromFinite . enumFrom . toFinite) (next x)
+
+-- | Produce every inhabitant of @a@, up to and including the argument, in
+-- ascending order of indexes.
+-- If you want descending order, use @Down a@ instead.
+{-# INLINABLE inhabitantsTo #-}
+inhabitantsTo :: forall (a :: Type). (Finitary a) => a -> NonEmpty a
+inhabitantsTo x = NE.fromList (fromFinite <$> [0 .. toFinite x])
+
+-- | Produce every inhabitant of @a@, starting with the first argument, up to
+-- the second argument, in ascending order of indexes. @inhabitantsFromTo x y@
+-- will produce the empty list if @toFinite x > toFinite y@.
+-- If you want descending order, use @Down a@ instead.
+{-# INLINABLE inhabitantsFromTo #-}
+inhabitantsFromTo :: forall (a :: Type). (Finitary a) => a -> a -> [a]
+inhabitantsFromTo lo hi = fromFinite <$> [toFinite lo .. toFinite hi]
+
+-- Helpers
+
+{-# INLINE combineProduct' #-}
+combineProduct' :: forall n m. (KnownNat n, KnownNat m) => (Finite n, Finite m) -> Finite (n * m)
+combineProduct' = fromIntegral . uncurry (+) . first ((natVal $ Proxy @m) *) . bimap @_ @_ @Natural @_ @Natural fromIntegral fromIntegral
+
+{-# INLINE separateProduct' #-}
+separateProduct' :: forall n m. (KnownNat n, KnownNat m) => Finite (n * m) -> (Finite n, Finite m)
+separateProduct' = bimap (fromIntegral . (\x -> fromIntegral x `div` natVal @m Proxy)) (fromIntegral . (\x -> fromIntegral x `mod` natVal @m Proxy)) . join (,)
+
+{-# INLINE inc #-}
+inc :: (Num a) => a -> a
+inc = (+ 1)
+
+{-# INLINE dec #-}
+dec :: (Num a) => a -> a
+dec = subtract 1
+
+{-# INLINABLE guarded #-}
+guarded :: forall (a :: Type) (f :: Type -> Type). (Alternative f) => (a -> Bool) -> a -> f a
+guarded p x = bool empty (pure x) (p x)
+
+{-# INLINE opp #-}
+opp :: forall a. (KnownNat (Cardinality a)) => Finite (Cardinality a) -> Finite (Cardinality a)
+opp = ( maxBound - )
diff --git a/src/Data/Finitary/TH.hs b/src/Data/Finitary/TH.hs
--- a/src/Data/Finitary/TH.hs
+++ b/src/Data/Finitary/TH.hs
@@ -1,34 +1,34 @@
-{-
- - Copyright (C) 2019  Koz Ross <koz.ross@retro-freedom.nz>
- -
- - This program is free software: you can redistribute it and/or modify
- - it under the terms of the GNU General Public License as published by
- - the Free Software Foundation, either version 3 of the License, or
- - (at your option) any later version.
- -
- - This program is distributed in the hope that it will be useful,
- - but WITHOUT ANY WARRANTY; without even the implied warranty of
- - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- - GNU General Public License for more details.
- -
- - You should have received a copy of the GNU General Public License
- - along with this program.  If not, see <http://www.gnu.org/licenses/>.
- -}
-
-{-# LANGUAGE AllowAmbiguousTypes #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE TypeApplications #-}
-
-module Data.Finitary.TH where
-
-import Foreign.Storable (Storable, sizeOf)
-import Language.Haskell.TH (Q, Type(..), TyLit(..), Exp(..), Lit(..))
-
-charCardinality :: Q Type
-charCardinality = pure . LitT . NumTyLit . fromIntegral . (+ 1) . fromEnum $ maxBound @Char
-
-cardinalityOf :: forall a . (Storable a) => Q Type
-cardinalityOf = pure . LitT . NumTyLit . product . replicate (sizeOf @a undefined * 8) $ 2
-
-adjustmentOf :: forall a . (Integral a, Bounded a) => Q Exp
-adjustmentOf = pure . LitE . IntegerL . (+ 1) . fromIntegral @_ @Integer $ maxBound @a
+{-
+ - Copyright (C) 2019  Koz Ross <koz.ross@retro-freedom.nz>
+ -
+ - This program is free software: you can redistribute it and/or modify
+ - it under the terms of the GNU General Public License as published by
+ - the Free Software Foundation, either version 3 of the License, or
+ - (at your option) any later version.
+ -
+ - This program is distributed in the hope that it will be useful,
+ - but WITHOUT ANY WARRANTY; without even the implied warranty of
+ - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ - GNU General Public License for more details.
+ -
+ - You should have received a copy of the GNU General Public License
+ - along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ -}
+
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+
+module Data.Finitary.TH where
+
+import Foreign.Storable (Storable, sizeOf)
+import Language.Haskell.TH (Q, Type(..), TyLit(..), Exp(..), Lit(..))
+
+charCardinality :: Q Type
+charCardinality = pure . LitT . NumTyLit . fromIntegral . (+ 1) . fromEnum $ maxBound @Char
+
+cardinalityOf :: forall a . (Storable a) => Q Type
+cardinalityOf = pure . LitT . NumTyLit $ 2 ^ ( sizeOf @a undefined * 8 )
+
+adjustmentOf :: forall a . (Integral a, Bounded a) => Q Exp
+adjustmentOf = pure . LitE . IntegerL . (+ 1) . fromIntegral @_ @Integer $ maxBound @a
diff --git a/test/Main.hs b/test/Main.hs
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -1,230 +1,230 @@
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE DeriveAnyClass #-}
-{-# LANGUAGE DeriveGeneric #-}
-{-# LANGUAGE DerivingStrategies #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE TypeApplications #-}
-
-{-
- - Copyright (C) 2019  Koz Ross <koz.ross@retro-freedom.nz>
- -
- - This program is free software: you can redistribute it and/or modify
- - it under the terms of the GNU General Public License as published by
- - the Free Software Foundation, either version 3 of the License, or
- - (at your option) any later version.
- -
- - This program is distributed in the hope that it will be useful,
- - but WITHOUT ANY WARRANTY; without even the implied warranty of
- - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- - GNU General Public License for more details.
- -
- - You should have received a copy of the GNU General Public License
- - along with this program.  If not, see <http://www.gnu.org/licenses/>.
- -}
-
-module Main where
-
-import Data.Finitary (Finitary (..))
-import Data.Int (Int16, Int32, Int8)
-import Data.Ord (Down (..))
-import qualified Data.Vector.Sized as V
-import qualified Data.Vector.Storable.Sized as VS
-import Data.Vector.Unboxed.Sized (Unbox)
-import qualified Data.Vector.Unboxed.Sized as VU
-import Data.Word (Word16, Word32, Word8)
-import Foreign.Storable (Storable)
-import GHC.Generics (Generic)
-import Hedgehog ((===), Gen, PropertyT, forAll)
-import qualified Hedgehog.Gen as Gen
-import Hedgehog.Range (constantBounded)
-import Test.Hspec (SpecWith, describe, hspec, it, parallel)
-import Test.Hspec.Hedgehog (hedgehog, modifyMaxSize)
-
-main :: IO ()
-main = hspec . parallel $ do
-  describe "Bijectivity and order preservation" $ do
-    checkBijection "Char" Gen.unicode
-    checkBijection "Word8" (Gen.enumBounded @_ @Word8)
-    modifyMaxSize (const 10000)
-      . checkBijection "Word16"
-      $ Gen.enumBounded @_ @Word16
-    modifyMaxSize (const 10000)
-      . checkBijection "Word32"
-      $ Gen.enumBounded @_ @Word32
-    modifyMaxSize (const 10000)
-      . checkBijection "Word64"
-      $ Gen.word64 constantBounded
-    checkBijection "Int8" (Gen.enumBounded @_ @Int8)
-    modifyMaxSize (const 10000)
-      . checkBijection "Int16"
-      $ Gen.enumBounded @_ @Int16
-    modifyMaxSize (const 10000)
-      . checkBijection "Int32"
-      $ Gen.enumBounded @_ @Int32
-    modifyMaxSize (const 10000)
-      . checkBijection "Int64"
-      $ Gen.int64 constantBounded
-    modifyMaxSize (const 10000)
-      . checkBijection "Int"
-      $ Gen.int constantBounded
-    modifyMaxSize (const 10000)
-      . checkBijection "Word"
-      $ Gen.word constantBounded
-  describe "Down" $ do
-    checkMonotonic "Bool" Gen.bool
-    modifyMaxSize (const 10000)
-      . checkMonotonic "Int"
-      $ (Gen.enumBounded @_ @Int)
-    modifyMaxSize (const 10000)
-      . checkMonotonic "(Either Int Bool)"
-      $ Gen.choice
-        [ Left <$> Gen.enumBounded @_ @Int,
-          Right <$> Gen.enumBounded @_ @Bool
-        ]
-    modifyMaxSize (const 10000)
-      . checkMonotonic "(Int, Bool)"
-      $ ( (,)
-            <$> Gen.enumBounded @_ @Int
-            <*> Gen.enumBounded @_ @Bool
-        )
-    modifyMaxSize (const 10000)
-      . checkMonotonic "of a user-defined type"
-      $ genFoo
-  describe "Fixed-length vectors" $ do
-    modifyMaxSize (const 10000)
-      . checkStorable "Int8"
-      . genStorable
-      $ Gen.enumBounded @_ @Int8
-    modifyMaxSize (const 10000)
-      . checkUnboxed "Int8"
-      . genUnboxed
-      $ Gen.enumBounded @_ @Int8
-    modifyMaxSize (const 10000)
-      . checkRegular "Int8"
-      . genRegular
-      $ Gen.enumBounded @_ @Int8
-    modifyMaxSize (const 10000)
-      . checkUnboxed "(Int8, Int8)"
-      . genUnboxed
-      $ ( (,) <$> Gen.enumBounded @_ @Int8
-            <*> Gen.enumBounded @_ @Int8
-        )
-    modifyMaxSize (const 10000)
-      . checkRegular "(Int8, Int8)"
-      . genRegular
-      $ ( (,) <$> Gen.enumBounded @_ @Int8
-            <*> Gen.enumBounded @_ @Int8
-        )
-    modifyMaxSize (const 10000)
-      . checkRegular "Either Int8 Bool"
-      . genRegular
-      . Gen.choice
-      $ [ Left <$> Gen.enumBounded @_ @Int8,
-          Right <$> Gen.bool
-        ]
-    modifyMaxSize (const 10000)
-      . checkRegular "a user defined type"
-      . genRegular
-      $ genFoo
-
--- Helpers
-
-data Foo
-  = Bar
-  | Baz Int8
-  | Quux (Int8, Int8)
-  deriving stock (Eq, Ord, Generic, Show)
-  deriving anyclass (Finitary)
-
-checkStorable ::
-  forall a.
-  (Storable a, Finitary a, Show a, Ord a) =>
-  String ->
-  Gen (VS.Vector 10 a) ->
-  SpecWith ()
-checkStorable name =
-  it ("should biject a Storable Vector of " <> name)
-    . hedgehog
-    . bicheck @(VS.Vector 10 a)
-
-checkRegular ::
-  forall a.
-  (Finitary a, Show a, Ord a) =>
-  String ->
-  Gen (V.Vector 10 a) ->
-  SpecWith ()
-checkRegular name =
-  it ("should biject a Vector of " <> name)
-    . hedgehog
-    . bicheck @(V.Vector 10 a)
-
-checkUnboxed ::
-  forall a.
-  (Unbox a, Finitary a, Show a, Ord a) =>
-  String ->
-  Gen (VU.Vector 10 a) ->
-  SpecWith ()
-checkUnboxed name =
-  it ("should biject an Unboxed Vector of " <> name)
-    . hedgehog
-    . bicheck @(VU.Vector 10 a)
-
-bicheck :: forall a. (Show a, Finitary a, Ord a) => Gen a -> PropertyT IO ()
-bicheck gen = do
-  v <- forAll gen
-  let iv = toFinite v
-  v === (fromFinite . toFinite $ v)
-  iv === (toFinite @a . fromFinite $ iv)
-  v' <- forAll gen
-  let iv' = toFinite v'
-  compare v v' === compare iv iv'
-
-genStorable :: (Storable a) => Gen a -> Gen (VS.Vector 10 a)
-genStorable = VS.replicateM
-
-genUnboxed :: (Unbox a) => Gen a -> Gen (VU.Vector 10 a)
-genUnboxed = VU.replicateM
-
-genRegular :: Gen a -> Gen (V.Vector 10 a)
-genRegular = V.replicateM
-
-genFoo :: Gen Foo
-genFoo =
-  Gen.choice
-    [ pure Bar,
-      Baz <$> Gen.enumBounded,
-      Quux <$> ((,) <$> Gen.enumBounded <*> Gen.enumBounded)
-    ]
-
-checkBijection :: forall a. (Show a, Ord a, Finitary a) => String -> Gen a -> SpecWith ()
-checkBijection name gen =
-  it ("should biject " <> name <> " with fromFinite and toFinite preserving order")
-    . hedgehog
-    $ go
-  where
-    go = do
-      x <- forAll gen
-      let ix = toFinite x
-      x === (fromFinite . toFinite $ x)
-      ix === (toFinite @a . fromFinite $ ix)
-      y <- forAll gen
-      let iy = toFinite y
-      compare x y === compare ix iy
-
-checkMonotonic :: (Show a, Finitary a) => String -> Gen a -> SpecWith ()
-checkMonotonic name gen =
-  it ("should be Ord-monotonic on Down " <> name)
-    . hedgehog
-    $ go
-  where
-    go = do
-      x <- forAll gen
-      y <- forAll gen
-      let dx = toFinite . Down $ x
-      let dy = toFinite . Down $ y
-      let ix = toFinite x
-      let iy = toFinite y
-      case compare ix iy of
-        LT -> compare dx dy === GT
-        EQ -> compare dx dy === EQ
-        GT -> compare dx dy === LT
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DeriveAnyClass #-}
+{-# LANGUAGE DeriveGeneric #-}
+{-# LANGUAGE DerivingStrategies #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+
+{-
+ - Copyright (C) 2019  Koz Ross <koz.ross@retro-freedom.nz>
+ -
+ - This program is free software: you can redistribute it and/or modify
+ - it under the terms of the GNU General Public License as published by
+ - the Free Software Foundation, either version 3 of the License, or
+ - (at your option) any later version.
+ -
+ - This program is distributed in the hope that it will be useful,
+ - but WITHOUT ANY WARRANTY; without even the implied warranty of
+ - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ - GNU General Public License for more details.
+ -
+ - You should have received a copy of the GNU General Public License
+ - along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ -}
+
+module Main where
+
+import Data.Finitary (Finitary (..))
+import Data.Int (Int16, Int32, Int8)
+import Data.Ord (Down (..))
+import qualified Data.Vector.Sized as V
+import qualified Data.Vector.Storable.Sized as VS
+import Data.Vector.Unboxed.Sized (Unbox)
+import qualified Data.Vector.Unboxed.Sized as VU
+import Data.Word (Word16, Word32, Word8)
+import Foreign.Storable (Storable)
+import GHC.Generics (Generic)
+import Hedgehog ((===), Gen, PropertyT, forAll)
+import qualified Hedgehog.Gen as Gen
+import Hedgehog.Range (constantBounded)
+import Test.Hspec (SpecWith, describe, hspec, it, parallel)
+import Test.Hspec.Hedgehog (hedgehog, modifyMaxSize)
+
+main :: IO ()
+main = hspec . parallel $ do
+  describe "Bijectivity and order preservation" $ do
+    checkBijection "Char" Gen.unicode
+    checkBijection "Word8" (Gen.enumBounded @_ @Word8)
+    modifyMaxSize (const 10000)
+      . checkBijection "Word16"
+      $ Gen.enumBounded @_ @Word16
+    modifyMaxSize (const 10000)
+      . checkBijection "Word32"
+      $ Gen.enumBounded @_ @Word32
+    modifyMaxSize (const 10000)
+      . checkBijection "Word64"
+      $ Gen.word64 constantBounded
+    checkBijection "Int8" (Gen.enumBounded @_ @Int8)
+    modifyMaxSize (const 10000)
+      . checkBijection "Int16"
+      $ Gen.enumBounded @_ @Int16
+    modifyMaxSize (const 10000)
+      . checkBijection "Int32"
+      $ Gen.enumBounded @_ @Int32
+    modifyMaxSize (const 10000)
+      . checkBijection "Int64"
+      $ Gen.int64 constantBounded
+    modifyMaxSize (const 10000)
+      . checkBijection "Int"
+      $ Gen.int constantBounded
+    modifyMaxSize (const 10000)
+      . checkBijection "Word"
+      $ Gen.word constantBounded
+  describe "Down" $ do
+    checkMonotonic "Bool" Gen.bool
+    modifyMaxSize (const 10000)
+      . checkMonotonic "Int"
+      $ (Gen.enumBounded @_ @Int)
+    modifyMaxSize (const 10000)
+      . checkMonotonic "(Either Int Bool)"
+      $ Gen.choice
+        [ Left <$> Gen.enumBounded @_ @Int,
+          Right <$> Gen.enumBounded @_ @Bool
+        ]
+    modifyMaxSize (const 10000)
+      . checkMonotonic "(Int, Bool)"
+      $ ( (,)
+            <$> Gen.enumBounded @_ @Int
+            <*> Gen.enumBounded @_ @Bool
+        )
+    modifyMaxSize (const 10000)
+      . checkMonotonic "of a user-defined type"
+      $ genFoo
+  describe "Fixed-length vectors" $ do
+    modifyMaxSize (const 10000)
+      . checkStorable "Int8"
+      . genStorable
+      $ Gen.enumBounded @_ @Int8
+    modifyMaxSize (const 10000)
+      . checkUnboxed "Int8"
+      . genUnboxed
+      $ Gen.enumBounded @_ @Int8
+    modifyMaxSize (const 10000)
+      . checkRegular "Int8"
+      . genRegular
+      $ Gen.enumBounded @_ @Int8
+    modifyMaxSize (const 10000)
+      . checkUnboxed "(Int8, Int8)"
+      . genUnboxed
+      $ ( (,) <$> Gen.enumBounded @_ @Int8
+            <*> Gen.enumBounded @_ @Int8
+        )
+    modifyMaxSize (const 10000)
+      . checkRegular "(Int8, Int8)"
+      . genRegular
+      $ ( (,) <$> Gen.enumBounded @_ @Int8
+            <*> Gen.enumBounded @_ @Int8
+        )
+    modifyMaxSize (const 10000)
+      . checkRegular "Either Int8 Bool"
+      . genRegular
+      . Gen.choice
+      $ [ Left <$> Gen.enumBounded @_ @Int8,
+          Right <$> Gen.bool
+        ]
+    modifyMaxSize (const 10000)
+      . checkRegular "a user defined type"
+      . genRegular
+      $ genFoo
+
+-- Helpers
+
+data Foo
+  = Bar
+  | Baz Int8
+  | Quux (Int8, Int8)
+  deriving stock (Eq, Ord, Generic, Show)
+  deriving anyclass (Finitary)
+
+checkStorable ::
+  forall a.
+  (Storable a, Finitary a, Show a, Ord a) =>
+  String ->
+  Gen (VS.Vector 10 a) ->
+  SpecWith ()
+checkStorable name =
+  it ("should biject a Storable Vector of " <> name)
+    . hedgehog
+    . bicheck @(VS.Vector 10 a)
+
+checkRegular ::
+  forall a.
+  (Finitary a, Show a, Ord a) =>
+  String ->
+  Gen (V.Vector 10 a) ->
+  SpecWith ()
+checkRegular name =
+  it ("should biject a Vector of " <> name)
+    . hedgehog
+    . bicheck @(V.Vector 10 a)
+
+checkUnboxed ::
+  forall a.
+  (Unbox a, Finitary a, Show a, Ord a) =>
+  String ->
+  Gen (VU.Vector 10 a) ->
+  SpecWith ()
+checkUnboxed name =
+  it ("should biject an Unboxed Vector of " <> name)
+    . hedgehog
+    . bicheck @(VU.Vector 10 a)
+
+bicheck :: forall a. (Show a, Finitary a, Ord a) => Gen a -> PropertyT IO ()
+bicheck gen = do
+  v <- forAll gen
+  let iv = toFinite v
+  v === (fromFinite . toFinite $ v)
+  iv === (toFinite @a . fromFinite $ iv)
+  v' <- forAll gen
+  let iv' = toFinite v'
+  compare v v' === compare iv iv'
+
+genStorable :: (Storable a) => Gen a -> Gen (VS.Vector 10 a)
+genStorable = VS.replicateM
+
+genUnboxed :: (Unbox a) => Gen a -> Gen (VU.Vector 10 a)
+genUnboxed = VU.replicateM
+
+genRegular :: Gen a -> Gen (V.Vector 10 a)
+genRegular = V.replicateM
+
+genFoo :: Gen Foo
+genFoo =
+  Gen.choice
+    [ pure Bar,
+      Baz <$> Gen.enumBounded,
+      Quux <$> ((,) <$> Gen.enumBounded <*> Gen.enumBounded)
+    ]
+
+checkBijection :: forall a. (Show a, Ord a, Finitary a) => String -> Gen a -> SpecWith ()
+checkBijection name gen =
+  it ("should biject " <> name <> " with fromFinite and toFinite preserving order")
+    . hedgehog
+    $ go
+  where
+    go = do
+      x <- forAll gen
+      let ix = toFinite x
+      x === (fromFinite . toFinite $ x)
+      ix === (toFinite @a . fromFinite $ ix)
+      y <- forAll gen
+      let iy = toFinite y
+      compare x y === compare ix iy
+
+checkMonotonic :: (Show a, Finitary a) => String -> Gen a -> SpecWith ()
+checkMonotonic name gen =
+  it ("should be Ord-monotonic on Down " <> name)
+    . hedgehog
+    $ go
+  where
+    go = do
+      x <- forAll gen
+      y <- forAll gen
+      let dx = toFinite . Down $ x
+      let dy = toFinite . Down $ y
+      let ix = toFinite x
+      let iy = toFinite y
+      case compare ix iy of
+        LT -> compare dx dy === GT
+        EQ -> compare dx dy === EQ
+        GT -> compare dx dy === LT