finitary 2.0.0.0 → 2.1.0.1
raw patch · 8 files changed
+1945/−1914 lines, 8 filesdep +finitarydep ~bitvecsetup-changednew-uploaderPVP ok
version bump matches the API change (PVP)
Dependencies added: finitary
Dependency ranges changed: bitvec
API changes (from Hackage documentation)
Files
- CHANGELOG.md +55/−49
- LICENSE.md +675/−675
- README.md +148/−152
- Setup.hs +3/−3
- finitary.cabal +98/−81
- src/Data/Finitary.hs +702/−690
- src/Data/Finitary/TH.hs +34/−34
- test/Main.hs +230/−230
CHANGELOG.md view
@@ -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.
LICENSE.md view
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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>.
README.md view
@@ -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
Setup.hs view
@@ -1,3 +1,3 @@-import Distribution.Simple--main = defaultMain+import Distribution.Simple + +main = defaultMain
finitary.cabal view
@@ -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
src/Data/Finitary.hs view
@@ -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 - )
src/Data/Finitary/TH.hs view
@@ -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
test/Main.hs view
@@ -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