├── .gitignore ├── .travis.yml ├── LICENSE ├── README.md ├── stlc ├── Makefile ├── doc │ ├── Hutton │ │ ├── Base.agda │ │ └── Constant.agda │ ├── Makefile │ ├── background.tex │ └── hutton.agda-lib ├── examples │ ├── hid.stlc │ ├── silly.stlc │ └── swap2.stlc └── src │ ├── Data │ ├── List │ │ └── Relation │ │ │ └── Unary │ │ │ └── All │ │ │ └── Extras.agda │ └── Map.agda │ ├── Eval.agda │ ├── Language.agda │ ├── LetInline.agda │ ├── Main.agda │ ├── Parse.agda │ ├── Pipeline.agda │ ├── Print.agda │ ├── Scopecheck.agda │ ├── System │ └── Environment.agda │ ├── Typecheck.agda │ ├── Types.agda │ └── stlc.agda-lib └── travis ├── install_agda.sh └── libraries-2.5.4.2 /.gitignore: -------------------------------------------------------------------------------- 1 | *.agdai 2 | *~ 3 | *MAlonzo/ 4 | *.aux 5 | *.log 6 | *.nav 7 | *.out 8 | *.snm 9 | *.toc 10 | *.fdb_latexmk 11 | *.fls 12 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: C 2 | sudo: false 3 | 4 | branches: 5 | only: 6 | - master 7 | 8 | addons: 9 | apt: 10 | packages: 11 | - cabal-install-2.0 12 | - ghc-8.2.2 13 | sources: 14 | - hvr-ghc 15 | 16 | cache: 17 | directories: 18 | - $HOME/.cabal/ 19 | - $HOME/.ghc/ 20 | 21 | install: 22 | - export PATH=$HOME/.cabal/bin:/opt/ghc/8.2.2/bin:/opt/cabal/2.0/bin:$PATH 23 | - cd travis/ 24 | - travis_wait 50 ./install_agda.sh 25 | 26 | script: 27 | - cd ../stlc/ 28 | - make 29 | - cd src/ 30 | - agda --html Main.agda 31 | - cd ../../ 32 | - mkdir -p stlc/ 33 | - mv stlc/src/html/* stlc/ 34 | 35 | after_success: 36 | # uploading to gh-pages 37 | - git init 38 | - git config --global user.name "Travis CI bot" 39 | - git config --global user.email "travis-ci-bot@travis.fake" 40 | - git remote add upstream https://$GH_TOKEN@github.com/gallais/agdarky.git &>/dev/null 41 | - git fetch upstream && git reset upstream/gh-pages 42 | - git add -f \*.html \*.css 43 | - git commit -m "Automatic HTML update via Travis" 44 | - git push -q upstream HEAD:gh-pages &>/dev/null; 45 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. We, the Free Software Foundation, use the 18 | GNU General Public License for most of our software; it applies also to 19 | any other work released this way by its authors. You can apply it to 20 | your programs, too. 21 | 22 | When we speak of free software, we are referring to freedom, not 23 | price. Our General Public Licenses are designed to make sure that you 24 | have the freedom to distribute copies of free software (and charge for 25 | them if you wish), that you receive source code or can get it if you 26 | want it, that you can change the software or use pieces of it in new 27 | free programs, and that you know you can do these things. 28 | 29 | To protect your rights, we need to prevent others from denying you 30 | these rights or asking you to surrender the rights. Therefore, you have 31 | certain responsibilities if you distribute copies of the software, or if 32 | you modify it: responsibilities to respect the freedom of others. 33 | 34 | For example, if you distribute copies of such a program, whether 35 | gratis or for a fee, you must pass on to the recipients the same 36 | freedoms that you received. You must make sure that they, too, receive 37 | or can get the source code. And you must show them these terms so they 38 | know their rights. 39 | 40 | Developers that use the GNU GPL protect your rights with two steps: 41 | (1) assert copyright on the software, and (2) offer you this License 42 | giving you legal permission to copy, distribute and/or modify it. 43 | 44 | For the developers' and authors' protection, the GPL clearly explains 45 | that there is no warranty for this free software. For both users' and 46 | authors' sake, the GPL requires that modified versions be marked as 47 | changed, so that their problems will not be attributed erroneously to 48 | authors of previous versions. 49 | 50 | Some devices are designed to deny users access to install or run 51 | modified versions of the software inside them, although the manufacturer 52 | can do so. This is fundamentally incompatible with the aim of 53 | protecting users' freedom to change the software. The systematic 54 | pattern of such abuse occurs in the area of products for individuals to 55 | use, which is precisely where it is most unacceptable. Therefore, we 56 | have designed this version of the GPL to prohibit the practice for those 57 | products. If such problems arise substantially in other domains, we 58 | stand ready to extend this provision to those domains in future versions 59 | of the GPL, as needed to protect the freedom of users. 60 | 61 | Finally, every program is threatened constantly by software patents. 62 | States should not allow patents to restrict development and use of 63 | software on general-purpose computers, but in those that do, we wish to 64 | avoid the special danger that patents applied to a free program could 65 | make it effectively proprietary. To prevent this, the GPL assures that 66 | patents cannot be used to render the program non-free. 67 | 68 | The precise terms and conditions for copying, distribution and 69 | modification follow. 70 | 71 | TERMS AND CONDITIONS 72 | 73 | 0. Definitions. 74 | 75 | "This License" refers to version 3 of the GNU General Public License. 76 | 77 | "Copyright" also means copyright-like laws that apply to other kinds of 78 | works, such as semiconductor masks. 79 | 80 | "The Program" refers to any copyrightable work licensed under this 81 | License. Each licensee is addressed as "you". "Licensees" and 82 | "recipients" may be individuals or organizations. 83 | 84 | To "modify" a work means to copy from or adapt all or part of the work 85 | in a fashion requiring copyright permission, other than the making of an 86 | exact copy. The resulting work is called a "modified version" of the 87 | earlier work or a work "based on" the earlier work. 88 | 89 | A "covered work" means either the unmodified Program or a work based 90 | on the Program. 91 | 92 | To "propagate" a work means to do anything with it that, without 93 | permission, would make you directly or secondarily liable for 94 | infringement under applicable copyright law, except executing it on a 95 | computer or modifying a private copy. Propagation includes copying, 96 | distribution (with or without modification), making available to the 97 | public, and in some countries other activities as well. 98 | 99 | To "convey" a work means any kind of propagation that enables other 100 | parties to make or receive copies. Mere interaction with a user through 101 | a computer network, with no transfer of a copy, is not conveying. 102 | 103 | An interactive user interface displays "Appropriate Legal Notices" 104 | to the extent that it includes a convenient and prominently visible 105 | feature that (1) displays an appropriate copyright notice, and (2) 106 | tells the user that there is no warranty for the work (except to the 107 | extent that warranties are provided), that licensees may convey the 108 | work under this License, and how to view a copy of this License. If 109 | the interface presents a list of user commands or options, such as a 110 | menu, a prominent item in the list meets this criterion. 111 | 112 | 1. Source Code. 113 | 114 | The "source code" for a work means the preferred form of the work 115 | for making modifications to it. "Object code" means any non-source 116 | form of a work. 117 | 118 | A "Standard Interface" means an interface that either is an official 119 | standard defined by a recognized standards body, or, in the case of 120 | interfaces specified for a particular programming language, one that 121 | is widely used among developers working in that language. 122 | 123 | The "System Libraries" of an executable work include anything, other 124 | than the work as a whole, that (a) is included in the normal form of 125 | packaging a Major Component, but which is not part of that Major 126 | Component, and (b) serves only to enable use of the work with that 127 | Major Component, or to implement a Standard Interface for which an 128 | implementation is available to the public in source code form. A 129 | "Major Component", in this context, means a major essential component 130 | (kernel, window system, and so on) of the specific operating system 131 | (if any) on which the executable work runs, or a compiler used to 132 | produce the work, or an object code interpreter used to run it. 133 | 134 | The "Corresponding Source" for a work in object code form means all 135 | the source code needed to generate, install, and (for an executable 136 | work) run the object code and to modify the work, including scripts to 137 | control those activities. However, it does not include the work's 138 | System Libraries, or general-purpose tools or generally available free 139 | programs which are used unmodified in performing those activities but 140 | which are not part of the work. For example, Corresponding Source 141 | includes interface definition files associated with source files for 142 | the work, and the source code for shared libraries and dynamically 143 | linked subprograms that the work is specifically designed to require, 144 | such as by intimate data communication or control flow between those 145 | subprograms and other parts of the work. 146 | 147 | The Corresponding Source need not include anything that users 148 | can regenerate automatically from other parts of the Corresponding 149 | Source. 150 | 151 | The Corresponding Source for a work in source code form is that 152 | same work. 153 | 154 | 2. Basic Permissions. 155 | 156 | All rights granted under this License are granted for the term of 157 | copyright on the Program, and are irrevocable provided the stated 158 | conditions are met. This License explicitly affirms your unlimited 159 | permission to run the unmodified Program. The output from running a 160 | covered work is covered by this License only if the output, given its 161 | content, constitutes a covered work. This License acknowledges your 162 | rights of fair use or other equivalent, as provided by copyright law. 163 | 164 | You may make, run and propagate covered works that you do not 165 | convey, without conditions so long as your license otherwise remains 166 | in force. You may convey covered works to others for the sole purpose 167 | of having them make modifications exclusively for you, or provide you 168 | with facilities for running those works, provided that you comply with 169 | the terms of this License in conveying all material for which you do 170 | not control copyright. Those thus making or running the covered works 171 | for you must do so exclusively on your behalf, under your direction 172 | and control, on terms that prohibit them from making any copies of 173 | your copyrighted material outside their relationship with you. 174 | 175 | Conveying under any other circumstances is permitted solely under 176 | the conditions stated below. Sublicensing is not allowed; section 10 177 | makes it unnecessary. 178 | 179 | 3. Protecting Users' Legal Rights From Anti-Circumvention Law. 180 | 181 | No covered work shall be deemed part of an effective technological 182 | measure under any applicable law fulfilling obligations under article 183 | 11 of the WIPO copyright treaty adopted on 20 December 1996, or 184 | similar laws prohibiting or restricting circumvention of such 185 | measures. 186 | 187 | When you convey a covered work, you waive any legal power to forbid 188 | circumvention of technological measures to the extent such circumvention 189 | is effected by exercising rights under this License with respect to 190 | the covered work, and you disclaim any intention to limit operation or 191 | modification of the work as a means of enforcing, against the work's 192 | users, your or third parties' legal rights to forbid circumvention of 193 | technological measures. 194 | 195 | 4. Conveying Verbatim Copies. 196 | 197 | You may convey verbatim copies of the Program's source code as you 198 | receive it, in any medium, provided that you conspicuously and 199 | appropriately publish on each copy an appropriate copyright notice; 200 | keep intact all notices stating that this License and any 201 | non-permissive terms added in accord with section 7 apply to the code; 202 | keep intact all notices of the absence of any warranty; and give all 203 | recipients a copy of this License along with the Program. 204 | 205 | You may charge any price or no price for each copy that you convey, 206 | and you may offer support or warranty protection for a fee. 207 | 208 | 5. Conveying Modified Source Versions. 209 | 210 | You may convey a work based on the Program, or the modifications to 211 | produce it from the Program, in the form of source code under the 212 | terms of section 4, provided that you also meet all of these conditions: 213 | 214 | a) The work must carry prominent notices stating that you modified 215 | it, and giving a relevant date. 216 | 217 | b) The work must carry prominent notices stating that it is 218 | released under this License and any conditions added under section 219 | 7. This requirement modifies the requirement in section 4 to 220 | "keep intact all notices". 221 | 222 | c) You must license the entire work, as a whole, under this 223 | License to anyone who comes into possession of a copy. This 224 | License will therefore apply, along with any applicable section 7 225 | additional terms, to the whole of the work, and all its parts, 226 | regardless of how they are packaged. This License gives no 227 | permission to license the work in any other way, but it does not 228 | invalidate such permission if you have separately received it. 229 | 230 | d) If the work has interactive user interfaces, each must display 231 | Appropriate Legal Notices; however, if the Program has interactive 232 | interfaces that do not display Appropriate Legal Notices, your 233 | work need not make them do so. 234 | 235 | A compilation of a covered work with other separate and independent 236 | works, which are not by their nature extensions of the covered work, 237 | and which are not combined with it such as to form a larger program, 238 | in or on a volume of a storage or distribution medium, is called an 239 | "aggregate" if the compilation and its resulting copyright are not 240 | used to limit the access or legal rights of the compilation's users 241 | beyond what the individual works permit. Inclusion of a covered work 242 | in an aggregate does not cause this License to apply to the other 243 | parts of the aggregate. 244 | 245 | 6. Conveying Non-Source Forms. 246 | 247 | You may convey a covered work in object code form under the terms 248 | of sections 4 and 5, provided that you also convey the 249 | machine-readable Corresponding Source under the terms of this License, 250 | in one of these ways: 251 | 252 | a) Convey the object code in, or embodied in, a physical product 253 | (including a physical distribution medium), accompanied by the 254 | Corresponding Source fixed on a durable physical medium 255 | customarily used for software interchange. 256 | 257 | b) Convey the object code in, or embodied in, a physical product 258 | (including a physical distribution medium), accompanied by a 259 | written offer, valid for at least three years and valid for as 260 | long as you offer spare parts or customer support for that product 261 | model, to give anyone who possesses the object code either (1) a 262 | copy of the Corresponding Source for all the software in the 263 | product that is covered by this License, on a durable physical 264 | medium customarily used for software interchange, for a price no 265 | more than your reasonable cost of physically performing this 266 | conveying of source, or (2) access to copy the 267 | Corresponding Source from a network server at no charge. 268 | 269 | c) Convey individual copies of the object code with a copy of the 270 | written offer to provide the Corresponding Source. This 271 | alternative is allowed only occasionally and noncommercially, and 272 | only if you received the object code with such an offer, in accord 273 | with subsection 6b. 274 | 275 | d) Convey the object code by offering access from a designated 276 | place (gratis or for a charge), and offer equivalent access to the 277 | Corresponding Source in the same way through the same place at no 278 | further charge. You need not require recipients to copy the 279 | Corresponding Source along with the object code. If the place to 280 | copy the object code is a network server, the Corresponding Source 281 | may be on a different server (operated by you or a third party) 282 | that supports equivalent copying facilities, provided you maintain 283 | clear directions next to the object code saying where to find the 284 | Corresponding Source. Regardless of what server hosts the 285 | Corresponding Source, you remain obligated to ensure that it is 286 | available for as long as needed to satisfy these requirements. 287 | 288 | e) Convey the object code using peer-to-peer transmission, provided 289 | you inform other peers where the object code and Corresponding 290 | Source of the work are being offered to the general public at no 291 | charge under subsection 6d. 292 | 293 | A separable portion of the object code, whose source code is excluded 294 | from the Corresponding Source as a System Library, need not be 295 | included in conveying the object code work. 296 | 297 | A "User Product" is either (1) a "consumer product", which means any 298 | tangible personal property which is normally used for personal, family, 299 | or household purposes, or (2) anything designed or sold for incorporation 300 | into a dwelling. In determining whether a product is a consumer product, 301 | doubtful cases shall be resolved in favor of coverage. For a particular 302 | product received by a particular user, "normally used" refers to a 303 | typical or common use of that class of product, regardless of the status 304 | of the particular user or of the way in which the particular user 305 | actually uses, or expects or is expected to use, the product. A product 306 | is a consumer product regardless of whether the product has substantial 307 | commercial, industrial or non-consumer uses, unless such uses represent 308 | the only significant mode of use of the product. 309 | 310 | "Installation Information" for a User Product means any methods, 311 | procedures, authorization keys, or other information required to install 312 | and execute modified versions of a covered work in that User Product from 313 | a modified version of its Corresponding Source. The information must 314 | suffice to ensure that the continued functioning of the modified object 315 | code is in no case prevented or interfered with solely because 316 | modification has been made. 317 | 318 | If you convey an object code work under this section in, or with, or 319 | specifically for use in, a User Product, and the conveying occurs as 320 | part of a transaction in which the right of possession and use of the 321 | User Product is transferred to the recipient in perpetuity or for a 322 | fixed term (regardless of how the transaction is characterized), the 323 | Corresponding Source conveyed under this section must be accompanied 324 | by the Installation Information. But this requirement does not apply 325 | if neither you nor any third party retains the ability to install 326 | modified object code on the User Product (for example, the work has 327 | been installed in ROM). 328 | 329 | The requirement to provide Installation Information does not include a 330 | requirement to continue to provide support service, warranty, or updates 331 | for a work that has been modified or installed by the recipient, or for 332 | the User Product in which it has been modified or installed. Access to a 333 | network may be denied when the modification itself materially and 334 | adversely affects the operation of the network or violates the rules and 335 | protocols for communication across the network. 336 | 337 | Corresponding Source conveyed, and Installation Information provided, 338 | in accord with this section must be in a format that is publicly 339 | documented (and with an implementation available to the public in 340 | source code form), and must require no special password or key for 341 | unpacking, reading or copying. 342 | 343 | 7. Additional Terms. 344 | 345 | "Additional permissions" are terms that supplement the terms of this 346 | License by making exceptions from one or more of its conditions. 347 | Additional permissions that are applicable to the entire Program shall 348 | be treated as though they were included in this License, to the extent 349 | that they are valid under applicable law. If additional permissions 350 | apply only to part of the Program, that part may be used separately 351 | under those permissions, but the entire Program remains governed by 352 | this License without regard to the additional permissions. 353 | 354 | When you convey a copy of a covered work, you may at your option 355 | remove any additional permissions from that copy, or from any part of 356 | it. (Additional permissions may be written to require their own 357 | removal in certain cases when you modify the work.) You may place 358 | additional permissions on material, added by you to a covered work, 359 | for which you have or can give appropriate copyright permission. 360 | 361 | Notwithstanding any other provision of this License, for material you 362 | add to a covered work, you may (if authorized by the copyright holders of 363 | that material) supplement the terms of this License with terms: 364 | 365 | a) Disclaiming warranty or limiting liability differently from the 366 | terms of sections 15 and 16 of this License; or 367 | 368 | b) Requiring preservation of specified reasonable legal notices or 369 | author attributions in that material or in the Appropriate Legal 370 | Notices displayed by works containing it; or 371 | 372 | c) Prohibiting misrepresentation of the origin of that material, or 373 | requiring that modified versions of such material be marked in 374 | reasonable ways as different from the original version; or 375 | 376 | d) Limiting the use for publicity purposes of names of licensors or 377 | authors of the material; or 378 | 379 | e) Declining to grant rights under trademark law for use of some 380 | trade names, trademarks, or service marks; or 381 | 382 | f) Requiring indemnification of licensors and authors of that 383 | material by anyone who conveys the material (or modified versions of 384 | it) with contractual assumptions of liability to the recipient, for 385 | any liability that these contractual assumptions directly impose on 386 | those licensors and authors. 387 | 388 | All other non-permissive additional terms are considered "further 389 | restrictions" within the meaning of section 10. If the Program as you 390 | received it, or any part of it, contains a notice stating that it is 391 | governed by this License along with a term that is a further 392 | restriction, you may remove that term. If a license document contains 393 | a further restriction but permits relicensing or conveying under this 394 | License, you may add to a covered work material governed by the terms 395 | of that license document, provided that the further restriction does 396 | not survive such relicensing or conveying. 397 | 398 | If you add terms to a covered work in accord with this section, you 399 | must place, in the relevant source files, a statement of the 400 | additional terms that apply to those files, or a notice indicating 401 | where to find the applicable terms. 402 | 403 | Additional terms, permissive or non-permissive, may be stated in the 404 | form of a separately written license, or stated as exceptions; 405 | the above requirements apply either way. 406 | 407 | 8. Termination. 408 | 409 | You may not propagate or modify a covered work except as expressly 410 | provided under this License. Any attempt otherwise to propagate or 411 | modify it is void, and will automatically terminate your rights under 412 | this License (including any patent licenses granted under the third 413 | paragraph of section 11). 414 | 415 | However, if you cease all violation of this License, then your 416 | license from a particular copyright holder is reinstated (a) 417 | provisionally, unless and until the copyright holder explicitly and 418 | finally terminates your license, and (b) permanently, if the copyright 419 | holder fails to notify you of the violation by some reasonable means 420 | prior to 60 days after the cessation. 421 | 422 | Moreover, your license from a particular copyright holder is 423 | reinstated permanently if the copyright holder notifies you of the 424 | violation by some reasonable means, this is the first time you have 425 | received notice of violation of this License (for any work) from that 426 | copyright holder, and you cure the violation prior to 30 days after 427 | your receipt of the notice. 428 | 429 | Termination of your rights under this section does not terminate the 430 | licenses of parties who have received copies or rights from you under 431 | this License. If your rights have been terminated and not permanently 432 | reinstated, you do not qualify to receive new licenses for the same 433 | material under section 10. 434 | 435 | 9. Acceptance Not Required for Having Copies. 436 | 437 | You are not required to accept this License in order to receive or 438 | run a copy of the Program. Ancillary propagation of a covered work 439 | occurring solely as a consequence of using peer-to-peer transmission 440 | to receive a copy likewise does not require acceptance. However, 441 | nothing other than this License grants you permission to propagate or 442 | modify any covered work. These actions infringe copyright if you do 443 | not accept this License. Therefore, by modifying or propagating a 444 | covered work, you indicate your acceptance of this License to do so. 445 | 446 | 10. Automatic Licensing of Downstream Recipients. 447 | 448 | Each time you convey a covered work, the recipient automatically 449 | receives a license from the original licensors, to run, modify and 450 | propagate that work, subject to this License. You are not responsible 451 | for enforcing compliance by third parties with this License. 452 | 453 | An "entity transaction" is a transaction transferring control of an 454 | organization, or substantially all assets of one, or subdividing an 455 | organization, or merging organizations. If propagation of a covered 456 | work results from an entity transaction, each party to that 457 | transaction who receives a copy of the work also receives whatever 458 | licenses to the work the party's predecessor in interest had or could 459 | give under the previous paragraph, plus a right to possession of the 460 | Corresponding Source of the work from the predecessor in interest, if 461 | the predecessor has it or can get it with reasonable efforts. 462 | 463 | You may not impose any further restrictions on the exercise of the 464 | rights granted or affirmed under this License. For example, you may 465 | not impose a license fee, royalty, or other charge for exercise of 466 | rights granted under this License, and you may not initiate litigation 467 | (including a cross-claim or counterclaim in a lawsuit) alleging that 468 | any patent claim is infringed by making, using, selling, offering for 469 | sale, or importing the Program or any portion of it. 470 | 471 | 11. Patents. 472 | 473 | A "contributor" is a copyright holder who authorizes use under this 474 | License of the Program or a work on which the Program is based. The 475 | work thus licensed is called the contributor's "contributor version". 476 | 477 | A contributor's "essential patent claims" are all patent claims 478 | owned or controlled by the contributor, whether already acquired or 479 | hereafter acquired, that would be infringed by some manner, permitted 480 | by this License, of making, using, or selling its contributor version, 481 | but do not include claims that would be infringed only as a 482 | consequence of further modification of the contributor version. For 483 | purposes of this definition, "control" includes the right to grant 484 | patent sublicenses in a manner consistent with the requirements of 485 | this License. 486 | 487 | Each contributor grants you a non-exclusive, worldwide, royalty-free 488 | patent license under the contributor's essential patent claims, to 489 | make, use, sell, offer for sale, import and otherwise run, modify and 490 | propagate the contents of its contributor version. 491 | 492 | In the following three paragraphs, a "patent license" is any express 493 | agreement or commitment, however denominated, not to enforce a patent 494 | (such as an express permission to practice a patent or covenant not to 495 | sue for patent infringement). To "grant" such a patent license to a 496 | party means to make such an agreement or commitment not to enforce a 497 | patent against the party. 498 | 499 | If you convey a covered work, knowingly relying on a patent license, 500 | and the Corresponding Source of the work is not available for anyone 501 | to copy, free of charge and under the terms of this License, through a 502 | publicly available network server or other readily accessible means, 503 | then you must either (1) cause the Corresponding Source to be so 504 | available, or (2) arrange to deprive yourself of the benefit of the 505 | patent license for this particular work, or (3) arrange, in a manner 506 | consistent with the requirements of this License, to extend the patent 507 | license to downstream recipients. "Knowingly relying" means you have 508 | actual knowledge that, but for the patent license, your conveying the 509 | covered work in a country, or your recipient's use of the covered work 510 | in a country, would infringe one or more identifiable patents in that 511 | country that you have reason to believe are valid. 512 | 513 | If, pursuant to or in connection with a single transaction or 514 | arrangement, you convey, or propagate by procuring conveyance of, a 515 | covered work, and grant a patent license to some of the parties 516 | receiving the covered work authorizing them to use, propagate, modify 517 | or convey a specific copy of the covered work, then the patent license 518 | you grant is automatically extended to all recipients of the covered 519 | work and works based on it. 520 | 521 | A patent license is "discriminatory" if it does not include within 522 | the scope of its coverage, prohibits the exercise of, or is 523 | conditioned on the non-exercise of one or more of the rights that are 524 | specifically granted under this License. You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # agdarky 2 | Agda suffices: software written from A to Z in Agda 3 | -------------------------------------------------------------------------------- /stlc/Makefile: -------------------------------------------------------------------------------- 1 | AGDA=agda 2 | 3 | all: executable tests 4 | 5 | executable: 6 | cd src/ && ${AGDA} --compile-dir=.. -c Main.agda 7 | 8 | tests: 9 | ./Main examples/silly.stlc 10 | ./Main examples/swap2.stlc 11 | ./Main examples/hid.stlc 12 | -------------------------------------------------------------------------------- /stlc/doc/Hutton/Base.agda: -------------------------------------------------------------------------------- 1 | module Hutton.Base where 2 | 3 | open import Data.Unit 4 | open import Data.List.Base as List 5 | open import Generic.Syntax 6 | 7 | ------------------------------------------------------------------------ 8 | -- SYNTAX: description in the universe of syntaxes with binding 9 | 10 | -- Hutton's Razor: the smallest language needed to demonstrate a feature 11 | -- Here we take: H = x | H + H 12 | 13 | hutton : Desc ⊤ 14 | 15 | -- hutton is a description of a language where the notion of type is unit (⊤) 16 | -- aka. there is no typing information 17 | 18 | hutton = `X [] _ (`X [] _ (`∎ _)) 19 | 20 | -- it declares one constructor 21 | -- (for the _+_ operator) 22 | 23 | -- _+_ takes two subterms 24 | -- (declared using the constructor `X) 25 | 26 | -- both of which live in the same context 27 | -- (the extension is the empty list []) 28 | 29 | -- both of which don't have an interesting type 30 | -- (_ is filled in by Agda: ⊤'s only value is tt) 31 | 32 | -- And the return type of that constructor is not interesting 33 | -- (again: this is an untyped language) 34 | 35 | open import Data.Product 36 | open import Relation.Binary.PropositionalEquality 37 | 38 | -- We can use pattern synonyms to hide the fact we are using a universe of 39 | -- syntaxes with binding 40 | 41 | pattern add' l r = (l , r , refl) 42 | pattern add l r = `con (add' l r) 43 | 44 | -- They can be used on the RHS 45 | 46 | double : TM hutton _ → TM hutton _ 47 | double x = add x x 48 | 49 | -- But also on the LHS: 50 | 51 | right : ∀ {Γ} → Tm hutton _ _ Γ → Tm hutton _ _ Γ 52 | right (add l r) = r 53 | right (`var x) = `var x 54 | 55 | -- We discover here the notion of variables: syntaxes with binding are 56 | -- automatically endowed with variables. 57 | 58 | ------------------------------------------------------------------------ 59 | -- SEMANTICS: scope-and-type preserving fold-like traversal 60 | 61 | open import Data.Nat.Base 62 | open import var 63 | open import environment 64 | open import Generic.Semantics 65 | 66 | -- The notion of values for a Semantics are always scoped. This way we 67 | -- can write type-and-scope preserving traversals 68 | 69 | Value : ⊤ ─Scoped 70 | Value _ _ = ℕ 71 | 72 | Eval : Sem -- a semantics 73 | hutton -- for terms in hutton's razor 74 | Value -- where variables are assigned a Value 75 | Value -- and the overall computation returns a Value 76 | 77 | -- In general for a traversal on a syntax with binding to be scope preversing, 78 | -- we need to be able to embed the scoped values assigned to variables into 79 | -- larger contexts. This allows us to go under binder. 80 | -- Here Value is scope independent. As such it is trivially thinnable (i.e. 81 | -- stable under scope extensions). 82 | Sem.th^𝓥 Eval = λ v ρ → v 83 | 84 | -- When we look up the value associated to a variable, we need to return 85 | -- something which has the type of the overall computation. Here they match 86 | -- up so we can use the identity function 87 | Sem.var Eval = λ n → n 88 | 89 | -- Finally we have to define an algebra which interprets every constructor 90 | -- provided that the subterms already have been interpreted. Here we transform 91 | -- the syntactic construct add into the addition on natural numbers 92 | Sem.alg Eval = λ where 93 | (add' l r) → l + r 94 | 95 | -- We can evaluate terms by giving an interpretation to each of their variables 96 | eval : ∀ (n : ℕ) → let Γ = List.replicate n _ in (Γ ─Env) Value [] → Tm hutton _ _ Γ → ℕ 97 | eval n ρ t = Sem.sem Eval ρ t 98 | 99 | open import Relation.Binary.PropositionalEquality 100 | 101 | -- x₀ + x₁ ≡ 12 under the assumption that x₀ = 4 and x₁ = 8 102 | 103 | _ : eval 2 (ε ∙ 4 ∙ 8) (add (`var z) (`var (s z))) 104 | ≡ 12 105 | _ = refl 106 | -------------------------------------------------------------------------------- /stlc/doc/Hutton/Constant.agda: -------------------------------------------------------------------------------- 1 | module Hutton.Constant where 2 | 3 | open import Data.Unit 4 | open import Data.List.Base as List 5 | open import Data.Nat.Base 6 | open import Generic.Syntax 7 | 8 | ------------------------------------------------------------------------ 9 | -- SYNTAX: description in the universe of syntaxes with binding 10 | 11 | -- Hutton's Razor reloaded 12 | -- This time we take: H = x | n | H + H 13 | -- where n is a natural number 14 | 15 | data Tag : Set where 16 | Add Lit : Tag 17 | 18 | hutton : Desc ⊤ 19 | 20 | -- it uses a Tag to distinguish two constructors: 21 | -- the _+_ operator we have already seen 22 | -- and a constructor for literals 23 | 24 | hutton = `σ Tag λ where 25 | Add → `X [] _ (`X [] _ (`∎ _)) 26 | Lit → `σ ℕ λ _ → `∎ _ 27 | 28 | -- `σ is used in one case to offer a choice of construtors and in another 29 | -- to store a value in a constructor. 30 | 31 | open import Data.Product 32 | open import Relation.Binary.PropositionalEquality 33 | 34 | -- We can once more introduce pattern synonyms to hide the fact that we 35 | -- are using an encoding 36 | 37 | pattern add' l r = (Add , l , r , refl) 38 | pattern add l r = `con (add' l r) 39 | 40 | double : TM hutton _ → TM hutton _ 41 | double x = add x x 42 | 43 | pattern lit' n = (Lit , n , refl) 44 | pattern lit n = `con (lit' n) 45 | 46 | five : TM hutton _ 47 | five = lit 5 48 | 49 | ------------------------------------------------------------------------ 50 | -- SEMANTICS: scope-and-type preserving fold-like traversal 51 | 52 | -- We can once more define our language's denotational semantics 53 | 54 | open import Data.Nat.Base 55 | open import var 56 | open import environment 57 | open import Generic.Semantics 58 | 59 | Value : ⊤ ─Scoped 60 | Value _ _ = ℕ 61 | 62 | -- It is essentially the same except for the new lit' case we had to add. 63 | 64 | Eval : Sem hutton Value Value 65 | Sem.th^𝓥 Eval = λ v ρ → v 66 | Sem.var Eval = λ n → n 67 | Sem.alg Eval = λ where 68 | (add' l r) → l + r 69 | (lit' n) → n 70 | 71 | eval : TM hutton _ → ℕ 72 | eval = Sem.closed Eval 73 | 74 | -- 5 + 5 ≡ 10 75 | 76 | _ : eval (double five) ≡ 10 77 | _ = refl 78 | 79 | ------------------------------------------------------------------------ 80 | 81 | -- But we can also have more subtle semantics e.g. constant folding: 82 | -- where values are now terms of the language itself. 83 | 84 | open import Generic.Semantics.Syntactic 85 | 86 | Fold : Sem hutton (Tm hutton _) (Tm hutton _) 87 | Sem.th^𝓥 Fold = th^Tm -- generic lemma: terms are always thinnable 88 | Sem.var Fold = λ t → t -- values and result are the same type 89 | Sem.alg Fold = λ where 90 | -- Here is the interesting part: we are simplifying the terms. 91 | -- Note that the subterms l and r in the pattern (add' l r) have 92 | -- already been simplified. 93 | (add' (lit 0) t) → t 94 | (add' t (lit 0)) → t 95 | (add' (lit m) (lit n)) → lit (m + n) 96 | (add' t u) → add t u 97 | (lit' n) → lit n 98 | 99 | fold : ∀ n → let Γ = List.replicate n _ in Tm hutton _ _ Γ → Tm hutton _ _ Γ 100 | fold n = Sem.sem Fold (pack `var) 101 | 102 | -- (0 + (x₂ + 0)) + (3 + 4) ≡ x₂ + 7 103 | 104 | _ : fold 3 (add (add (lit 0) (add (`var (s (s z))) (lit 0))) 105 | (add (lit 3) (lit 4))) 106 | ≡ add (`var (s (s z))) (lit 7) 107 | _ = refl 108 | 109 | -- Or even more subtle ones where we collapse *all* constants and quotient 110 | -- the tree modulo associativity 111 | 112 | -- Values are then a constant together with a list of variables read from left 113 | -- to right in the tree: 114 | 115 | record Essence (_ : ⊤) (Γ : List ⊤) : Set where 116 | constructor _:+_ 117 | field literal : ℕ 118 | variables : List (Var _ Γ) 119 | 120 | -- Variables are interpreted as themselves and the computation delivers the 121 | -- 'essence' of a computation. 122 | 123 | Simpl : Sem hutton Var Essence 124 | Sem.th^𝓥 Simpl = th^Var -- Variables are always thinnable (≈ renaming) 125 | Sem.var Simpl = λ s → (0 :+ (s ∷ [])) -- Their essence is the singleton list 126 | Sem.alg Simpl = λ where 127 | -- The addition of two essences yields a new one by: 128 | -- taking the sum of both literals 129 | -- appending the lists of variables (while respecting the left to right ordering) 130 | (add' (m :+ xs) (n :+ ys)) → (m + n) :+ (xs ++ ys) 131 | -- The essence of a literal is its value together with the empty list of variables 132 | (lit' n) → n :+ [] 133 | 134 | open import Function 135 | 136 | simplify : ∀ n → let Γ = List.replicate n _ in Tm hutton _ _ Γ → Tm hutton _ _ Γ 137 | simplify Γ t = case Sem.sem Simpl (pack (λ v → v)) t of λ where 138 | -- we clean up after ourselves: if the literal is 0, 139 | -- we don't bother returning it 140 | (0 :+ (x ∷ xs)) → List.foldl cons (`var x) xs 141 | (n :+ xs) → List.foldl cons (lit n) xs 142 | 143 | where cons = λ t v → add t (`var v) 144 | 145 | 146 | -- (3 + (x₀ + x₁)) + (x₂ + (2 + 12)) ≡ 15 + x₀ + x₁ + x₂ 147 | 148 | _ : simplify 3 (add (add (lit 3) (add (`var z) (`var (s z)))) 149 | (add (`var (s (s z))) (add (lit 2) (lit 10)))) 150 | ≡ add (add (add (lit 15) (`var z)) (`var (s z))) (`var (s (s z))) 151 | _ = refl 152 | 153 | -- ((x₀ + 0) + x₁) + (x₂ + (x₀ + x₀)) ≡ x₀ + x₁ + x₂ + x₀ + x₀ 154 | 155 | _ : simplify 3 (add (add (add (`var z) (lit 0)) (`var (s z))) 156 | (add (`var (s (s z))) (add (`var z) (`var z)))) 157 | ≡ add (add (add (add (`var z) 158 | (`var (s z))) 159 | (`var (s (s z)))) 160 | (`var z)) 161 | (`var z) 162 | _ = refl 163 | 164 | 165 | 166 | -- But all of this is really language specific... 167 | -------------------------------------------------------------------------------- /stlc/doc/Makefile: -------------------------------------------------------------------------------- 1 | all: 2 | latexmk -pdf background.tex 3 | 4 | clean: 5 | rm *.aux *.log *.nav *.out *.snm *.toc *.fdb_latexmk *.fls *.pdf 6 | -------------------------------------------------------------------------------- /stlc/doc/background.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | \newcommand{\codehere}[1]{ 3 | \begin{center} 4 | {\large[#1.agda]} 5 | \end{center} 6 | } 7 | 8 | \begin{document} 9 | 10 | \author{Guillaume ALLAIS 11 | \\ University of Strathclyde 12 | \\ guillaume.allais@strath.ac.uk} 13 | \title{Scrap Your DSL Boilerplate\\ 14 | With a Universe of Syntaxes With Binding} 15 | \institute{CoCoDo 2019} 16 | \date{April 2nd, 2019} 17 | 18 | \begin{frame} 19 | \maketitle 20 | \end{frame} 21 | 22 | \begin{frame}{Quick Presentation} 23 | \begin{itemize} 24 | \item Background in Interactive Theorem Provers 25 | \item (User and) Developer of Agda and its standard library 26 | \begin{itemize} 27 | \item \url{https://github.com/agda/agda} 28 | \item \url{https://github.com/agda/agda-stdlib} 29 | \end{itemize} 30 | \item Excited about \emph{running} correct by construction code 31 | \end{itemize} 32 | \end{frame} 33 | 34 | \begin{frame}{Don't hesitate to ask questions} 35 | \end{frame} 36 | 37 | \begin{frame}{Background of this Work} 38 | 39 | \begin{itemize} 40 | \item Theoretic: DSLs with Strong invariants 41 | \uncover<2-> 42 | { 43 | \begin{itemize} 44 | \item Universe of Syntaxes with Binding 45 | \item Type and Scope Preserving Programs and their Proofs 46 | \item Not in: Resource-Aware Type Systems (Linear Logic) 47 | \end{itemize} 48 | } 49 | \medskip 50 | \item Practical: User Interactions 51 | \uncover<3-> 52 | { 53 | \begin{itemize} 54 | \item Total Parser Combinators 55 | \item Not in (yet): Declarative Hierarchical Command Line Interfaces 56 | \item Not in (yet): Sized IO 57 | \end{itemize} 58 | } 59 | \end{itemize} 60 | \end{frame} 61 | 62 | \begin{frame}{Intro to Agda: Description} 63 | Agda is: 64 | \begin{itemize} 65 | \item pure 66 | \begin{itemize} 67 | \item No undocumented side effects 68 | \item No undocumented mutations 69 | \uncover<2->{\item No undocumented non-termination} 70 | \end{itemize} 71 | \item functional 72 | \begin{itemize} 73 | \item first class functions 74 | \item powerful notion of inductive families (GADTs++) 75 | \end{itemize} 76 | \item dependently typed 77 | \begin{itemize} 78 | \item Types can (mention / be) arbitrary terms 79 | \end{itemize} 80 | \item<1> total 81 | \end{itemize} 82 | 83 | \end{frame} 84 | 85 | \begin{frame}{Intro to Agda: Interactive Programming} 86 | \codehere{Gentle} 87 | \end{frame} 88 | 89 | \begin{frame}{Warming up: Hutton's Razor(s)} 90 | \href{run:Hutton/Base.agda}{Hutton.Base} 91 | \href{run:Hutton/Constant.agda}{Hutton.Constant} 92 | \end{frame} 93 | 94 | \begin{frame}{Generic Pass: Let-inlining} 95 | \href{run:/home/gallais/projects/generic-syntax/src/Generic/Syntax/LetBinder.agda}{Let Binders} 96 | \newline 97 | \href{run:/home/gallais/projects/generic-syntax/src/Generic/Semantics/Elaboration/LetBinder.agda}{Elaboration} 98 | \end{frame} 99 | 100 | \begin{frame}{Generic Pass: Let-inlining, II} 101 | \begin{itemize} 102 | \item Either: IR with usage counting for variables 103 | \newline 104 | \href{run:/home/gallais/projects/generic-syntax/src/Generic/Syntax/LetCounter.agda}{Let Counters} 105 | \newline 106 | \href{run:/home/gallais/projects/generic-syntax/src/Generic/Semantics/Elaboration/LetCounter.agda}{Elaboration} 107 | 108 | \item Or: Different IR with usage information ("co-deBruijn") 109 | \end{itemize} 110 | \end{frame} 111 | 112 | \begin{frame}{Going Further: Intro to Type Theory / Agda} 113 | 114 | \begin{itemize} 115 | \item The Little Typer (\url{http://www.thelittletyper.com/}) 116 | \item Verified Functional Programming in Agda (\url{https://dl.acm.org/citation.cfm?id=2841316}) 117 | \item Programming Language Foundations in Agda (\url{https://plfa.github.io/}) 118 | \end{itemize} 119 | \end{frame} 120 | 121 | \begin{frame}{Going Further: This Tutorial's Dependencies} 122 | 123 | \begin{itemize} 124 | \item Theory: 125 | \begin{itemize} 126 | \item Type-and-scope safe programs and their proofs (\url{https://dl.acm.org/citation.cfm?id=3018613}) 127 | \item A type and scope safe universe of syntaxes with binding: their semantics and proofs (\url{https://dl.acm.org/citation.cfm?id=3236785}) 128 | 129 | \item Generic Syntax library (\url{https://github.com/gallais/generic-syntax}) 130 | \end{itemize} 131 | \item User Interactions: 132 | \begin{itemize} 133 | \item agdarsec -- Total Parser Combinators (\url{https://gallais.github.io/pdf/agdarsec18.pdf}) 134 | \item agdARGS -- Declarative Hierarchical Command Line Interfaces (\url{https://gallais.github.io/pdf/TTT-2017.pdf}) 135 | \end{itemize} 136 | \end{itemize} 137 | \end{frame} 138 | \end{document} 139 | -------------------------------------------------------------------------------- /stlc/doc/hutton.agda-lib: -------------------------------------------------------------------------------- 1 | name: stlc 2 | include: . 3 | depend: standard-library 4 | , agdarsec 5 | , generic-syntax 6 | -------------------------------------------------------------------------------- /stlc/examples/hid.stlc: -------------------------------------------------------------------------------- 1 | def idh : ('a → 'a) → ('a → 'a) = λf.λx. f x 2 | def id : ('a → 'a) = λx.x 3 | have idh id 4 | 5 | -------------------------------------------------------------------------------- /stlc/examples/silly.stlc: -------------------------------------------------------------------------------- 1 | def id : 'a -> 'a = \x. x 2 | def un : 'a -> 'b -> 'a = \x.\y.id (let y = x in y) 3 | def deux : 'a -> 'b -> 'b = \x. \y .y 4 | have un 5 | -------------------------------------------------------------------------------- /stlc/examples/swap2.stlc: -------------------------------------------------------------------------------- 1 | def swapab : ('a * 'b) -> ('b * 'a) = \p. (snd p, fst p) 2 | def swapba : ('b * 'a) -> ('a * 'b) = \p. (snd p, fst p) 3 | have (\p. swapba (swapab p) : ('a * 'b) -> ('a * 'b)) 4 | -------------------------------------------------------------------------------- /stlc/src/Data/List/Relation/Unary/All/Extras.agda: -------------------------------------------------------------------------------- 1 | module Data.List.Relation.Unary.All.Extras where 2 | 3 | open import Data.List.Base as List 4 | open import Data.List.All as Listₚ 5 | open import Data.Product 6 | open import Function 7 | open import Relation.Unary 8 | 9 | module _ {a p} {A : Set a} {P : Pred A p} where 10 | 11 | fromList : (xs : List (∃ P)) → All P (List.map proj₁ xs) 12 | fromList [] = [] 13 | fromList ((x , p) ∷ xps) = p ∷ fromList xps 14 | 15 | toList : ∀ {xs} → All P xs → List (∃ P) 16 | toList [] = [] 17 | toList (px ∷ pxs) = (-, px) ∷ toList pxs 18 | 19 | self : ∀ {a} {A : Set a} {xs : List A} → All (const A) xs 20 | self = Listₚ.tabulate (λ {x} _ → x) 21 | -------------------------------------------------------------------------------- /stlc/src/Data/Map.agda: -------------------------------------------------------------------------------- 1 | module Data.Map where 2 | 3 | open import Data.Bool 4 | open import Data.Product 5 | open import Data.List as List 6 | open import Data.Maybe 7 | open import Function 8 | 9 | open import Relation.Nullary 10 | open import Relation.Nullary.Decidable 11 | open import Relation.Binary 12 | open import Relation.Binary.PropositionalEquality 13 | 14 | module Map {A : Set} (eq? : Decidable {A = A} _≡_) (B : Set) where 15 | 16 | Map : Set 17 | Map = List (A × B) 18 | 19 | RMap : Set 20 | RMap = List (B × A) 21 | 22 | empty : Map 23 | empty = [] 24 | 25 | set : A → B → Map → Map 26 | set a b mp = (a , b) ∷ mp 27 | 28 | assoc : A → Map → Maybe B 29 | assoc a = flip foldr nothing $ uncurry $ λ a′ b ih → 30 | if ⌊ eq? a a′ ⌋ then just b else ih 31 | 32 | invert : Map → RMap 33 | invert = List.map swap 34 | -------------------------------------------------------------------------------- /stlc/src/Eval.agda: -------------------------------------------------------------------------------- 1 | module Eval where 2 | 3 | open import Data.Nat.Base using (ℕ) 4 | open import Data.List.Base using (List; []) 5 | open import Data.Product as Prod 6 | open import Function 7 | open import Relation.Unary renaming (_⇒_ to _⟶_) 8 | open import var 9 | open import environment 10 | open import Generic.Syntax 11 | open import Generic.Semantics 12 | open import Generic.Semantics.Syntactic using (th^Tm) 13 | open import Language; open Internal 14 | open import Text.Parser.Position 15 | 16 | Model' : Type ℕ → List (Mode × Type ℕ) → Set 17 | Model' (α k) Γ = Position × Typed (Infer , α k) Γ 18 | Model' (σ ⊗ τ) Γ = Position × Model' σ Γ × Model' τ Γ 19 | Model' (σ ⇒ τ) Γ = Position × □ (Model' σ ⟶ Model' τ) Γ 20 | 21 | Model : (Mode × Type ℕ) ─Scoped 22 | Model (m , σ) = Model' σ 23 | 24 | th^Model' : ∀ {σ} → Thinnable (Model' σ) 25 | th^Model' {α k} (r , t) ρ = r , th^Tm t ρ 26 | th^Model' {σ ⇒ τ} (r , f) ρ = r , th^□ f ρ 27 | th^Model' {σ ⊗ τ} (r , a , b) ρ = r , th^Model' a ρ , th^Model' b ρ 28 | 29 | Eval : ∀ {P} → Sem (internal P) Model Model 30 | Sem.th^𝓥 Eval = th^Model' 31 | Sem.var Eval = id 32 | Sem.alg Eval = λ where 33 | (r , `λ' b) → r , λ inc v → b inc (ε ∙ v) 34 | (r , f `$' t) → extract (proj₂ f) t 35 | (r , `fst' t) → proj₁ $ proj₂ t 36 | (r , `snd' t) → proj₂ $ proj₂ t 37 | (r , a `,' b) → (r , a , b) 38 | (r , t `∶' σ) → t 39 | (r , `-' t) → t 40 | (r , `let' e `in t) → extract t (ε ∙ e) 41 | 42 | reify : ∀ σ → ∀[ Model' σ ⟶ Typed (Check , σ) ] 43 | reflect : ∀ σ → ∀[ const Position ⟶ Typed (_ , σ) ⟶ Model' σ ] 44 | 45 | reify (α k) (r , t) = r >`- t 46 | reify (σ ⇒ τ) (r , t) = r >`λ reify τ (t extend (reflect σ r (`var z))) 47 | reify (σ ⊗ τ) (r , a , b) = r >[ reify σ a `, reify τ b ] 48 | 49 | reflect (α k) r t = r , t 50 | reflect (σ ⊗ τ) r t = r , reflect σ r (r >`fst t) , reflect τ r (r >`snd t) 51 | reflect (σ ⇒ τ) r t = r , λ inc v → reflect τ r (r >[ th^Tm t inc `$ reify σ v ]) 52 | 53 | norm : ∀ {P m σ} → Internal P (m , σ) [] → Typed (Check , σ) [] 54 | norm = reify _ ∘′ Sem.closed Eval 55 | -------------------------------------------------------------------------------- /stlc/src/Language.agda: -------------------------------------------------------------------------------- 1 | module Language where 2 | 3 | open import Data.Unit 4 | open import Data.Empty 5 | open import Data.Product as Prod 6 | open import Data.Nat 7 | open import Data.List as List using (List; []; _∷_) 8 | open import Data.List.All -- important for the pattern synonyms! 9 | open import Data.String as String using (String; _++_) 10 | open import Function 11 | open import Function.Equivalence 12 | open import Relation.Nullary 13 | open import Relation.Nullary.Decidable as RNDec 14 | open import Relation.Nullary.Product 15 | open import Relation.Binary using (Decidable) 16 | open import Relation.Binary.PropositionalEquality 17 | 18 | open import var using (z; s; _─Scoped) 19 | open import environment 20 | open import Generic.Syntax 21 | open import Generic.AltSyntax 22 | open import Generic.Semantics.Syntactic using (sub) 23 | open import Text.Parser.Position as Position using (Position; _∶_; start) 24 | 25 | infixr 6 _⇒_ 26 | infixr 7 _⊗_ 27 | data Type (A : Set) : Set where 28 | α : A → Type A 29 | _⊗_ : (σ τ : Type A) → Type A 30 | _⇒_ : (σ τ : Type A) → Type A 31 | 32 | show : Type String → String 33 | pshow : Type String → String 34 | 35 | show (α str) = "'" ++ str 36 | show (σ ⊗ τ) = pshow σ ++ " * " ++ show τ 37 | show (σ ⇒ τ) = pshow σ ++ " → " ++ show τ 38 | 39 | pshow σ@(α _) = show σ 40 | pshow σ@(_ ⊗ _) = "(" ++ show σ ++ ")" 41 | pshow σ@(_ ⇒ _) = "(" ++ show σ ++ ")" 42 | 43 | data Mode : Set where 44 | Infer Check : Mode 45 | 46 | eqdecMode : Decidable {A = Mode} _≡_ 47 | eqdecMode Infer Infer = yes refl 48 | eqdecMode Infer Check = no (λ ()) 49 | eqdecMode Check Infer = no (λ ()) 50 | eqdecMode Check Check = yes refl 51 | 52 | module _ {A : Set} where 53 | 54 | α-equivalence : {a₁ a₂ : A} → (a₁ ≡ a₂) ⇔ (α a₁ ≡ α a₂) 55 | α-equivalence = equivalence (cong α) (λ where refl → refl) 56 | 57 | ⇒-equivalence : {σ₁ σ₂ τ₁ τ₂ : Type A} → 58 | (σ₁ ≡ σ₂ × τ₁ ≡ τ₂) ⇔ (σ₁ ⇒ τ₁ ≡ σ₂ ⇒ τ₂) 59 | ⇒-equivalence = equivalence (uncurry (cong₂ _⇒_)) (λ where refl → refl , refl) 60 | 61 | ⊗-equivalence : {σ₁ σ₂ τ₁ τ₂ : Type A} → 62 | (σ₁ ≡ σ₂ × τ₁ ≡ τ₂) ⇔ (σ₁ ⊗ τ₁ ≡ σ₂ ⊗ τ₂) 63 | ⊗-equivalence = equivalence (uncurry (cong₂ _⊗_)) (λ where refl → refl , refl) 64 | 65 | module _ {A : Set} (eq : Decidable {A = A} _≡_) where 66 | 67 | eqdecType : Decidable {A = Type A} _≡_ 68 | eqdecType (α a₁) (α a₂) = RNDec.map α-equivalence (eq a₁ a₂) 69 | eqdecType (σ₁ ⊗ τ₁) (σ₂ ⊗ τ₂) = 70 | RNDec.map ⊗-equivalence (eqdecType σ₁ σ₂ ×-dec eqdecType τ₁ τ₂) 71 | eqdecType (σ₁ ⇒ τ₁) (σ₂ ⇒ τ₂) = 72 | RNDec.map ⇒-equivalence (eqdecType σ₁ σ₂ ×-dec eqdecType τ₁ τ₂) 73 | 74 | eqdecType (α _) (_ ⇒ _) = no (λ ()) 75 | eqdecType (_ ⇒ _) (α _) = no (λ ()) 76 | eqdecType (α _) (_ ⊗ _) = no (λ ()) 77 | eqdecType (_ ⊗ _) (α _) = no (λ ()) 78 | eqdecType (_ ⊗ _) (_ ⇒ _) = no (λ ()) 79 | eqdecType (_ ⇒ _) (_ ⊗ _) = no (λ ()) 80 | 81 | data `Bidi (P : Set) : Set where 82 | Cut App Fst Snd : `Bidi P 83 | Lam Prd Emb : `Bidi P 84 | Let : {p : P} → `Bidi P 85 | 86 | -- Throwing in some useful combinators 87 | 88 | module _ {I : Set} where 89 | 90 | `κ_`×_ : Set → Desc I → Desc I 91 | `κ A `× d = `σ A $ const d 92 | 93 | Located : Desc I → Desc I 94 | Located d = `κ Position `× d 95 | 96 | module Surface where 97 | 98 | -- I'm adding useless `κ_`×_ parts to keep the layout the 99 | -- same between surface and internal. This will allow us to 100 | -- use the same pattern synonyms for both! 101 | surface : Set → Desc Mode 102 | surface A = Located $ `σ (`Bidi ⊤) $ λ where 103 | Cut → `κ Type A `× `X [] Check (`∎ Infer) 104 | App → `κ ⊤ `× `X [] Infer (`X [] Check (`∎ Infer)) 105 | Fst → `κ ⊤ `× `X [] Infer (`∎ Infer) 106 | Snd → `κ ⊤ `× `X [] Infer (`∎ Infer) 107 | Lam → `κ ⊤ `× `X (Infer ∷ []) Check (`∎ Check) 108 | Prd → `κ ⊤ `× `X [] Check (`X [] Check (`∎ Check)) 109 | Emb → `κ ⊤ `× `X [] Infer (`∎ Check) 110 | Let → `κ ⊤ `× `X [] Infer (`X (Infer ∷ []) Check (`∎ Check)) 111 | 112 | 113 | Parsed : Mode → Set 114 | Parsed = Raw Position (surface String) _ 115 | 116 | Scoped : Mode → List Mode → Set 117 | Scoped = Tm (surface ℕ) _ 118 | 119 | 120 | module Internal where 121 | 122 | internal : (P : Set) → Desc (Mode × Type ℕ) 123 | internal P = Located $ `σ (`Bidi P) $ λ where 124 | Cut → `σ (Type ℕ) $ λ σ → 125 | `X [] (Check , σ) (`∎ (Infer , σ)) 126 | App → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 127 | `X [] (Infer , σ ⇒ τ) (`X [] (Check , σ) (`∎ (Infer , τ))) 128 | Fst → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 129 | `X [] (Infer , σ ⊗ τ) (`∎ (Infer , σ)) 130 | Snd → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 131 | `X [] (Infer , σ ⊗ τ) (`∎ (Infer , τ)) 132 | Lam → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 133 | `X ((Infer , σ) ∷ []) (Check , τ) (`∎ (Check , σ ⇒ τ)) 134 | Prd → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 135 | `X [] (Check , σ) (`X [] (Check , τ) (`∎ (Check , σ ⊗ τ))) 136 | Emb → `σ (Type ℕ) $ λ σ → 137 | `X [] (Infer , σ) (`∎ (Check , σ)) 138 | Let → `σ (Type ℕ × Type ℕ) $ uncurry $ λ σ τ → 139 | `X [] (Infer , σ) (`X ((Infer , σ) ∷ []) (Check , τ) (`∎ (Check , τ))) 140 | 141 | Internal : (P : Set) → (Mode × Type ℕ) ─Scoped 142 | Internal P = Tm (internal P) _ 143 | 144 | getPosition : ∀ {P σ Γ} → Internal P σ Γ → Position 145 | getPosition (`var _) = start 146 | getPosition (`con (r , _)) = r 147 | 148 | typed = internal ⊤ 149 | 150 | Typed : (Mode × Type ℕ) ─Scoped 151 | Typed = Tm typed _ 152 | 153 | letfree = internal ⊥ 154 | 155 | LetFree : (Mode × Type ℕ) ─Scoped 156 | LetFree = Tm letfree _ 157 | 158 | erase : ∀ {X σ Γ} → ⟦ letfree ⟧ X σ Γ → ⟦ typed ⟧ X σ Γ 159 | erase (r , Cut , p) = r , Cut , p 160 | erase (r , App , p) = r , App , p 161 | erase (r , Fst , p) = r , Fst , p 162 | erase (r , Snd , p) = r , Snd , p 163 | erase (r , Lam , p) = r , Lam , p 164 | erase (r , Emb , p) = r , Emb , p 165 | erase (r , Prd , p) = r , Prd , p 166 | erase (r , Let {} , p) 167 | 168 | data LetView {X Γ} : ∀ {σ} → ⟦ typed ⟧ X σ Γ → Set where 169 | Let : ∀ r {σ τ} e b → LetView (r , Let , (σ , τ) , e , b , refl) 170 | ¬Let : ∀ {σ} (t : ⟦ letfree ⟧ X σ Γ) → LetView (erase t) 171 | 172 | letView : ∀ {X Γ σ} (t : ⟦ typed ⟧ X σ Γ) → LetView t 173 | letView (r , Cut , p) = ¬Let (r , Cut , p) 174 | letView (r , App , p) = ¬Let (r , App , p) 175 | letView (r , Fst , p) = ¬Let (r , Fst , p) 176 | letView (r , Snd , p) = ¬Let (r , Snd , p) 177 | letView (r , Lam , p) = ¬Let (r , Lam , p) 178 | letView (r , Emb , p) = ¬Let (r , Emb , p) 179 | letView (r , Prd , p) = ¬Let (r , Prd , p) 180 | letView (r , Let , _ , e , b , refl) = Let r e b 181 | 182 | -- Traditional pattern synonyms (usable on the LHS only) 183 | pattern _`∶'_ t σ = (Cut , σ , t , refl) 184 | pattern _`∶_ t σ = `con (_ , t `∶' σ) 185 | pattern _`$'_ f t = (App , _ , f , t , refl) 186 | pattern _`$_ f t = `con (_ , f `$' t) 187 | pattern `fst'_ e = (Fst , _ , e , refl) 188 | pattern `fst_ e = `con (_ , `fst' e) 189 | pattern `snd'_ e = (Snd , _ , e , refl) 190 | pattern `snd_ e = `con (_ , `snd' e) 191 | pattern `λ'_ b = (Lam , _ , b , refl) 192 | pattern `λ_ b = `con (_ , `λ' b) 193 | pattern `λ'_↦_ x b = (_ , Lam , _ , (x ∷ [] , b) , refl) 194 | pattern `λ_↦_ x b = `con (`λ' x ↦ b) 195 | pattern _`,'_ a b = (Prd , _ , a , b , refl) 196 | pattern _`,_ a b = `con (_ , a `,' b) 197 | pattern `let'_`in_ e b = (Let , _ , e , b , refl) 198 | pattern `let_`in_ e b = `con (_ , `let' e `in b) 199 | pattern `-'_ t = (Emb , _ , t , refl) 200 | pattern `-_ t = `con (_ , `-' t) 201 | 202 | -- Position-aware pattern synonyms (usable both on the LHS and RHS) 203 | pattern _>[_`∶'_] r t σ = (r , Cut , σ , t , refl) 204 | pattern _>[_`∶_] r t σ = `con (r >[ t `∶' σ ]) 205 | pattern _>[_`$'_] r f t = (r , App , _ , f , t , refl) 206 | pattern _>[_`$_] r f t = `con (r >[ f `$' t ]) 207 | pattern _>`fst'_ r e = (r , Fst , _ , e , refl) 208 | pattern _>`fst_ r e = `con (r >`fst' e) 209 | pattern _>`snd'_ r e = (r , Snd , _ , e , refl) 210 | pattern _>`snd_ r e = `con (r >`snd' e) 211 | pattern _>`λ'_ r b = (r , Lam , _ , b , refl) 212 | pattern _>`λ_ r b = `con (r >`λ' b) 213 | pattern _>[_`,'_] r a b = (r , Prd , _ , a , b , refl) 214 | pattern _>[_`,_] r a b = `con (r >[ a `,' b ]) 215 | pattern _>`let'_`in_ r e b = (r , Let , _ , e , b , refl) 216 | pattern _>`let_`in_ r e b = `con (r >`let' e `in b) 217 | pattern _>`-'_ r t = (r , Emb , _ , t , refl) 218 | pattern _>`-_ r t = `con (r >`-' t) 219 | 220 | pattern _>`λ'_↦_ r x b = (r , Lam , _ , (x ∷ [] , b) , refl) 221 | pattern _>`λ_↦_ r x b = `con (r >`λ' x ↦ b) 222 | pattern _>`let'_↦_`in_ r x e b = (r , Let , _ , e , (x ∷ [] , b) , refl) 223 | pattern _>`let_↦_`in_ r x e b = `con (r >`let' x ↦ e `in b) 224 | 225 | -- Examples of terms of differnent languages using the same pattern synonyms 226 | -- Here we use `start' as a placeholder for positions 227 | 228 | _ : Surface.Scoped Check [] 229 | _ = start >`λ (start >`- `var z) 230 | 231 | _ : ∀ {σ} → Internal.Typed (Check , σ ⇒ σ) [] 232 | _ = start >`λ (start >`- `var z) 233 | 234 | toCheck : ∀ {m σ Γ} → Internal.Typed (m , σ) Γ → Internal.Typed (Check , σ) Γ 235 | toCheck {Infer} t = Internal.getPosition t >`- t 236 | toCheck {Check} t = t 237 | 238 | toInfer : ∀ {m σ Γ} → Internal.Typed (m , σ) Γ → Internal.Typed (Infer , σ) Γ 239 | toInfer {Infer} t = t 240 | toInfer {Check} t = Internal.getPosition t >[ t `∶ _ ] 241 | 242 | infersOf : List (Type ℕ) → List (Mode × Type ℕ) 243 | infersOf = List.map (Infer ,_) 244 | 245 | data Definitions : List (Type ℕ) → Set 246 | record Definition {ds} (p : Definitions ds) : Set 247 | 248 | infixl 11 _>_∶_≔_ _∶_≔_ 249 | record Definition {ds} p where 250 | constructor _>_∶_≔_ 251 | field pos : Position 252 | name : String 253 | type : Type ℕ 254 | term : Internal.Typed (Check , type) (infersOf ds) 255 | 256 | pattern _∶_≔_ x σ t = _ > x ∶ σ ≔ t 257 | 258 | infixl 10 _&_ 259 | data Definitions where 260 | [] : Definitions [] 261 | _&_ : ∀ {ds} (p : Definitions ds) (d : Definition p) → 262 | Definitions (Definition.type d ∷ ds) 263 | 264 | modes : ∀ {Γ} → Definitions Γ → List Mode 265 | modes {Γ} _ = List.map (const Infer) Γ 266 | 267 | names : ∀ {Γ} (ds : Definitions Γ) → All (const String) (modes ds) 268 | names [] = [] 269 | names (ds & d) = Definition.name d ∷ names ds 270 | 271 | toEnv : ∀ {Γ} → Definitions Γ → (infersOf Γ ─Env) Internal.Typed [] 272 | toEnv [] = ε 273 | toEnv (Γ & r > _ ∶ σ ≔ d) = let ρ = toEnv Γ in ρ ∙ sub ρ (r >[ d `∶ σ ]) 274 | 275 | Expression : Type ℕ ─Scoped 276 | Expression σ Γ = Internal.Typed (Infer , σ) (infersOf Γ) 277 | 278 | 279 | toLets : ∀ {σ Γ} → Definitions Γ → 280 | Internal.Typed (Check , σ) (infersOf Γ) → Internal.Typed (Check , σ) [] 281 | toLets [] e = e 282 | toLets (ds & d) e = toLets ds $ Definition.pos d 283 | >`let toInfer (Definition.term d) 284 | `in e 285 | 286 | infix 9 _&&_ 287 | data Program : Set where 288 | _&&_ : ∀ {σ Γ} → Definitions Γ → Expression σ Γ → Program 289 | 290 | pattern assuming_have_ defs expr = defs && expr 291 | 292 | {- 293 | -- Can't quite write this: we would have to also write down the position of each node 294 | 295 | _ : Program 296 | _ = let nat = α 0 ⇒ (α 0 ⇒ α 0) ⇒ α 0 in assuming [] 297 | & "id" ∶ nat ⇒ nat ≔ `λ `- `var z 298 | & "zero" ∶ nat ≔ `λ `λ `- `var (s z) 299 | & "suc" ∶ nat ⇒ nat ≔ `λ `λ `λ `- (`var z 300 | `$ (`- ((`var (s (s z)) 301 | `$ (`- (`var (s z)))) 302 | `$ (`- (`var z))))) 303 | have `var (s (s z)) `$ (`- (`var z `$ (`- (`var z `$ (`- `var (s z)))))) 304 | -} 305 | -------------------------------------------------------------------------------- /stlc/src/LetInline.agda: -------------------------------------------------------------------------------- 1 | module LetInline where 2 | 3 | open import Data.List.Base 4 | open import Data.Product 5 | open import environment 6 | open import Language 7 | open import Generic.Semantics 8 | open import Generic.Semantics.Syntactic 9 | open import Function 10 | 11 | open Internal 12 | 13 | LetInline : Sem typed LetFree LetFree 14 | Sem.th^𝓥 LetInline = th^Tm 15 | Sem.var LetInline = id 16 | Sem.alg LetInline = λ t → case letView t of λ where 17 | (Let r e b) → extract b (ε ∙ e) 18 | (¬Let p) → Sem.alg Substitution p 19 | 20 | let-inline : ∀ {σ} → Typed σ [] → LetFree σ [] 21 | let-inline = Sem.closed LetInline 22 | -------------------------------------------------------------------------------- /stlc/src/Main.agda: -------------------------------------------------------------------------------- 1 | module Main where 2 | 3 | open import Data.List.Base using ([]; _∷_) 4 | open import Data.Sum.Base 5 | open import Data.Product 6 | open import Data.String.Base 7 | open import Function 8 | 9 | open import System.Environment 10 | open import IO 11 | open import Codata.Musical.Notation 12 | 13 | import Types 14 | open import Pipeline 15 | open import Print 16 | 17 | main = run $ 18 | ♯ getArgs >>= λ where 19 | [] → ♯ (return _) 20 | (fp ∷ _) → ♯ (♯ readFiniteFile fp >>= λ str → 21 | ♯ putStrLn ([ Types.show , unlines3 ]′ (pipeline str))) 22 | 23 | where unlines3 = λ where (a , b , c) → a ++ "\n" ++ b ++ "\n" ++ c 24 | -------------------------------------------------------------------------------- /stlc/src/Parse.agda: -------------------------------------------------------------------------------- 1 | module Parse where 2 | 3 | open import Level 4 | open import Data.Unit using (⊤) 5 | open import Data.Bool.Base using (Bool; true; false) 6 | open import Data.Nat.Properties using (≤-refl) 7 | open import Data.Empty 8 | open import Data.Product 9 | 10 | open import Data.Maybe 11 | open import Data.Bool using (if_then_else_) 12 | open import Data.Char as Char using (Char; isSpace; isAlpha) 13 | open import Data.String as String using (String; toList) 14 | import Data.String.Unsafe as String 15 | open import Data.Sum.Base using (_⊎_; inj₁; inj₂; [_,_]′) 16 | open import Data.List.Base as List using (List; []; _∷_) 17 | open import Data.List.NonEmpty as List⁺ using (List⁺; _∷_) 18 | open import Data.Vec as Vec using (Vec) 19 | open import Function 20 | 21 | open import Category.Monad 22 | 23 | open import Induction.Nat.Strong as INS 24 | 25 | open import Data.Nat.Base using (ℕ) 26 | open import Data.Subset 27 | open import Data.List.Sized.Interface 28 | open import Relation.Binary using (Decidable) 29 | open import Relation.Binary.PropositionalEquality 30 | open import Relation.Binary.PropositionalEquality.Decidable 31 | open import Relation.Nullary 32 | open import Relation.Nullary.Decidable using (map′) 33 | open import Relation.Unary using (IUniversal) renaming (_⇒_ to _⟶_) 34 | 35 | open import Text.Parser.Types 36 | open import Text.Parser.Position 37 | open import Text.Parser.Combinators hiding (_>>=_) 38 | open import Text.Parser.Monad 39 | 40 | open import Generic.AltSyntax 41 | 42 | open import Language 43 | open Surface 44 | open import Types 45 | 46 | module ParserM = Agdarsec (Error String) ⊥ (record { into = At_ParseError ∘′ proj₁ }) 47 | open ParserM 48 | 49 | data Tok : Set where 50 | ID : String → Tok 51 | ARR PRD : Tok 52 | DEF HVE : Tok 53 | LET EQ IN : Tok 54 | LAM DOT : Tok 55 | FST SND : Tok 56 | LPAR COL COM RPAR : Tok 57 | 58 | _≟_ : Decidable {A = Tok} _≡_ 59 | ID x ≟ ID y = map′ (cong ID) (λ where refl → refl) (x String.≟ y) 60 | ARR ≟ ARR = yes refl 61 | PRD ≟ PRD = yes refl 62 | DEF ≟ DEF = yes refl 63 | HVE ≟ HVE = yes refl 64 | LET ≟ LET = yes refl 65 | EQ ≟ EQ = yes refl 66 | IN ≟ IN = yes refl 67 | LAM ≟ LAM = yes refl 68 | DOT ≟ DOT = yes refl 69 | FST ≟ FST = yes refl 70 | SND ≟ SND = yes refl 71 | LPAR ≟ LPAR = yes refl 72 | COL ≟ COL = yes refl 73 | COM ≟ COM = yes refl 74 | RPAR ≟ RPAR = yes refl 75 | _ ≟ _ = no p where postulate p : _ 76 | 77 | Token : Set 78 | Token = Position × Tok 79 | 80 | keywords : List⁺ (String × Tok) 81 | keywords = ("→" , ARR) 82 | ∷ ("->" , ARR) 83 | ∷ ("*" , PRD) 84 | ∷ ("λ" , LAM) 85 | ∷ ("\\" , LAM) 86 | ∷ (":" , COL) 87 | ∷ ("let" , LET) 88 | ∷ ("in" , IN) 89 | ∷ ("fst" , FST) 90 | ∷ ("snd" , SND) 91 | ∷ ("def" , DEF) 92 | ∷ ("have", HVE) 93 | ∷ [] 94 | 95 | breaking : Char → ∃ λ b → if b then Maybe Tok else Lift _ ⊤ 96 | breaking c = case c of λ where 97 | '(' → true , just LPAR 98 | ')' → true , just RPAR 99 | '.' → true , just DOT 100 | ',' → true , just COM 101 | '=' → true , just EQ 102 | c → if isSpace c then true , nothing else false , _ 103 | 104 | open import Text.Lexer keywords breaking ID using (tokenize) 105 | 106 | instance 107 | _ = ParserM.monadZero 108 | _ = ParserM.monadPlus 109 | _ = ParserM.monad 110 | 111 | P = ParserM.param Token (Vec Token) λ where (p , _) _ → Value (_ , p , []) 112 | 113 | theTok : Tok → ∀[ Parser P Token ] 114 | theTok t = maybeTok $ λ where 115 | tok@(p , t') → case t ≟ t' of λ where 116 | (yes eq) → just tok 117 | (no ¬eq) → nothing 118 | 119 | name : ∀[ Parser P String ] 120 | name = maybeTok λ where (p , ID str) → just str; _ → nothing 121 | 122 | parens : ∀ {A} → ∀[ □ Parser P A ⟶ Parser P A ] 123 | parens □p = theTok LPAR &> □p <& box (theTok RPAR) 124 | 125 | type : ∀[ Parser P (Type String) ] 126 | type = fix _ $ λ rec → 127 | let varlike str = case String.toList str of λ where 128 | ('\'' ∷ nm) → just (String.fromList nm) 129 | _ → nothing 130 | in chainr1 (α <$> guardM varlike name <|> parens rec) 131 | (box $ (_⇒_ <$ theTok ARR) <|> _⊗_ <$ theTok PRD) 132 | 133 | record Bidirectional n : Set where 134 | field infer : Parser P (Parsed Infer) n 135 | check : Parser P (Parsed Check) n 136 | open Bidirectional 137 | 138 | bidirectional : ∀[ Bidirectional ] 139 | bidirectional = fix Bidirectional $ λ rec → 140 | let □check = INS.map check rec 141 | □infer = INS.map infer rec 142 | var = uncurry (flip `var) <$> (guard (List.all isAlpha ∘′ toList) name <&M> getPosition) 143 | cut = (λ where ((t , (p , _)) , σ) → p >[ t `∶ σ ]) 144 | <$> (theTok LPAR 145 | &> □check <&> box (theTok COL) <&> box (commit type) 146 | <& box (theTok RPAR)) 147 | app = (λ where (p , c) e → p >[ e `$ c ]) <$> 148 | (getPosition ((uncurry _>`-_ <$> (getPosition var)) 149 | <|> parens □check)) 150 | 151 | proj = (λ where ((p , t) , e) → [ const (p >`fst e) , const (p >`snd e) ]′ t) 152 | <$> (getPosition (theTok FST <⊎> theTok SND) 153 | <&> box (var <|> parens □infer)) 154 | infer = iterate (var <|> cut <|> proj <|> parens (INS.map commit □infer)) 155 | (box app) 156 | lam = (λ where ((p , x) , c) → p >`λ x ↦ c) 157 | <$> (theTok LAM &> box (getPosition name) 158 | <&> box (theTok DOT &> INS.map commit □check)) 159 | letin = (λ where (((p , x) , e) , c) → p >`let x ↦ e `in c) 160 | <$> (theTok LET &> box (getPosition name) 161 | <&> box (theTok EQ &> INS.map commit □infer) 162 | <&> box (theTok IN &> INS.map commit □check) 163 | ) 164 | 165 | paredc = (λ p → let (c , r) = p; cons c = uncurry (_>[ c `,_]) in 166 | [ cons c ∘′ List⁺.foldr₁ (λ where (p , c) → (p ,_) ∘′ cons c) 167 | , const c ]′ r) <$> 168 | -- opening parenthesis 169 | ((theTok LPAR &> □check) <&> box ( 170 | -- followed by either 171 | -- either a list of other values 172 | (list⁺ ((getPosition INS.map commit □check) 173 | <& box (theTok RPAR)) 174 | -- or a closing parenthesis 175 | <⊎> theTok RPAR 176 | )) 177 | emb = uncurry _>`-_ <$> (getPosition infer) 178 | check = lam <|> letin <|> emb 179 | in record { infer = infer <|> parens (INS.map commit □infer) 180 | ; check = check <|> paredc 181 | } 182 | 183 | definitions : ∀[ Parser P (List⁺ (Position × String × Type String × Parsed Check)) ] 184 | definitions = list⁺ $ getPosition 185 | box (name 187 | <&> box (theTok COL 188 | &> box (type 189 | <&> box (theTok EQ 190 | &> box (check bidirectional))))) 191 | 192 | program : ∀[ Parser P (List⁺ (Position × String × Type String × Parsed Check) 193 | × Parsed Infer) ] 194 | program = definitions <&> box (theTok HVE &> box (infer bidirectional)) 195 | 196 | parse : String → Types.Result String 197 | (List⁺ (Position × String × Type String × Parsed Check) × Parsed Infer) 198 | parse str = result inj₁ inj₁ (inj₂ ∘′ Success.value ∘′ proj₁) 199 | $′ runParser program ≤-refl input (start , []) 200 | where input = Vec.fromList $ tokenize str 201 | 202 | open import Agda.Builtin.Equality 203 | 204 | _ : tokenize "(λ x . 1 : `a → `a)" 205 | ≡ (0 ∶ 0 , LPAR) 206 | ∷ (0 ∶ 1 , LAM) 207 | ∷ (0 ∶ 3 , ID "x") 208 | ∷ (0 ∶ 5 , DOT) 209 | ∷ (0 ∶ 7 , ID "1") 210 | ∷ (0 ∶ 9 , COL) 211 | ∷ (0 ∶ 11 , ID "`a") 212 | ∷ (0 ∶ 14 , ARR) 213 | ∷ (0 ∶ 16 , ID "`a") 214 | ∷ (0 ∶ 18 , RPAR) 215 | ∷ [] 216 | _ = refl 217 | 218 | _ : parse "def ida : 'a → 'a = λ x . x 219 | \ \def idb : 'a → 'a = λ y . ida y 220 | \ \have idb" 221 | ≡ (inj₂ (((start , "ida" , _ , `λ "x" ↦ (`- `var (0 ∶ 27) "x")) 222 | ∷ (record { line = 0 ; offset = 27 } , "idb" , _ , `λ "y" ↦ `- (`var _ "ida" `$ (`- `var (1 ∶ 31) "y"))) 223 | ∷ [] 224 | ) , `var (2 ∶ 5) "idb" 225 | )) 226 | _ = refl 227 | 228 | _ : parse "def thd : ('a * 'b * 'c) -> 'c = λ p. fst (fst p) 229 | \ \have thd" 230 | ≡ inj₂ (((start , "thd" , (α "a" ⊗ (α "b" ⊗ α "c")) ⇒ α "c" 231 | , `λ "p" ↦ `- `fst `fst `var (0 ∶ 48) "p" 232 | ) 233 | ∷ [] 234 | ) 235 | , `var (1 ∶ 5) "thd" 236 | ) 237 | _ = refl 238 | 239 | _ : parse "def swap : ('a * 'b) → ('b * 'a) = λp. (snd p, fst p, snd p) 240 | \ \have swap" 241 | ≡ inj₂ ((start , "swap" , (α "a" ⊗ α "b") ⇒ (α "b" ⊗ α "a") 242 | , (0 ∶ 35) >`λ "p" ↦ ((`- `snd `var (0 ∶ 44) "p") 243 | `, ((`- `fst `var (0 ∶ 51) "p") 244 | `, (`- `snd `var (0 ∶ 58) "p"))) 245 | ) 246 | ∷ [] 247 | , `var (1 ∶ 5) "swap" 248 | ) 249 | _ = refl 250 | 251 | _ : tokenize "(λ x . x : `a → `a)" 252 | ≡ (start , LPAR) 253 | ∷ (0 ∶ 1 , LAM) 254 | ∷ (0 ∶ 3 , ID "x") 255 | ∷ (0 ∶ 5 , DOT) 256 | ∷ (0 ∶ 7 , ID "x") 257 | ∷ (0 ∶ 9 , COL) 258 | ∷ (0 ∶ 11 , ID "`a") 259 | ∷ (0 ∶ 14 , ARR) 260 | ∷ (0 ∶ 16 , ID "`a") 261 | ∷ (0 ∶ 18 , RPAR) 262 | ∷ [] 263 | _ = refl 264 | -------------------------------------------------------------------------------- /stlc/src/Pipeline.agda: -------------------------------------------------------------------------------- 1 | module Pipeline where 2 | 3 | open import Data.Product 4 | open import Data.String 5 | open import Data.Sum 6 | open import Data.List.Base as List 7 | import Data.List.NonEmpty as List⁺ 8 | open import Data.List.All 9 | open import Data.List.All.Properties 10 | open import Data.List.Relation.Unary.All.Extras as Allₑ 11 | open import Text.Parser.Position 12 | open import Function 13 | open import Relation.Binary.PropositionalEquality 14 | 15 | open import var using (z; s) 16 | import environment as E 17 | open import Generic.Syntax using (`var) 18 | open import Generic.Semantics.Syntactic using (sub) 19 | open import Language; open Surface 20 | open import Types 21 | open import Parse 22 | open import Scopecheck 23 | open import Typecheck 24 | open import LetInline 25 | open import Eval 26 | open import Print 27 | 28 | open import Category.Monad 29 | 30 | open Compiler 31 | 32 | module _ where 33 | 34 | open RawMonad (Compiler.monad String) 35 | 36 | declarations : List (Position × String × Type String × Parsed Check) → 37 | ∀ {Γ} → Definitions Γ → Compiler String (∃ Definitions) 38 | declarations [] p = pure $ -, p 39 | declarations ((r , str , sig , decl) ∷ decls) p = do 40 | scoped ← scopecheck p decl 41 | σ ← liftState $ cleanupType sig 42 | typed ← ppCompiler $ liftResult $ type- Check _ scoped (map⁺ Allₑ.self) σ 43 | let x = r > str ∶ σ ≔ subst (Internal.Typed _) (eq^fromTyping _) typed 44 | declarations decls (p & x) 45 | 46 | declaration : ∀ {Γ} → Definitions Γ → Parsed Infer → 47 | Compiler String (∃ λ σ → Expression σ Γ) 48 | declaration {Γ} p d = do 49 | scoped ← scopecheck p d 50 | (σ , typed) ← ppCompiler $ liftResult $ type- Infer Γ scoped (map⁺ self) 51 | pure (σ , subst (Internal.Typed _) (eq^fromTyping _) typed) 52 | 53 | toProgram : String → Compiler String Program 54 | toProgram str = do 55 | (decls , expr) ← liftResult $ parse str 56 | (Γ , defs) ← declarations (List⁺.toList decls) [] 57 | (σ , eval) ← declaration defs expr 58 | pure $ assuming defs have eval 59 | 60 | pipeline : String → Error String ⊎ (String × String × String) 61 | pipeline str = Compiler.run $ do 62 | (defs && eval) ← toProgram str 63 | let lets = toLets defs (toCheck eval) 64 | let unlets = let-inline lets 65 | let val = norm unlets 66 | rm ← Map.invert <$> getMap 67 | pure $ print lets rm 68 | , print unlets rm 69 | , print val rm 70 | 71 | open import Agda.Builtin.Equality 72 | 73 | _ : Compiler.run (toProgram "def id : 'a → 'a = λx. x 74 | \ \def deux : 'a → 'b → 'b = λx. λy.y 75 | \ \have id") 76 | ≡ inj₂ (assuming [] 77 | & "id" ∶ α 0 ⇒ α 0 ≔ `λ `- `var z 78 | & "deux" ∶ α 0 ⇒ α 1 ⇒ α 1 ≔ `λ `λ `- `var z 79 | have `var (s z)) 80 | _ = refl 81 | 82 | -- normalisation test 83 | 84 | _ : pipeline "def idh : ('a → 'a) → ('a → 'a) = λf.λx. f x 85 | \ \def id : ('a → 'a) = λx.x 86 | \ \have idh id" 87 | ≡ inj₂ ("let c = (λa.λb.a b : (`a → `a) → `a → `a) in \ 88 | \let e = (λd.d : `a → `a) in \ 89 | \c e" 90 | , "(λa.λb.a b : (`a → `a) → `a → `a) (λc.c : `a → `a)" 91 | , "λa.a") 92 | _ = refl 93 | -------------------------------------------------------------------------------- /stlc/src/Print.agda: -------------------------------------------------------------------------------- 1 | module Print where 2 | 3 | open import Data.Bool using (true; false; if_then_else_; _∧_) 4 | open import Data.Nat as Nat 5 | import Data.Nat.Show as NShow 6 | open import Data.String 7 | open import Data.Char 8 | open import Data.Char.Unsafe 9 | open import Data.Product 10 | open import Data.Maybe 11 | open import Data.List.Base as List using ([]) 12 | open import Function 13 | 14 | open import var 15 | open import environment 16 | import Generic.Semantics.Printing as Printing 17 | 18 | open import Language 19 | open Internal 20 | 21 | import Data.Map as M 22 | private 23 | module Map = M.Map Nat._≟_ String 24 | open Map using (Map) 25 | 26 | type : Type ℕ → Map → String 27 | type (α k) mp = maybe ("`" ++_) (NShow.show k) (Map.assoc k mp) 28 | type (σ@(α _) ⇒ τ) mp = type σ mp ++ " → " ++ type τ mp 29 | type (σ ⇒ τ) mp = "(" ++ type σ mp ++ ") → " ++ type τ mp 30 | type (σ@(α _) ⊗ τ) mp = type σ mp ++ " * " ++ type τ mp 31 | type (σ ⊗ τ) mp = "(" ++ type σ mp ++ ") * " ++ type τ mp 32 | 33 | print : ∀ {P mσ} → Internal P mσ [] → Map → String 34 | print t mp = Printing.print display t where 35 | 36 | display = Printing.mkD $ λ where 37 | (p , t `∶' σ) → "(" ++ t ++ " : " ++ type σ mp ++ ")" 38 | (p , f `$' t) → f ++ " " ++ parens? t 39 | (p , `fst' e) → "fst " ++ parens? e 40 | (p , `snd' e) → "snd " ++ parens? e 41 | (p , `λ' (x , b)) → "λ" ++ lookup x z ++ "." ++ b 42 | (p , a `,' b) → "(" ++ a ++ ", " ++ b ++ ")" 43 | (p , `let' e `in (x , b)) → "let " ++ lookup x z ++ " = " ++ e ++ " in " ++ b 44 | (p , `-' t) → t 45 | 46 | 47 | where parens? : String → String 48 | parens? t = let cs = toList t in 49 | if maybe′ ('(' ==_) true (List.head cs) 50 | ∧ maybe′ (')' ==_) true (List.head (List.reverse cs)) then t 51 | else if List.any isSpace cs then "(" ++ t ++ ")" else t 52 | -------------------------------------------------------------------------------- /stlc/src/Scopecheck.agda: -------------------------------------------------------------------------------- 1 | module Scopecheck where 2 | 3 | open import Data.Product as Product 4 | open import Data.Nat 5 | open import Data.String 6 | open import Data.String.Unsafe as String 7 | open import Data.Maybe.Base using (Maybe; nothing; just; maybe′) 8 | open import Data.Sum.Base as Sum using (inj₁; inj₂; [_,_]′) 9 | open import Data.List as List using ([]) 10 | open import Data.List.All as All using (All) 11 | open import Data.List.All.Properties 12 | open import Function 13 | 14 | open import Category.Monad 15 | open import Category.Monad.State 16 | 17 | open import Generic.Syntax 18 | open import Generic.AltSyntax 19 | 20 | open import Text.Parser.Position 21 | 22 | open import Language 23 | open Surface 24 | open import Types 25 | 26 | module _ where 27 | 28 | M = State (Map × ℕ) 29 | open RawMonadState (StateMonadState (Map × ℕ)) hiding (_⊗_) 30 | 31 | resolve : String → M ℕ 32 | resolve str = do 33 | (mp , gen) ← get 34 | case Map.assoc str mp of λ where 35 | (just n) → return n 36 | nothing → do 37 | put (Map.set str gen mp , suc gen) 38 | return gen 39 | 40 | cleanupType : Type String → M (Type ℕ) 41 | cleanupType (α str) = α <$> resolve str 42 | cleanupType (σ ⇒ τ) = _⇒_ <$> cleanupType σ ⊛ cleanupType τ 43 | cleanupType (σ ⊗ τ) = _⊗_ <$> cleanupType σ ⊛ cleanupType τ 44 | 45 | cleanupTerm : ∀ {i σ Γ} → Tm (surface String) i σ Γ → M (Scoped σ Γ) 46 | cleanupTerm (`var k) = return $ `var k 47 | cleanupTerm (r >[ t `∶ σ ]) = r >[_`∶_] <$> cleanupTerm t ⊛ cleanupType σ 48 | cleanupTerm (r >[ f `$ t ]) = r >[_`$_] <$> cleanupTerm f ⊛ cleanupTerm t 49 | cleanupTerm (r >`fst b) = r >`fst_ <$> cleanupTerm b 50 | cleanupTerm (r >`snd b) = r >`snd_ <$> cleanupTerm b 51 | cleanupTerm (r >`λ b) = r >`λ_ <$> cleanupTerm b 52 | cleanupTerm (r >[ a `, b ]) = r >[_`,_] <$> cleanupTerm a ⊛ cleanupTerm b 53 | cleanupTerm (r >`let e `in b) = r >`let_`in_ <$> cleanupTerm e ⊛ cleanupTerm b 54 | cleanupTerm (r >`- t) = r >`-_ <$> cleanupTerm t 55 | 56 | open RawMonad (Compiler.monad String) 57 | open Compiler 58 | open ScopeCheck 59 | 60 | scopecheck : ∀ {Σ m} (p : Definitions Σ) → Parsed m → 61 | Compiler String (Scoped m (modes p)) 62 | scopecheck p r = do 63 | let scopeError = uncurry At_OutOfScope_ 64 | t ← liftResult $ Sum.map₁ scopeError $ scopeCheck eqdecMode _ _ (names p) r 65 | liftState $ cleanupTerm t 66 | -------------------------------------------------------------------------------- /stlc/src/System/Environment.agda: -------------------------------------------------------------------------------- 1 | module System.Environment where 2 | 3 | open import Data.List.Base using (List) 4 | open import Data.String.Base using (String) 5 | 6 | import IO.Primitive as Prim 7 | open import IO 8 | 9 | private 10 | postulate 11 | primGetArgs : Prim.IO (List String) 12 | 13 | {-# FOREIGN GHC import qualified System.Environment as Env #-} 14 | {-# FOREIGN GHC import qualified Data.Text as T #-} 15 | {-# COMPILE GHC primGetArgs = fmap (fmap T.pack) Env.getArgs #-} 16 | 17 | getArgs : IO (List String) 18 | getArgs = lift primGetArgs 19 | -------------------------------------------------------------------------------- /stlc/src/Typecheck.agda: -------------------------------------------------------------------------------- 1 | module Typecheck where 2 | 3 | open import Data.Product as Prod 4 | open import Data.Nat as ℕ using (ℕ; _≟_) 5 | open import Data.List as List hiding (lookup ; fromMaybe) 6 | open import Data.List.All as All hiding (lookup) 7 | import Data.List.All.Properties as Allₚ 8 | open import Data.List.Relation.Unary.All.Extras as Allₑ 9 | open import Data.List.Any using (here; there) 10 | open import Data.List.Membership.Propositional 11 | open import Relation.Binary.PropositionalEquality as P using (_≡_; refl) 12 | open import Data.Maybe hiding (fromMaybe; All) 13 | open import Function 14 | 15 | open import Category.Monad 16 | 17 | open import var hiding (_<$>_) 18 | open import varlike using (base; vl^Var) 19 | open import environment hiding (_<$>_) 20 | open import Generic.Syntax 21 | open import Generic.Semantics 22 | 23 | open import Text.Parser.Position 24 | 25 | open import Language 26 | open Surface 27 | open Internal 28 | open import Types 29 | 30 | Typing : List Mode → Set 31 | Typing = All (const (Type ℕ)) 32 | 33 | fromTyping : ∀ ms → Typing ms → List (Mode × Type ℕ) 34 | fromTyping ms = Allₑ.toList 35 | 36 | eq^fromTyping : 37 | ∀ Γ → fromTyping (List.map (const Infer) Γ) (Allₚ.map⁺ Allₑ.self) 38 | ≡ List.map (Infer ,_) Γ 39 | eq^fromTyping [] = refl 40 | eq^fromTyping (σ ∷ Γ) = P.cong (_ ∷_) (eq^fromTyping Γ) 41 | 42 | Elab : (Mode × Type ℕ) ─Scoped → Mode × Type ℕ → (ms : List Mode) → Typing ms → Set 43 | Elab T σ ms Γ = T σ (fromTyping ms Γ) 44 | 45 | data Var- : Mode ─Scoped where 46 | `var : ∀ {ms} → (infer : ∀ Γ → Σ[ σ ∈ Type ℕ ] Elab Var (Infer , σ) ms Γ) → 47 | Var- Infer ms 48 | 49 | var0 : ∀ {ms} → Var- Infer (Infer ∷ ms) 50 | var0 = `var (λ where (σ ∷ _) → σ , z) 51 | 52 | var : ∀ {m} (Σ : List (Type ℕ)) → let Γ = List.map (const Infer) Σ in 53 | Var m Γ → Var- m Γ 54 | var [] () 55 | var (m ∷ Σ) z = var0 56 | var (m ∷ Σ) (s v) with var Σ v 57 | ... | `var infer = `var (λ where (σ ∷ Γ) → Prod.map₂ s $ infer Γ) 58 | 59 | toVar : ∀ {m : Mode} {ms} → m ∈ ms → Var m ms 60 | toVar (here refl) = z 61 | toVar (there v) = s (toVar v) 62 | 63 | fromVar : ∀ {m : Mode} {ms} → Var m ms → m ∈ ms 64 | fromVar z = here refl 65 | fromVar (s v) = there (fromVar v) 66 | 67 | coth^Typing : ∀ {ms ns} → Typing ns → Thinning ms ns → Typing ms 68 | coth^Typing Δ ρ = All.tabulate (λ x∈Γ → All.lookup Δ (fromVar (lookup ρ (toVar x∈Γ)))) 69 | 70 | lookup-fromVar : ∀ {m ms} Δ (v : Var m ms) → 71 | Var (m , All.lookup Δ (fromVar v)) (fromTyping ms Δ) 72 | lookup-fromVar (_ ∷ _) z = z 73 | lookup-fromVar (_ ∷ _) (s v) = s (lookup-fromVar _ v) 74 | 75 | erase^coth : ∀ ms {m σ ns} Δ (ρ : Thinning ms ns) → 76 | Var (m , σ) (fromTyping ms (coth^Typing Δ ρ)) → Var (m , σ) (fromTyping ns Δ) 77 | erase^coth [] Δ ρ () 78 | erase^coth (m ∷ ms) Δ ρ z = lookup-fromVar Δ (lookup ρ z) 79 | erase^coth (m ∷ ms) Δ ρ (s v) = erase^coth ms Δ (select extend ρ) v 80 | 81 | th^Var- : ∀ {m} → Thinnable (Var- m) 82 | th^Var- (`var infer) ρ = `var λ Δ → 83 | let (σ , v) = infer (coth^Typing Δ ρ) in 84 | σ , erase^coth _ Δ ρ v 85 | 86 | isArrow : (σ⇒τ : Type ℕ) → Maybe (Σ[ στ ∈ Type ℕ × Type ℕ ] σ⇒τ ≡ uncurry _⇒_ στ) 87 | isArrow (σ ⇒ τ) = just ( _ , refl) 88 | isArrow _ = nothing 89 | 90 | isProduct : (σ⊗τ : Type ℕ) → Maybe (Σ[ στ ∈ Type ℕ × Type ℕ ] σ⊗τ ≡ uncurry _⊗_ στ) 91 | isProduct (σ ⊗ τ) = just ( _ , refl) 92 | isProduct _ = nothing 93 | 94 | Type- : Mode → List Mode → Set 95 | Type- Infer Γ = ∀ γ → Result ℕ (∃ λ σ → Typed (Infer , σ) (fromTyping Γ γ)) 96 | Type- Check Γ = ∀ γ σ → Result ℕ (Typed (Check , σ) (fromTyping Γ γ)) 97 | 98 | open RawMonad (Result.monad ℕ) hiding (return) 99 | open Result 100 | 101 | Typecheck : Sem (surface ℕ) Var- Type- 102 | Sem.th^𝓥 Typecheck = th^Var- 103 | Sem.var Typecheck = λ where (`var infer) γ → pure $ map₂ `var (infer γ) 104 | Sem.alg Typecheck = λ where 105 | (r >[ t `∶' σ ]) γ → (-,_ ∘ (r >[_`∶ σ ])) <$> t γ σ 106 | (r >[ f `$' t ]) γ → do 107 | (σ⇒τ , f′) ← f γ 108 | ((σ , τ) , refl) ← fromMaybe (At r NotAnArrow σ⇒τ) (isArrow σ⇒τ) 109 | t′ ← t γ σ 110 | pure $ -, r >[ f′ `$ t′ ] 111 | (r >`fst' e) γ → do 112 | (σ⊗τ , e′) ← e γ 113 | ((σ , τ) , refl) ← fromMaybe (At r NotAProduct σ⊗τ) (isProduct σ⊗τ) 114 | pure $ -, r >`fst e′ 115 | (r >`snd' e) γ → do 116 | (σ⊗τ , e′) ← e γ 117 | ((σ , τ) , refl) ← fromMaybe (At r NotAProduct σ⊗τ) (isProduct σ⊗τ) 118 | pure $ -, r >`snd e′ 119 | (r >`λ' b) γ σ⇒τ → do 120 | ((σ , τ) , refl) ← fromMaybe (At r NotAnArrow σ⇒τ) (isArrow σ⇒τ) 121 | b′ ← b extend (ε ∙ var0) (σ ∷ γ) τ 122 | pure $ r >`λ b′ 123 | (r >[ a `,' b ]) Γ σ⊗τ → do 124 | ((σ , τ) , refl) ← fromMaybe (At r NotAProduct σ⊗τ) (isProduct σ⊗τ) 125 | a′ ← a Γ σ 126 | b′ ← b Γ τ 127 | pure $ r >[ a′ `, b′ ] 128 | (r >`let' e `in b) γ τ → do 129 | (σ , e′) ← e γ 130 | b′ ← b extend (ε ∙ var0) (σ ∷ γ) τ 131 | pure $ r >`let e′ `in b′ 132 | (r >`-' t) γ σ → do 133 | (τ , t′) ← t γ 134 | refl ← fromMaybe (At r Expected σ Got τ) (decToMaybe $ eqdecType ℕ._≟_ τ σ) 135 | pure $ r >`- t′ 136 | 137 | type- : ∀ (m : Mode) (Σ : List (Type ℕ)) → let Γ = List.map (const Infer) Σ in 138 | Scoped m Γ → Type- m Γ 139 | type- Infer Σ t γ = Sem.sem Typecheck (pack (var Σ)) t γ 140 | type- Check Σ t γ σ = Sem.sem Typecheck (pack (var Σ)) t γ σ 141 | -------------------------------------------------------------------------------- /stlc/src/Types.agda: -------------------------------------------------------------------------------- 1 | module Types where 2 | 3 | import Level as L 4 | open import Category.Monad 5 | open import Category.Monad.State 6 | open import Data.String as String using (String; _++_) 7 | import Data.String.Unsafe as String 8 | open import Data.Product as Prod using (_×_; _,_; proj₁) 9 | open import Data.List.Base using ([]) 10 | open import Data.Nat as ℕ using (ℕ) 11 | open import Data.Maybe.Base using (Maybe; just; nothing; maybe′) 12 | import Data.Maybe.Categorical as MC 13 | open import Data.Sum.Base as Sum 14 | import Data.Sum.Categorical.Left as Sumₗ 15 | open import Function 16 | 17 | open import Text.Parser.Position as Position using (Position) 18 | 19 | open import Language hiding (show) 20 | 21 | -------------------------------------------------------------------------------- 22 | -- Error type 23 | 24 | data Error (A : Set) : Set where 25 | At_ParseError : Position → Error A 26 | At_OutOfScope_ : Position → String → Error A 27 | At_Expected_Got_ : Position → Type A → Type A → Error A 28 | At_NotAnArrow_ : Position → Type A → Error A 29 | At_NotAProduct_ : Position → Type A → Error A 30 | At_ErrorWhenPrintingError : Position → Error A 31 | 32 | show : Error String → String 33 | show err = case err of λ where 34 | (At p ParseError) → at p "parse error." 35 | (At p OutOfScope x) → at p $ x ++ " is out of scope." 36 | (At p Expected σ Got τ) → at p $ "expected type " ++ Language.show σ 37 | ++ " but got type " ++ Language.show τ ++ " instead." 38 | (At p NotAnArrow σ) → at p $ "the type " ++ Language.show σ ++ " is not an arrow type." 39 | (At p NotAProduct σ) → at p $ "the type " ++ Language.show σ ++ " is not a product type." 40 | (At p ErrorWhenPrintingError) → at p $ "error when printing error." 41 | 42 | where at : Position → String → String 43 | at p str = "At " ++ Position.show p ++ ": " ++ str 44 | 45 | Result : Set → Set → Set 46 | Result E = Sumₗ.Sumₗ (Error E) L.zero 47 | 48 | module Result where 49 | 50 | monad : ∀ E → RawMonad (Result E) 51 | monad E = Sumₗ.monad (Error E) L.zero 52 | 53 | fail : ∀ {E A} → Error E → Result E A 54 | fail = inj₁ 55 | 56 | fromMaybe : ∀ {E A} → Error E → Maybe A → Result E A 57 | fromMaybe = maybe′ inj₂ ∘′ fail 58 | 59 | -- Data.AVL is not quite usable with String at the moment IIRC 60 | -- So instead I'm using a quick and dirty representation 61 | import Data.Map as M 62 | 63 | private 64 | module RMap = M.Map ℕ._≟_ String 65 | module Map = M.Map String._≟_ ℕ 66 | open Map using (Map; RMap) public 67 | 68 | Compiler : Set → Set → Set 69 | Compiler E = State (Map × ℕ) ∘′ (Error E ⊎_) 70 | 71 | module Compiler where 72 | 73 | monad : ∀ E → RawMonad (Compiler E) 74 | monad E = Sumₗ.monadT (Error E) L.zero (StateMonad _) 75 | 76 | liftResult : ∀ {E A} → Error E ⊎ A → Compiler E A 77 | liftResult = _,_ 78 | 79 | liftState : ∀ {E A} → State (Map × ℕ) A → Compiler E A 80 | liftState = let open RawMonad (StateMonad _) in inj₂ <$>_ 81 | 82 | getMap : ∀ {E} → Compiler E Map 83 | getMap = liftState $ λ where s@(mp , n) → (mp , s) 84 | 85 | fail : ∀ {E A} → Error E → Compiler E A 86 | fail = liftResult ∘′ Result.fail 87 | 88 | fromMaybe : ∀ {E A} → Error E → Maybe A → Compiler E A 89 | fromMaybe e ma = liftResult $ Result.fromMaybe e ma 90 | 91 | run : ∀ {E A} → Compiler E A → Result E A 92 | run m = proj₁ (m ([] , 0)) 93 | 94 | 95 | module PrettyPrint where 96 | 97 | open RawMonad (MC.monad {L.zero}) using (_<$>_; _⊛_) 98 | 99 | ppType : RMap → Type ℕ → Maybe (Type String) 100 | ppType rm (α k) = α <$> RMap.assoc k rm 101 | ppType rm (σ ⊗ τ) = _⊗_ <$> ppType rm σ ⊛ ppType rm τ 102 | ppType rm (σ ⇒ τ) = _⇒_ <$> ppType rm σ ⊛ ppType rm τ 103 | 104 | ppError : RMap → Error ℕ → Error String 105 | ppError rm err = case err of λ where 106 | (At p ParseError) → At p ParseError 107 | (At p OutOfScope x) → At p OutOfScope x 108 | (At p Expected σ Got τ) → 109 | case At p Expected_Got_ <$> ppType rm σ ⊛ ppType rm τ of λ where 110 | nothing → At p ErrorWhenPrintingError 111 | (just err) → err 112 | (At p NotAnArrow σ) → 113 | case At p NotAnArrow_ <$> ppType rm σ of λ where 114 | nothing → At p ErrorWhenPrintingError 115 | (just err) → err 116 | (At p NotAProduct σ) → 117 | case At p NotAProduct_ <$> ppType rm σ of λ where 118 | nothing → At p ErrorWhenPrintingError 119 | (just err) → err 120 | (At p ErrorWhenPrintingError) → At p ErrorWhenPrintingError 121 | 122 | 123 | ppCompiler : ∀ {A} → Compiler ℕ A → Compiler String A 124 | ppCompiler m = let open RawMonadState (StateMonadState _) in do 125 | v ← m 126 | mp ← proj₁ <$> get 127 | pure $ Sum.map₁ (PrettyPrint.ppError (Map.invert mp)) v 128 | -------------------------------------------------------------------------------- /stlc/src/stlc.agda-lib: -------------------------------------------------------------------------------- 1 | name: stlc 2 | include: . 3 | depend: standard-library 4 | , agdarsec 5 | , generic-syntax 6 | -------------------------------------------------------------------------------- /travis/install_agda.sh: -------------------------------------------------------------------------------- 1 | #!/bin/sh 2 | AGDA_VERSION=2.5.4.2 3 | 4 | if ! type "agda" > /dev/null || [ ! `agda -V | sed "s/[^2]*//"` = "$AGDA_VERSION" ]; then 5 | cabal update 6 | cabal install alex happy cpphs --force-reinstalls 7 | cabal install Agda-"$AGDA_VERSION" --force-reinstalls 8 | fi 9 | 10 | mkdir -p $HOME/.agda 11 | cp libraries-"$AGDA_VERSION" $HOME/.agda/ 12 | cd $HOME/.agda/ 13 | # install stdlib 14 | wget https://github.com/agda/agda-stdlib/archive/v0.17.tar.gz 15 | tar -xvzf v0.17.tar.gz 16 | # install agdarsec 17 | wget https://github.com/gallais/agdarsec/archive/v0.3.0.tar.gz 18 | tar -xvzf v0.3.0.tar.gz 19 | # install generic-syntax 20 | wget https://github.com/gallais/generic-syntax/archive/v0.2.tar.gz 21 | tar -xvzf v0.2.tar.gz 22 | -------------------------------------------------------------------------------- /travis/libraries-2.5.4.2: -------------------------------------------------------------------------------- 1 | $HOME/.agda/agda-stdlib-0.17/standard-library.agda-lib 2 | $HOME/.agda/agdarsec-0.3.0/agdarsec.agda-lib 3 | $HOME/.agda/generic-syntax-0.2/src/generic-syntax.agda-lib 4 | --------------------------------------------------------------------------------