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Anupam Jain 2024-10-21 01:41:56 +05:30
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attic/
bower_components/
node_modules/
.pulp-cache/
output/
output-es/
generated-docs/
.psc-package/
.psc*
.purs*
.psa*
.spago

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README.md Normal file
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Some Singletons for PureScript

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spago.lock Normal file
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{
"workspace": {
"packages": {
"singletons": {
"path": "./",
"core": {
"dependencies": [
"arrays",
"console",
"effect",
"exists",
"leibniz",
"maybe",
"prelude",
"typelevel-prelude"
],
"build_plan": [
"arrays",
"bifunctors",
"console",
"const",
"contravariant",
"control",
"distributive",
"effect",
"either",
"exists",
"foldable-traversable",
"functions",
"functors",
"identity",
"invariant",
"leibniz",
"maybe",
"newtype",
"nonempty",
"orders",
"partial",
"prelude",
"profunctor",
"refs",
"safe-coerce",
"st",
"tailrec",
"tuples",
"type-equality",
"typelevel-prelude",
"unfoldable",
"unsafe-coerce"
]
},
"test": {
"dependencies": [],
"build_plan": []
}
}
},
"package_set": {
"address": {
"registry": "60.6.0"
},
"compiler": ">=0.15.15 <0.16.0",
"content": {
"abc-parser": "2.0.1",
"ace": "9.1.0",
"address-rfc2821": "0.1.1",
"aff": "8.0.0",
"aff-bus": "6.0.0",
"aff-coroutines": "9.0.0",
"aff-promise": "4.0.0",
"aff-retry": "2.0.0",
"affjax": "13.0.0",
"affjax-node": "1.0.0",
"affjax-web": "1.0.0",
"ansi": "7.0.0",
"apexcharts": "0.5.0",
"applicative-phases": "1.0.0",
"argonaut": "9.0.0",
"argonaut-aeson-generic": "0.4.1",
"argonaut-codecs": "9.1.0",
"argonaut-core": "7.0.0",
"argonaut-generic": "8.0.0",
"argonaut-traversals": "10.0.0",
"argparse-basic": "2.0.0",
"array-builder": "0.1.2",
"array-search": "0.6.0",
"arraybuffer": "13.2.0",
"arraybuffer-builder": "3.1.0",
"arraybuffer-types": "3.0.2",
"arrays": "7.3.0",
"arrays-extra": "0.6.1",
"arrays-zipper": "2.0.1",
"ask": "1.0.0",
"assert": "6.0.0",
"assert-multiple": "0.4.0",
"avar": "5.0.0",
"b64": "0.0.8",
"barbies": "1.0.1",
"barlow-lens": "0.9.0",
"bifunctors": "6.0.0",
"bigints": "7.0.1",
"bolson": "0.3.9",
"bookhound": "0.1.7",
"bower-json": "3.0.0",
"call-by-name": "4.0.1",
"canvas": "6.0.0",
"canvas-action": "9.0.0",
"cartesian": "1.0.6",
"catenable-lists": "7.0.0",
"cbor-stream": "1.3.0",
"chameleon": "1.0.0",
"chameleon-halogen": "1.0.3",
"chameleon-react-basic": "1.1.0",
"chameleon-styled": "2.5.0",
"chameleon-transformers": "1.0.0",
"channel": "1.0.0",
"checked-exceptions": "3.1.1",
"choku": "1.0.1",
"classless": "0.1.1",
"classless-arbitrary": "0.1.1",
"classless-decode-json": "0.1.1",
"classless-encode-json": "0.1.3",
"classnames": "2.0.0",
"codec": "6.1.0",
"codec-argonaut": "10.0.0",
"codec-json": "2.0.0",
"colors": "7.0.1",
"concur-core": "0.5.0",
"concur-react": "0.5.0",
"concurrent-queues": "3.0.0",
"console": "6.1.0",
"const": "6.0.0",
"contravariant": "6.0.0",
"control": "6.0.0",
"convertable-options": "1.0.0",
"coroutines": "7.0.0",
"css": "6.0.0",
"css-frameworks": "1.0.1",
"csv-stream": "2.3.0",
"data-mvc": "0.0.2",
"datetime": "6.1.0",
"datetime-parsing": "0.2.0",
"debounce": "0.1.0",
"debug": "6.0.2",
"decimals": "7.1.0",
"default-values": "1.0.1",
"deku": "0.9.23",
"deno": "0.0.5",
"dissect": "1.0.0",
"distributive": "6.0.0",
"dom-filereader": "7.0.0",
"dom-indexed": "12.0.0",
"dom-simple": "0.4.0",
"dotenv": "4.0.3",
"droplet": "0.6.0",
"dts": "1.0.0",
"dual-numbers": "1.0.3",
"dynamic-buffer": "3.0.1",
"echarts-simple": "0.0.1",
"effect": "4.0.0",
"either": "6.1.0",
"elmish": "0.13.0",
"elmish-enzyme": "0.1.1",
"elmish-hooks": "0.10.3",
"elmish-html": "0.9.0",
"elmish-testing-library": "0.3.2",
"email-validate": "7.0.0",
"encoding": "0.0.9",
"enums": "6.0.1",
"env-names": "0.4.0",
"error": "2.0.0",
"eta-conversion": "0.3.2",
"exceptions": "6.1.0",
"exists": "6.0.0",
"exitcodes": "4.0.0",
"expect-inferred": "3.0.0",
"ezfetch": "1.0.0",
"fahrtwind": "2.0.0",
"fallback": "0.1.0",
"fast-vect": "1.2.0",
"fetch": "4.1.0",
"fetch-argonaut": "1.0.1",
"fetch-core": "5.1.0",
"fetch-yoga-json": "1.1.0",
"ffi-simple": "0.5.1",
"fft-js": "0.1.0",
"filterable": "5.0.0",
"fix-functor": "0.1.0",
"fixed-points": "7.0.0",
"fixed-precision": "5.0.0",
"flame": "1.3.0",
"float32": "2.0.0",
"fmt": "0.2.1",
"foldable-traversable": "6.0.0",
"foldable-traversable-extra": "0.0.6",
"foreign": "7.0.0",
"foreign-object": "4.1.0",
"foreign-readwrite": "3.4.0",
"forgetmenot": "0.1.0",
"fork": "6.0.0",
"form-urlencoded": "7.0.0",
"formatters": "7.0.0",
"framer-motion": "1.0.1",
"free": "7.1.0",
"freeap": "7.0.0",
"freer-free": "0.0.1",
"freet": "7.0.0",
"functions": "6.0.0",
"functor1": "3.0.0",
"functors": "5.0.0",
"fuzzy": "0.4.0",
"gen": "4.0.0",
"generate-values": "1.0.1",
"generic-router": "0.0.1",
"geojson": "0.0.5",
"geometria": "2.2.0",
"gojs": "0.1.1",
"grain": "3.0.0",
"grain-router": "3.0.0",
"grain-virtualized": "3.0.0",
"graphs": "8.1.0",
"group": "4.1.1",
"halogen": "7.0.0",
"halogen-bootstrap5": "5.3.2",
"halogen-canvas": "1.0.0",
"halogen-css": "10.0.0",
"halogen-echarts-simple": "0.0.4",
"halogen-formless": "4.0.3",
"halogen-helix": "1.0.1",
"halogen-hooks": "0.6.3",
"halogen-hooks-extra": "0.9.0",
"halogen-infinite-scroll": "1.1.0",
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"halogen-storybook": "2.0.0",
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"halogen-svg-elems": "8.0.0",
"halogen-typewriter": "1.0.4",
"halogen-vdom": "8.0.0",
"halogen-vdom-string-renderer": "0.5.0",
"halogen-xterm": "2.0.0",
"heckin": "2.0.1",
"heterogeneous": "0.6.0",
"homogeneous": "0.4.0",
"http-methods": "6.0.0",
"httpurple": "4.0.0",
"huffman": "0.4.0",
"humdrum": "0.0.1",
"hyrule": "2.3.8",
"identity": "6.0.0",
"identy": "4.0.1",
"indexed-db": "1.0.0",
"indexed-monad": "3.0.0",
"int64": "3.0.0",
"integers": "6.0.0",
"interpolate": "5.0.2",
"intersection-observer": "1.0.1",
"invariant": "6.0.0",
"jarilo": "1.0.1",
"jelly": "0.10.0",
"jelly-router": "0.3.0",
"jelly-signal": "0.4.0",
"jest": "1.0.0",
"js-abort-controller": "1.0.0",
"js-bigints": "2.2.1",
"js-date": "8.0.0",
"js-fetch": "0.2.1",
"js-fileio": "3.0.0",
"js-intl": "1.0.4",
"js-iterators": "0.1.1",
"js-maps": "0.1.2",
"js-promise": "1.0.0",
"js-promise-aff": "1.0.0",
"js-timers": "6.1.0",
"js-uri": "3.1.0",
"jsdom": "1.0.0",
"json": "1.1.0",
"json-codecs": "5.0.0",
"justifill": "0.5.0",
"jwt": "0.0.9",
"labeled-data": "0.2.0",
"language-cst-parser": "0.14.0",
"lazy": "6.0.0",
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"liminal": "1.0.1",
"linalg": "6.0.0",
"lists": "7.0.0",
"literals": "1.0.2",
"logging": "3.0.0",
"logging-journald": "0.4.0",
"lumi-components": "18.0.0",
"machines": "7.0.0",
"maps-eager": "0.5.0",
"marionette": "1.0.0",
"marionette-react-basic-hooks": "0.1.1",
"marked": "0.1.0",
"matrices": "5.0.1",
"matryoshka": "1.0.0",
"maybe": "6.0.0",
"media-types": "6.0.0",
"meowclient": "1.0.0",
"midi": "4.0.0",
"milkis": "9.0.0",
"minibench": "4.0.1",
"mmorph": "7.0.0",
"monad-control": "5.0.0",
"monad-logger": "1.3.1",
"monad-loops": "0.5.0",
"monad-unlift": "1.0.1",
"monoid-extras": "0.0.1",
"monoidal": "0.16.0",
"morello": "0.4.0",
"mote": "3.0.0",
"motsunabe": "2.0.0",
"mvc": "0.0.1",
"mysql": "6.0.1",
"n3": "0.1.0",
"nano-id": "1.1.0",
"nanoid": "0.1.0",
"naturals": "3.0.0",
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"nextui": "0.2.0",
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"node-child-process": "11.1.0",
"node-event-emitter": "3.0.0",
"node-execa": "5.0.0",
"node-fs": "9.2.0",
"node-glob-basic": "1.3.0",
"node-http": "9.1.0",
"node-http2": "1.1.1",
"node-human-signals": "1.0.0",
"node-net": "5.1.0",
"node-os": "5.1.0",
"node-path": "5.0.0",
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"node-stream-pipes": "2.1.6",
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"node-tls": "0.3.1",
"node-url": "7.0.1",
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"oak": "3.1.1",
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"rdf": "0.1.0",
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"refs": "6.0.0",
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"return": "0.2.0",
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"rito": "0.3.4",
"roman": "0.4.0",
"rough-notation": "1.0.2",
"routing": "11.0.0",
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"run": "5.0.0",
"safe-coerce": "2.0.0",
"safely": "4.0.1",
"school-of-music": "1.3.0",
"selection-foldable": "0.2.0",
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"semirings": "7.0.0",
"signal": "13.0.0",
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"simple-ulid": "3.0.0",
"sized-matrices": "1.0.0",
"sized-vectors": "5.0.2",
"slug": "3.1.0",
"small-ffi": "4.0.1",
"soundfonts": "4.1.0",
"sparse-matrices": "2.0.1",
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"spec": "8.1.0",
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"st": "6.2.0",
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"undefined": "2.0.0",
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"unfoldable": "6.0.0",
"unicode": "6.0.0",
"unique": "0.6.1",
"unlift": "1.0.1",
"unordered-collections": "3.1.0",
"unsafe-coerce": "6.0.0",
"unsafe-reference": "5.0.0",
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"untagged-union": "1.0.0",
"uri": "9.0.0",
"url-immutable": "1.0.0",
"uuid": "9.0.0",
"uuidv4": "1.0.0",
"validation": "6.0.0",
"variant": "8.0.0",
"variant-encodings": "2.0.0",
"vectorfield": "1.0.1",
"vectors": "2.1.0",
"versions": "7.0.0",
"visx": "0.0.2",
"web-clipboard": "6.0.0",
"web-cssom": "2.0.0",
"web-cssom-view": "0.1.0",
"web-dom": "6.0.0",
"web-dom-parser": "8.0.0",
"web-dom-xpath": "3.0.0",
"web-encoding": "3.0.0",
"web-events": "4.0.0",
"web-fetch": "4.0.1",
"web-file": "4.0.0",
"web-geometry": "0.1.0",
"web-html": "4.1.0",
"web-pointerevents": "2.0.0",
"web-proletarian": "1.0.0",
"web-promise": "3.2.0",
"web-resize-observer": "2.1.0",
"web-router": "1.0.0",
"web-socket": "4.0.0",
"web-storage": "5.0.0",
"web-streams": "4.0.0",
"web-touchevents": "4.0.0",
"web-uievents": "5.0.0",
"web-url": "2.0.0",
"web-workers": "1.1.0",
"web-xhr": "5.0.1",
"webextension-polyfill": "0.1.0",
"webgpu": "0.0.1",
"which": "2.0.0",
"xterm": "1.0.0",
"yoga-fetch": "1.0.1",
"yoga-json": "5.1.0",
"yoga-om": "0.1.0",
"yoga-postgres": "6.0.0",
"yoga-tree": "1.0.0",
"z3": "0.0.2",
"zipperarray": "2.0.0"
}
},
"extra_packages": {}
},
"packages": {
"arrays": {
"type": "registry",
"version": "7.3.0",
"integrity": "sha256-tmcklBlc/muUtUfr9RapdCPwnlQeB3aSrC4dK85gQlc=",
"dependencies": [
"bifunctors",
"control",
"foldable-traversable",
"functions",
"maybe",
"nonempty",
"partial",
"prelude",
"safe-coerce",
"st",
"tailrec",
"tuples",
"unfoldable",
"unsafe-coerce"
]
},
"bifunctors": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-/gZwC9YhNxZNQpnHa5BIYerCGM2jeX9ukZiEvYxm5Nw=",
"dependencies": [
"const",
"either",
"newtype",
"prelude",
"tuples"
]
},
"console": {
"type": "registry",
"version": "6.1.0",
"integrity": "sha256-CxmAzjgyuGDmt9FZW51VhV6rBPwR6o0YeKUzA9rSzcM=",
"dependencies": [
"effect",
"prelude"
]
},
"const": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-tNrxDW8D8H4jdHE2HiPzpLy08zkzJMmGHdRqt5BQuTc=",
"dependencies": [
"invariant",
"newtype",
"prelude"
]
},
"contravariant": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-TP+ooAp3vvmdjfQsQJSichF5B4BPDHp3wAJoWchip6c=",
"dependencies": [
"const",
"either",
"newtype",
"prelude",
"tuples"
]
},
"control": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-sH7Pg9E96JCPF9PIA6oQ8+BjTyO/BH1ZuE/bOcyj4Jk=",
"dependencies": [
"newtype",
"prelude"
]
},
"distributive": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-HTDdmEnzigMl+02SJB88j+gAXDx9VKsbvR4MJGDPbOQ=",
"dependencies": [
"identity",
"newtype",
"prelude",
"tuples",
"type-equality"
]
},
"effect": {
"type": "registry",
"version": "4.0.0",
"integrity": "sha256-eBtZu+HZcMa5HilvI6kaDyVX3ji8p0W9MGKy2K4T6+M=",
"dependencies": [
"prelude"
]
},
"either": {
"type": "registry",
"version": "6.1.0",
"integrity": "sha256-6hgTPisnMWVwQivOu2PKYcH8uqjEOOqDyaDQVUchTpY=",
"dependencies": [
"control",
"invariant",
"maybe",
"prelude"
]
},
"exists": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-A0JQHpTfo1dNOj9U5/Fd3xndlRSE0g2IQWOGor2yXn8=",
"dependencies": [
"unsafe-coerce"
]
},
"foldable-traversable": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-fLeqRYM4jUrZD5H4WqcwUgzU7XfYkzO4zhgtNc3jcWM=",
"dependencies": [
"bifunctors",
"const",
"control",
"either",
"functors",
"identity",
"maybe",
"newtype",
"orders",
"prelude",
"tuples"
]
},
"functions": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-adMyJNEnhGde2unHHAP79gPtlNjNqzgLB8arEOn9hLI=",
"dependencies": [
"prelude"
]
},
"functors": {
"type": "registry",
"version": "5.0.0",
"integrity": "sha256-zfPWWYisbD84MqwpJSZFlvM6v86McM68ob8p9s27ywU=",
"dependencies": [
"bifunctors",
"const",
"contravariant",
"control",
"distributive",
"either",
"invariant",
"maybe",
"newtype",
"prelude",
"profunctor",
"tuples",
"unsafe-coerce"
]
},
"identity": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-4wY0XZbAksjY6UAg99WkuKyJlQlWAfTi2ssadH0wVMY=",
"dependencies": [
"control",
"invariant",
"newtype",
"prelude"
]
},
"invariant": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-RGWWyYrz0Hs1KjPDA+87Kia67ZFBhfJ5lMGOMCEFoLo=",
"dependencies": [
"control",
"prelude"
]
},
"leibniz": {
"type": "registry",
"version": "5.0.0",
"integrity": "sha256-2tdNZoUjAU5cIdDqpx+r80z4spnx0bIRwYzpC3mDE9E=",
"dependencies": [
"prelude",
"unsafe-coerce"
]
},
"maybe": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-5cCIb0wPwbat2PRkQhUeZO0jcAmf8jCt2qE0wbC3v2Q=",
"dependencies": [
"control",
"invariant",
"newtype",
"prelude"
]
},
"newtype": {
"type": "registry",
"version": "5.0.0",
"integrity": "sha256-gdrQu8oGe9eZE6L3wOI8ql/igOg+zEGB5ITh2g+uttw=",
"dependencies": [
"prelude",
"safe-coerce"
]
},
"nonempty": {
"type": "registry",
"version": "7.0.0",
"integrity": "sha256-54ablJZUHGvvlTJzi3oXyPCuvY6zsrWJuH/dMJ/MFLs=",
"dependencies": [
"control",
"foldable-traversable",
"maybe",
"prelude",
"tuples",
"unfoldable"
]
},
"orders": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-nBA0g3/ai0euH8q9pSbGqk53W2q6agm/dECZTHcoink=",
"dependencies": [
"newtype",
"prelude"
]
},
"partial": {
"type": "registry",
"version": "4.0.0",
"integrity": "sha256-fwXerld6Xw1VkReh8yeQsdtLVrjfGiVuC5bA1Wyo/J4=",
"dependencies": []
},
"prelude": {
"type": "registry",
"version": "6.0.1",
"integrity": "sha256-o8p6SLYmVPqzXZhQFd2hGAWEwBoXl1swxLG/scpJ0V0=",
"dependencies": []
},
"profunctor": {
"type": "registry",
"version": "6.0.1",
"integrity": "sha256-E58hSYdJvF2Qjf9dnWLPlJKh2Z2fLfFLkQoYi16vsFk=",
"dependencies": [
"control",
"distributive",
"either",
"exists",
"invariant",
"newtype",
"prelude",
"tuples"
]
},
"refs": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-Vgwne7jIbD3ZMoLNNETLT8Litw6lIYo3MfYNdtYWj9s=",
"dependencies": [
"effect",
"prelude"
]
},
"safe-coerce": {
"type": "registry",
"version": "2.0.0",
"integrity": "sha256-a1ibQkiUcbODbLE/WAq7Ttbbh9ex+x33VCQ7GngKudU=",
"dependencies": [
"unsafe-coerce"
]
},
"st": {
"type": "registry",
"version": "6.2.0",
"integrity": "sha256-z9X0WsOUlPwNx9GlCC+YccCyz8MejC8Wb0C4+9fiBRY=",
"dependencies": [
"partial",
"prelude",
"tailrec",
"unsafe-coerce"
]
},
"tailrec": {
"type": "registry",
"version": "6.1.0",
"integrity": "sha256-Xx19ECVDRrDWpz9D2GxQHHV89vd61dnXxQm0IcYQHGk=",
"dependencies": [
"bifunctors",
"effect",
"either",
"identity",
"maybe",
"partial",
"prelude",
"refs"
]
},
"tuples": {
"type": "registry",
"version": "7.0.0",
"integrity": "sha256-1rXgTomes9105BjgXqIw0FL6Fz1lqqUTLWOumhWec1M=",
"dependencies": [
"control",
"invariant",
"prelude"
]
},
"type-equality": {
"type": "registry",
"version": "4.0.1",
"integrity": "sha256-Hs9D6Y71zFi/b+qu5NSbuadUQXe5iv5iWx0226vOHUw=",
"dependencies": []
},
"typelevel-prelude": {
"type": "registry",
"version": "7.0.0",
"integrity": "sha256-uFF2ph+vHcQpfPuPf2a3ukJDFmLhApmkpTMviHIWgJM=",
"dependencies": [
"prelude",
"type-equality"
]
},
"unfoldable": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-JtikvJdktRap7vr/K4ITlxUX1QexpnqBq0G/InLr6eg=",
"dependencies": [
"foldable-traversable",
"maybe",
"partial",
"prelude",
"tuples"
]
},
"unsafe-coerce": {
"type": "registry",
"version": "6.0.0",
"integrity": "sha256-IqIYW4Vkevn8sI+6aUwRGvd87tVL36BBeOr0cGAE7t0=",
"dependencies": []
}
}
}

23
spago.yaml Normal file
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package:
name: singletons
dependencies:
- arrays
- console
- effect
- exists
- maybe
- prelude
- typelevel-prelude
- leibniz
test:
main: Test.Main
dependencies: []
workspace:
packageSet:
registry: 60.6.0
extraPackages: {}
backend:
cmd: 'purs-backend-es'
args:
- 'build'

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src/Main.purs Normal file
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module Main where
import Prelude
import Effect (Effect)
import Effect.Console (log)
main :: Effect Unit
main = do
log "🍝"

85
src/Singletons.purs Normal file
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module Singletons where
import Control.Category (identity, (<<<))
import Data.Exists (Exists, mkExists, runExists)
import Data.Function (flip, (#))
import Data.Leibniz (type (~), runLeibniz, symm)
data Nat
= Zero
| Succ Nat
foreign import data PZero :: Nat
foreign import data PSucc :: Nat -> Nat
type POne = PSucc PZero
type PTwo = PSucc POne
type PThree = PSucc PTwo
data Prev p q = Prev (SNat q) (p ~ PSucc q)
data SNat p
= SZero (p ~ PZero)
| SSucc (Exists (Prev p))
-- Type -> Term
reflect :: forall @p. SNatOf p => Nat
reflect = reflect' (snat @p)
reflect' :: forall p. SNat p -> Nat
reflect' = case _ of
SZero _ -> Zero
SSucc p -> p # runExists \ (Prev s _) -> Succ (reflect' s)
-- Term -> Type
-- Why DOES this NOT work
-- reify :: forall r. (forall p. SNatOf p => r) -> Nat -> r
-- reify x n = runExists (withDNat x) (toSomeNat n)
-- Isomorphic to Nat
type SomeNat = Exists SNat
fromSomeNat :: SomeNat -> Nat
fromSomeNat = runExists reflect'
toSomeNat :: Nat -> SomeNat
toSomeNat Zero = mkExists (SZero identity)
toSomeNat (Succ n) = toSomeNat n # runExists \sn -> mkExists (SSucc (mkExists (Prev sn identity)))
-- Easy to apply Nat ops to SomeNat
ssucc :: SomeNat -> SomeNat
ssucc = toSomeNat <<< Succ <<< fromSomeNat
newtype DNat p = DNat (forall r. (SNatOf p => r) -> r)
captureDNat :: forall @p. SNatOf p => DNat p
captureDNat = DNat \r -> r
provideDNat :: forall p r. (SNatOf p => r) -> DNat p -> r
provideDNat = flip unDNat
unDNat :: forall p r. DNat p -> (SNatOf p => r) -> r
unDNat (DNat f) = f
dNat :: forall p. SNat p -> DNat p
dNat s = DNat (\x -> withDNat x s)
withDNat :: forall p r. (SNatOf p => r) -> SNat p -> r
withDNat x sn = case sn of
SZero w -> unDNat (runLeibniz (symm w) (captureDNat @PZero)) x
SSucc e -> e # runExists \ (Prev _ w) -> unDNat (runLeibniz (symm w) (dNat (runLeibniz w sn))) x
zero :: SNat PZero
zero = SZero identity
succ :: forall p. SNatOf p => SNat p -> SNat (PSucc p)
succ _ = snat @(PSucc p)
class SNatOf p where
snat :: SNat p
instance SNatOf PZero where
snat = SZero identity
instance SNatOf p => SNatOf (PSucc p) where
snat = SSucc (mkExists (Prev (snat @p) identity))

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module Test.Main where
import Prelude
import Effect (Effect)
import Effect.Class.Console (log)
main :: Effect Unit
main = do
log "🍕"
log "You should add some tests."