commit 08c9f02f31a5559eb61c755a7aa4ba159055413d Author: Anupam Jain Date: Mon Oct 21 01:41:56 2024 +0530 INIT diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..cc617f8 --- /dev/null +++ b/.gitignore @@ -0,0 +1,12 @@ +attic/ +bower_components/ +node_modules/ +.pulp-cache/ +output/ +output-es/ +generated-docs/ +.psc-package/ +.psc* +.purs* +.psa* +.spago diff --git a/README.md b/README.md new file mode 100644 index 0000000..5703cb0 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Some Singletons for PureScript + diff --git a/spago.lock b/spago.lock new file mode 100644 index 0000000..5d6e14f --- /dev/null +++ b/spago.lock @@ -0,0 +1,919 @@ +{ + "workspace": { + "packages": { + "singletons": { + "path": "./", + "core": { + "dependencies": [ + "arrays", + "console", + "effect", + "exists", + "leibniz", + "maybe", + "prelude", + "typelevel-prelude" + ], + "build_plan": [ + "arrays", + "bifunctors", + "console", + "const", + "contravariant", + "control", + 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b/src/Main.purs new file mode 100644 index 0000000..a4363b8 --- /dev/null +++ b/src/Main.purs @@ -0,0 +1,11 @@ +module Main where + +import Prelude + +import Effect (Effect) +import Effect.Console (log) + +main :: Effect Unit +main = do + log "🍝" + diff --git a/src/Singletons.purs b/src/Singletons.purs new file mode 100644 index 0000000..206fae0 --- /dev/null +++ b/src/Singletons.purs @@ -0,0 +1,85 @@ +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)) + diff --git a/test/Test/Main.purs b/test/Test/Main.purs new file mode 100644 index 0000000..e616930 --- /dev/null +++ b/test/Test/Main.purs @@ -0,0 +1,12 @@ +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." +