module BruijnSpec (spec) where

import Bruijn (toDeBruijn)
import Parser (Expr (Abstraction, Application, Variable))
import Test.Hspec

spec :: Spec
spec = do
  describe "toDeBruijn" $ do

    -- Free variables
    it "leaves a lone free variable unchanged" $
      toDeBruijn (Variable "x") `shouldBe` Variable "x"
    it "leaves free variables in abstraction body unchanged" $
      toDeBruijn (Abstraction "x" (Variable "y"))
        `shouldBe` Abstraction "0" (Variable "y")

    -- Single abstraction
    it "converts bound variable in identity" $
      toDeBruijn (Abstraction "x" (Variable "x"))
        `shouldBe` Abstraction "0" (Variable "0")
    it "leaves free variable in abstraction body unchanged" $
      toDeBruijn (Abstraction "x" (Variable "z"))
        `shouldBe` Abstraction "0" (Variable "z")

    -- Nested abstractions
    it "inner binder resolves to depth 1" $
      toDeBruijn (Abstraction "x" (Abstraction "y" (Variable "y")))
        `shouldBe` Abstraction "0" (Abstraction "1" (Variable "1"))
    it "outer binder resolves to depth 0 from within nested scope" $
      toDeBruijn (Abstraction "x" (Abstraction "y" (Variable "x")))
        `shouldBe` Abstraction "0" (Abstraction "1" (Variable "0"))
    it "outermost of three binders resolves correctly" $
      toDeBruijn (Abstraction "x" (Abstraction "y" (Abstraction "z" (Variable "x"))))
        `shouldBe` Abstraction "0" (Abstraction "1" (Abstraction "2" (Variable "0")))

    -- Application
    it "converts self-application" $
      toDeBruijn (Abstraction "x" (Application (Variable "x") (Variable "x")))
        `shouldBe` Abstraction "0" (Application (Variable "0") (Variable "0"))
    it "converts independent scopes in application" $
      toDeBruijn (Application (Abstraction "x" (Variable "x")) (Abstraction "y" (Variable "y")))
        `shouldBe` Application (Abstraction "0" (Variable "0")) (Abstraction "0" (Variable "0"))

    -- Alpha equivalence
    it "alpha-equivalent terms produce identical output" $
      toDeBruijn (Abstraction "x" (Variable "x"))
        `shouldBe` toDeBruijn (Abstraction "y" (Variable "y"))