52 lines
2.1 KiB
Haskell
52 lines
2.1 KiB
Haskell
module EvaluationSpec (spec) where
|
|
|
|
import Evaluation (beta, subst)
|
|
import Parser (Expr (Abstraction, Application, Variable))
|
|
import Test.Hspec
|
|
|
|
spec :: Spec
|
|
spec = do
|
|
describe "subst" $ do
|
|
it "cannot substitute mismatched variables" $
|
|
subst (Variable "x") "y" (Variable "z") `shouldBe` Variable "x"
|
|
it "can substitute matched variables" $
|
|
subst (Variable "x") "x" (Variable "z") `shouldBe` Variable "z"
|
|
it "can substitute nested variables" $
|
|
subst absWithZ "z" absI `shouldBe` absWithZMaker absI
|
|
describe "beta reduction" $ do
|
|
-- Normal forms (no redex)
|
|
it "returns Nothing for a bare variable" $
|
|
beta (Variable "x") `shouldBe` Nothing
|
|
it "returns Nothing for a bare abstraction" $
|
|
beta absI `shouldBe` Nothing
|
|
it "returns Nothing when application has no lambda on left" $
|
|
beta (Application (Variable "x") (Variable "y")) `shouldBe` Nothing
|
|
|
|
-- Basic reductions
|
|
it "reduces identity: (λi. i) y → y" $
|
|
beta (Application absI (Variable "y"))
|
|
`shouldBe` Just (Variable "y")
|
|
it "reduces constant function: (λx. z) y → z" $
|
|
beta (Application (Abstraction "x" (Variable "z")) (Variable "y"))
|
|
`shouldBe` Just (Variable "z")
|
|
|
|
-- Self-application
|
|
it "(λx. x x)(λi. i) → (λi. i)(λi. i)" $
|
|
beta (Application selfApp absI)
|
|
`shouldBe` Just (Application absI absI)
|
|
it "(λi. i)(λi. i) → (λi. i)" $
|
|
beta (Application absI absI)
|
|
`shouldBe` Just absI
|
|
|
|
-- Redex not at top level
|
|
it "reduces redex in function position: ((λi. i) y) z → y z" $
|
|
beta (Application (Application absI (Variable "y")) (Variable "z"))
|
|
`shouldBe` Just (Application (Variable "y") (Variable "z"))
|
|
it "reduces redex inside lambda body: λz. (λi. i) y → λz. y" $
|
|
beta (Abstraction "z" (Application absI (Variable "y")))
|
|
`shouldBe` Just (Abstraction "z" (Variable "y"))
|
|
where
|
|
absWithZMaker z = Abstraction "x" (Application z (Variable "x"))
|
|
absWithZ = absWithZMaker (Variable "z")
|
|
absI = Abstraction "i" (Variable "i")
|
|
selfApp = Abstraction "x" (Application (Variable "x") (Variable "x"))
|