132 lines
3.8 KiB
Idris
132 lines
3.8 KiB
Idris
module Tests.Reduce
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import Quox.Syntax as Lib
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import Quox.Syntax.Qty.Three
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import Quox.Equal
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import TermImpls
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import TAP
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testWhnf : Eq b => Show b => (a -> (Subset b _)) -> String -> a -> b -> Test
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testWhnf whnf label from to = test "\{label} (whnf)" $
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let result = fst (whnf from) in
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if result == to
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then Right ()
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else with Prelude.(::)
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Left [("expected", to), ("received", result)]
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testNoStep : Eq a => Show a => (a -> (Subset a _)) -> String -> a -> Test
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testNoStep whnf label e = test "\{label} (no step)" $
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let result = fst (whnf e) in
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if result == e
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then Right ()
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else with Prelude.(::)
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Left [("reduced", result)]
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parameters {default empty defs : Definitions Three} {default 0 d, n : Nat}
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testWhnfT : String -> Term Three d n -> Term Three d n -> Test
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testWhnfT = testWhnf (whnfD defs)
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testWhnfE : String -> Elim Three d n -> Elim Three d n -> Test
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testWhnfE = testWhnf (whnfD defs)
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testNoStepE : String -> Elim Three d n -> Test
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testNoStepE = testNoStep (whnfD defs)
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testNoStepT : String -> Term Three d n -> Test
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testNoStepT = testNoStep (whnfD defs)
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tests = "whnf" :- [
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"head constructors" :- [
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testNoStepT "★₀" $ TYPE 0,
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testNoStepT "[A] ⊸ [B]" $
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Arr One (FT "A") (FT "B"),
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testNoStepT "(x: [A]) ⊸ [B [x]]" $
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Pi One "x" (FT "A") (TUsed $ E $ F "B" :@ BVT 0),
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testNoStepT "λx. [x]" $
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Lam "x" $ TUsed $ BVT 0,
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testNoStepT "[f [a]]" $
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E $ F "f" :@ FT "a"
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],
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"neutrals" :- [
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testNoStepE "x" {n = 1} $ BV 0,
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testNoStepE "a" $ F "a",
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testNoStepE "f [a]" $ F "f" :@ FT "a",
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testNoStepE "★₀ ∷ ★₁" $ TYPE 0 :# TYPE 1
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],
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"redexes" :- [
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testWhnfE "[a] ∷ [A]"
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(FT "a" :# FT "A")
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(F "a"),
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testWhnfT "[★₁ ∷ ★₃]"
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(E (TYPE 1 :# TYPE 3))
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(TYPE 1),
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testWhnfE "(λx. [x] ∷ [A] ⊸ [A]) [a]"
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((Lam "x" (TUsed $ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(F "a")
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],
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"definitions" :- [
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testWhnfE "a (transparent)"
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{defs = fromList [("a", mkDef Zero (TYPE 1) (TYPE 0))]}
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(F "a") (TYPE 0 :# TYPE 1)
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],
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"elim closure" :- [
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testWhnfE "x{}" {n = 1}
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(CloE (BV 0) id)
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(BV 0),
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testWhnfE "x{a/x}"
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(CloE (BV 0) (F "a" ::: id))
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(F "a"),
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testWhnfE "x{x/x,a/y}" {n = 1}
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(CloE (BV 0) (BV 0 ::: F "a" ::: id))
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(BV 0),
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testWhnfE "x{(y{a/y})/x}"
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(CloE (BV 0) ((CloE (BV 0) (F "a" ::: id)) ::: id))
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(F "a"),
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testWhnfE "(x y){f/x,a/y}"
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(CloE (BV 0 :@ BVT 1) (F "f" ::: F "a" ::: id))
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(F "f" :@ FT "a"),
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testWhnfE "([y] ∷ [x]){A/x}" {n = 1}
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(CloE (BVT 1 :# BVT 0) (F "A" ::: id))
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(BV 0),
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testWhnfE "([y] ∷ [x]){A/x,a/y}"
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(CloE (BVT 1 :# BVT 0) (F "A" ::: F "a" ::: id))
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(F "a")
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],
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"term closure" :- [
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testWhnfT "(λy. x){a/x}"
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(CloT (Lam "y" $ TUnused $ BVT 0) (F "a" ::: id))
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(Lam "y" $ TUnused $ FT "a"),
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testWhnfT "(λy. y){a/x}"
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(CloT (Lam "y" $ TUsed $ BVT 0) (F "a" ::: id))
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(Lam "y" $ TUsed $ BVT 0)
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],
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"looking inside […]" :- [
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testWhnfT "[(λx. x ∷ A ⊸ A) [a]]"
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(E $ (Lam "x" (TUsed $ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a")
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(FT "a")
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],
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"nested redex" :- [
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note "whnf only looks at top level redexes",
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testNoStepT "λy. [(λx. [x] ∷ [A] ⊸ [A]) [y]]" $
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Lam "y" $ TUsed $ E $
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(Lam "x" (TUsed $ BVT 0) :# Arr One (FT "A") (FT "A")) :@ BVT 0,
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testNoStepE "f [(λx. [x] ∷ [A] ⊸ [A]) [a]]" $
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F "a" :@
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E ((Lam "x" (TUsed $ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
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testNoStepT "λx. [y [x]]{x/x,a/y}" {n = 1} $
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Lam "x" $ TUsed $ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id),
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testNoStepE "f ([y [x]]{x/x,a/y})" {n = 1} $
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F "f" :@ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)
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]
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]
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