quox/tests/Tests/Reduce.idr

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