585 lines
23 KiB
Idris
585 lines
23 KiB
Idris
module Tests.Typechecker
|
||
|
||
import Quox.Syntax
|
||
import Quox.Typechecker as Lib
|
||
import public TypingImpls
|
||
import TAP
|
||
import Quox.EffExtra
|
||
import AstExtra
|
||
import PrettyExtra
|
||
|
||
|
||
%hide Prelude.App
|
||
%hide Pretty.App
|
||
|
||
|
||
data Error'
|
||
= TCError Typing.Error
|
||
| WrongInfer (BContext d) (BContext n) (Term d n) (Term d n)
|
||
| WrongQOut (QOutput n) (QOutput n)
|
||
|
||
export
|
||
ToInfo Error' where
|
||
toInfo (TCError e) = toInfo e
|
||
toInfo (WrongInfer dnames tnames good bad) =
|
||
[("type", "WrongInfer"),
|
||
("wanted", prettyStr $ prettyTerm dnames tnames good),
|
||
("got", prettyStr $ prettyTerm dnames tnames bad)]
|
||
toInfo (WrongQOut good bad) =
|
||
[("type", "WrongQOut"),
|
||
("wanted", show good),
|
||
("wanted", show bad)]
|
||
|
||
0 M : Type -> Type
|
||
M = Eff [Except Error', DefsReader]
|
||
|
||
inj : TC a -> M a
|
||
inj act = rethrow $ mapFst TCError $ runTC !(askAt DEFS) act
|
||
|
||
|
||
reflTy : Term d n
|
||
reflTy =
|
||
^PiY Zero "A" (^TYPE 0)
|
||
(^PiY One "x" (^BVT 0)
|
||
(^Eq0 (^BVT 1) (^BVT 0) (^BVT 0)))
|
||
|
||
reflDef : Term d n
|
||
reflDef = ^LamY "A" (^LamY "x" (^DLamY "i" (^BVT 0)))
|
||
|
||
|
||
fstTy : Term d n
|
||
fstTy =
|
||
^PiY Zero "A" (^TYPE 0)
|
||
(^PiY Zero "B" (^Arr Any (^BVT 0) (^TYPE 0))
|
||
(^Arr Any (^SigY "x" (^BVT 1) (E $ ^App (^BV 1) (^BVT 0))) (^BVT 1)))
|
||
|
||
fstDef : Term d n
|
||
fstDef =
|
||
^LamY "A" (^LamY "B" (^LamY "p"
|
||
(E $ ^CasePair Any (^BV 0) (SN $ ^BVT 2)
|
||
(SY [< "x", "y"] $ ^BVT 1))))
|
||
|
||
sndTy : Term d n
|
||
sndTy =
|
||
^PiY Zero "A" (^TYPE 0)
|
||
(^PiY Zero "B" (^Arr Any (^BVT 0) (^TYPE 0))
|
||
(^PiY Any "p" (^SigY "x" (^BVT 1) (E $ ^App (^BV 1) (^BVT 0)))
|
||
(E $ ^App (^BV 1)
|
||
(E $ ^App (^App (^App (^F "fst" 0) (^BVT 2)) (^BVT 1)) (^BVT 0)))))
|
||
|
||
sndDef : Term d n
|
||
sndDef =
|
||
-- λ A B p ⇒ caseω p return p' ⇒ B (fst A B p') of { (x, y) ⇒ y }
|
||
^LamY "A" (^LamY "B" (^LamY "p"
|
||
(E $ ^CasePair Any (^BV 0)
|
||
(SY [< "p"] $ E $
|
||
^App (^BV 2)
|
||
(E $ ^App (^App (^App (^F "fst" 0) (^BVT 3)) (^BVT 2)) (^BVT 0)))
|
||
(SY [< "x", "y"] $ ^BVT 0))))
|
||
|
||
nat : Term d n
|
||
nat = ^Nat
|
||
|
||
apps : Elim d n -> List (Term d n) -> Elim d n
|
||
apps = foldl (\f, s => ^App f s)
|
||
|
||
|
||
defGlobals : Definitions
|
||
defGlobals = fromList
|
||
[("A", ^mkPostulate gzero (^TYPE 0)),
|
||
("B", ^mkPostulate gzero (^TYPE 0)),
|
||
("C", ^mkPostulate gzero (^TYPE 1)),
|
||
("D", ^mkPostulate gzero (^TYPE 1)),
|
||
("P", ^mkPostulate gzero (^Arr Any (^FT "A" 0) (^TYPE 0))),
|
||
("a", ^mkPostulate gany (^FT "A" 0)),
|
||
("a'", ^mkPostulate gany (^FT "A" 0)),
|
||
("b", ^mkPostulate gany (^FT "B" 0)),
|
||
("c", ^mkPostulate gany (^FT "C" 0)),
|
||
("d", ^mkPostulate gany (^FT "D" 0)),
|
||
("f", ^mkPostulate gany (^Arr One (^FT "A" 0) (^FT "A" 0))),
|
||
("fω", ^mkPostulate gany (^Arr Any (^FT "A" 0) (^FT "A" 0))),
|
||
("g", ^mkPostulate gany (^Arr One (^FT "A" 0) (^FT "B" 0))),
|
||
("f2", ^mkPostulate gany
|
||
(^Arr One (^FT "A" 0) (^Arr One (^FT "A" 0) (^FT "B" 0)))),
|
||
("p", ^mkPostulate gany
|
||
(^PiY One "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))),
|
||
("q", ^mkPostulate gany
|
||
(^PiY One "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))),
|
||
("refl", ^mkDef gany reflTy reflDef),
|
||
("fst", ^mkDef gany fstTy fstDef),
|
||
("snd", ^mkDef gany sndTy sndDef)]
|
||
|
||
parameters (label : String) (act : Lazy (M ()))
|
||
{default defGlobals globals : Definitions}
|
||
testTC : Test
|
||
testTC = test label {e = Error', a = ()} $
|
||
extract $ runExcept $ runReaderAt DEFS globals act
|
||
|
||
testTCFail : Test
|
||
testTCFail = testThrows label (const True) $
|
||
(extract $ runExcept $ runReaderAt DEFS globals act) $> "()"
|
||
|
||
|
||
inferredTypeEq : TyContext d n -> (exp, got : Term d n) -> M ()
|
||
inferredTypeEq ctx exp got =
|
||
wrapErr (const $ WrongInfer ctx.dnames ctx.tnames exp got) $ inj $ lift $
|
||
equalType noLoc ctx exp got
|
||
|
||
qoutEq : (exp, got : QOutput n) -> M ()
|
||
qoutEq qout res = unless (qout == res) $ throw $ WrongQOut qout res
|
||
|
||
inferAs : TyContext d n -> (sg : SQty) -> Elim d n -> Term d n -> M ()
|
||
inferAs ctx@(MkTyContext {dctx, _}) sg e ty = do
|
||
case !(inj $ infer ctx sg e) of
|
||
Just res => inferredTypeEq ctx ty res.type
|
||
Nothing => pure ()
|
||
|
||
inferAsQ : TyContext d n -> (sg : SQty) ->
|
||
Elim d n -> Term d n -> QOutput n -> M ()
|
||
inferAsQ ctx@(MkTyContext {dctx, _}) sg e ty qout = do
|
||
case !(inj $ infer ctx sg e) of
|
||
Just res => do
|
||
inferredTypeEq ctx ty res.type
|
||
qoutEq qout res.qout
|
||
Nothing => pure ()
|
||
|
||
infer_ : TyContext d n -> (sg : SQty) -> Elim d n -> M ()
|
||
infer_ ctx sg e = ignore $ inj $ infer ctx sg e
|
||
|
||
checkQ : TyContext d n -> SQty ->
|
||
Term d n -> Term d n -> QOutput n -> M ()
|
||
checkQ ctx@(MkTyContext {dctx, _}) sg s ty qout = do
|
||
case !(inj $ check ctx sg s ty) of
|
||
Just res => qoutEq qout res
|
||
Nothing => pure ()
|
||
|
||
check_ : TyContext d n -> SQty -> Term d n -> Term d n -> M ()
|
||
check_ ctx sg s ty = ignore $ inj $ check ctx sg s ty
|
||
|
||
checkType_ : TyContext d n -> Term d n -> Maybe Universe -> M ()
|
||
checkType_ ctx s u = inj $ checkType ctx s u
|
||
|
||
|
||
export
|
||
tests : Test
|
||
tests = "typechecker" :- [
|
||
"universes" :- [
|
||
testTC "0 · ★₀ ⇐ ★₁ # by checkType" $
|
||
checkType_ empty (^TYPE 0) (Just 1),
|
||
testTC "0 · ★₀ ⇐ ★₁ # by check" $
|
||
check_ empty szero (^TYPE 0) (^TYPE 1),
|
||
testTC "0 · ★₀ ⇐ ★₂" $
|
||
checkType_ empty (^TYPE 0) (Just 2),
|
||
testTC "0 · ★₀ ⇐ ★_" $
|
||
checkType_ empty (^TYPE 0) Nothing,
|
||
testTCFail "0 · ★₁ ⇍ ★₀" $
|
||
checkType_ empty (^TYPE 1) (Just 0),
|
||
testTCFail "0 · ★₀ ⇍ ★₀" $
|
||
checkType_ empty (^TYPE 0) (Just 0),
|
||
testTC "0=1 ⊢ 0 · ★₁ ⇐ ★₀" $
|
||
checkType_ empty01 (^TYPE 1) (Just 0),
|
||
testTCFail "1 · ★₀ ⇍ ★₁ # by check" $
|
||
check_ empty sone (^TYPE 0) (^TYPE 1)
|
||
],
|
||
|
||
"function types" :- [
|
||
note "A, B : ★₀; C, D : ★₁; P : 0.A → ★₀",
|
||
testTC "0 · 1.A → B ⇐ ★₀" $
|
||
check_ empty szero (^Arr One (^FT "A" 0) (^FT "B" 0)) (^TYPE 0),
|
||
note "subtyping",
|
||
testTC "0 · 1.A → B ⇐ ★₁" $
|
||
check_ empty szero (^Arr One (^FT "A" 0) (^FT "B" 0)) (^TYPE 1),
|
||
testTC "0 · 1.C → D ⇐ ★₁" $
|
||
check_ empty szero (^Arr One (^FT "C" 0) (^FT "D" 0)) (^TYPE 1),
|
||
testTCFail "0 · 1.C → D ⇍ ★₀" $
|
||
check_ empty szero (^Arr One (^FT "C" 0) (^FT "D" 0)) (^TYPE 0),
|
||
testTC "0 · 1.(x : A) → P x ⇐ ★₀" $
|
||
check_ empty szero
|
||
(^PiY One "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))
|
||
(^TYPE 0),
|
||
testTCFail "0 · 1.A → P ⇍ ★₀" $
|
||
check_ empty szero (^Arr One (^FT "A" 0) (^FT "P" 0)) (^TYPE 0),
|
||
testTC "0=1 ⊢ 0 · 1.A → P ⇐ ★₀" $
|
||
check_ empty01 szero (^Arr One (^FT "A" 0) (^FT "P" 0)) (^TYPE 0)
|
||
],
|
||
|
||
"pair types" :- [
|
||
testTC "0 · A × A ⇐ ★₀" $
|
||
check_ empty szero (^And (^FT "A" 0) (^FT "A" 0)) (^TYPE 0),
|
||
testTCFail "0 · A × P ⇍ ★₀" $
|
||
check_ empty szero (^And (^FT "A" 0) (^FT "P" 0)) (^TYPE 0),
|
||
testTC "0 · (x : A) × P x ⇐ ★₀" $
|
||
check_ empty szero
|
||
(^SigY "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))
|
||
(^TYPE 0),
|
||
testTC "0 · (x : A) × P x ⇐ ★₁" $
|
||
check_ empty szero
|
||
(^SigY "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))
|
||
(^TYPE 1),
|
||
testTC "0 · (A : ★₀) × A ⇐ ★₁" $
|
||
check_ empty szero
|
||
(^SigY "A" (^TYPE 0) (^BVT 0))
|
||
(^TYPE 1),
|
||
testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
|
||
check_ empty szero
|
||
(^SigY "A" (^TYPE 0) (^BVT 0))
|
||
(^TYPE 0),
|
||
testTCFail "1 · A × A ⇍ ★₀" $
|
||
check_ empty sone
|
||
(^And (^FT "A" 0) (^FT "A" 0))
|
||
(^TYPE 0)
|
||
],
|
||
|
||
"enum types" :- [
|
||
testTC "0 · {} ⇐ ★₀" $ check_ empty szero (^enum []) (^TYPE 0),
|
||
testTC "0 · {} ⇐ ★₃" $ check_ empty szero (^enum []) (^TYPE 3),
|
||
testTC "0 · {a,b,c} ⇐ ★₀" $
|
||
check_ empty szero (^enum ["a", "b", "c"]) (^TYPE 0),
|
||
testTC "0 · {a,b,c} ⇐ ★₃" $
|
||
check_ empty szero (^enum ["a", "b", "c"]) (^TYPE 3),
|
||
testTCFail "1 · {} ⇍ ★₀" $ check_ empty sone (^enum []) (^TYPE 0),
|
||
testTC "0=1 ⊢ 1 · {} ⇐ ★₀" $ check_ empty01 sone (^enum []) (^TYPE 0)
|
||
],
|
||
|
||
"free vars" :- [
|
||
note "A : ★₀",
|
||
testTC "0 · A ⇒ ★₀" $
|
||
inferAs empty szero (^F "A" 0) (^TYPE 0),
|
||
testTC "0 · [A] ⇐ ★₀" $
|
||
check_ empty szero (^FT "A" 0) (^TYPE 0),
|
||
note "subtyping",
|
||
testTC "0 · [A] ⇐ ★₁" $
|
||
check_ empty szero (^FT "A" 0) (^TYPE 1),
|
||
note "(fail) runtime-relevant type",
|
||
testTCFail "1 · A ⇏ ★₀" $
|
||
infer_ empty sone (^F "A" 0),
|
||
testTC "1 . f ⇒ 1.A → A" $
|
||
inferAs empty sone (^F "f" 0) (^Arr One (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 . f ⇐ 1.A → A" $
|
||
check_ empty sone (^FT "f" 0) (^Arr One (^FT "A" 0) (^FT "A" 0)),
|
||
testTCFail "1 . f ⇍ 0.A → A" $
|
||
check_ empty sone (^FT "f" 0) (^Arr Zero (^FT "A" 0) (^FT "A" 0)),
|
||
testTCFail "1 . f ⇍ ω.A → A" $
|
||
check_ empty sone (^FT "f" 0) (^Arr Any (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 . (λ x ⇒ f x) ⇐ 1.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "f" 0) (^BVT 0)))
|
||
(^Arr One (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 . (λ x ⇒ f x) ⇐ ω.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "f" 0) (^BVT 0)))
|
||
(^Arr Any (^FT "A" 0) (^FT "A" 0)),
|
||
testTCFail "1 . (λ x ⇒ f x) ⇍ 0.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "f" 0) (^BVT 0)))
|
||
(^Arr Zero (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 . fω ⇒ ω.A → A" $
|
||
inferAs empty sone (^F "fω" 0) (^Arr Any (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 . (λ x ⇒ fω x) ⇐ ω.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "fω" 0) (^BVT 0)))
|
||
(^Arr Any (^FT "A" 0) (^FT "A" 0)),
|
||
testTCFail "1 . (λ x ⇒ fω x) ⇍ 0.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "fω" 0) (^BVT 0)))
|
||
(^Arr Zero (^FT "A" 0) (^FT "A" 0)),
|
||
testTCFail "1 . (λ x ⇒ fω x) ⇍ 1.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (E $ ^App (^F "fω" 0) (^BVT 0)))
|
||
(^Arr One (^FT "A" 0) (^FT "A" 0)),
|
||
note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ δ _ ⇒ x)",
|
||
testTC "1 · refl ⇒ ⋯" $ inferAs empty sone (^F "refl" 0) reflTy,
|
||
testTC "1 · [refl] ⇐ ⋯" $ check_ empty sone (^FT "refl" 0) reflTy
|
||
],
|
||
|
||
"bound vars" :- [
|
||
testTC "x : A ⊢ 1 · x ⇒ A ⊳ 1·x" $
|
||
inferAsQ (ctx [< ("x", ^FT "A" 0)]) sone
|
||
(^BV 0) (^FT "A" 0) [< One],
|
||
testTC "x : A ⊢ 1 · x ⇐ A ⊳ 1·x" $
|
||
checkQ (ctx [< ("x", ^FT "A" 0)]) sone (^BVT 0) (^FT "A" 0) [< One],
|
||
note "f2 : 1.A → 1.A → B",
|
||
testTC "x : A ⊢ 1 · f2 x x ⇒ B ⊳ ω·x" $
|
||
inferAsQ (ctx [< ("x", ^FT "A" 0)]) sone
|
||
(^App (^App (^F "f2" 0) (^BVT 0)) (^BVT 0)) (^FT "B" 0) [< Any]
|
||
],
|
||
|
||
"lambda" :- [
|
||
note "linear & unrestricted identity",
|
||
testTC "1 · (λ x ⇒ x) ⇐ A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (^BVT 0))
|
||
(^Arr One (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 · (λ x ⇒ x) ⇐ ω.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (^BVT 0))
|
||
(^Arr Any (^FT "A" 0) (^FT "A" 0)),
|
||
note "(fail) zero binding used relevantly",
|
||
testTCFail "1 · (λ x ⇒ x) ⇍ 0.A → A" $
|
||
check_ empty sone
|
||
(^LamY "x" (^BVT 0))
|
||
(^Arr Zero (^FT "A" 0) (^FT "A" 0)),
|
||
note "(but ok in overall erased context)",
|
||
testTC "0 · (λ x ⇒ x) ⇐ A ⇾ A" $
|
||
check_ empty szero
|
||
(^LamY "x" (^BVT 0))
|
||
(^Arr Zero (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯ # (type of refl)" $
|
||
check_ empty sone
|
||
(^LamY "A" (^LamY "x"
|
||
(E $ ^App (^App (^F "refl" 0) (^BVT 1)) (^BVT 0))))
|
||
reflTy,
|
||
testTC "1 · (λ A x ⇒ δ i ⇒ x) ⇐ ⋯ # (def. and type of refl)" $
|
||
check_ empty sone reflDef reflTy
|
||
],
|
||
|
||
"pairs" :- [
|
||
testTC "1 · (a, a) ⇐ A × A" $
|
||
check_ empty sone
|
||
(^Pair (^FT "a" 0) (^FT "a" 0)) (^And (^FT "A" 0) (^FT "A" 0)),
|
||
testTC "x : A ⊢ 1 · (x, x) ⇐ A × A ⊳ ω·x" $
|
||
checkQ (ctx [< ("x", ^FT "A" 0)]) sone
|
||
(^Pair (^BVT 0) (^BVT 0)) (^And (^FT "A" 0) (^FT "A" 0)) [< Any],
|
||
testTC "1 · (a, δ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
|
||
check_ empty sone
|
||
(^Pair (^FT "a" 0) (^DLamN (^FT "a" 0)))
|
||
(^SigY "x" (^FT "A" 0) (^Eq0 (^FT "A" 0) (^BVT 0) (^FT "a" 0)))
|
||
],
|
||
|
||
"unpairing" :- [
|
||
testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
|
||
inferAsQ (ctx [< ("x", ^And (^FT "A" 0) (^FT "A" 0))]) sone
|
||
(^CasePair One (^BV 0) (SN $ ^FT "B" 0)
|
||
(SY [< "l", "r"] $ E $ ^App (^App (^F "f2" 0) (^BVT 1)) (^BVT 0)))
|
||
(^FT "B" 0) [< One],
|
||
testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
|
||
inferAsQ (ctx [< ("x", ^And (^FT "A" 0) (^FT "A" 0))]) sone
|
||
(^CasePair Any (^BV 0) (SN $ ^FT "B" 0)
|
||
(SY [< "l", "r"] $ E $ ^App (^App (^F "f2" 0) (^BVT 1)) (^BVT 0)))
|
||
(^FT "B" 0) [< Any],
|
||
testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
|
||
inferAsQ (ctx [< ("x", ^And (^FT "A" 0) (^FT "A" 0))]) szero
|
||
(^CasePair Any (^BV 0) (SN $ ^FT "B" 0)
|
||
(SY [< "l", "r"] $ E $ ^App (^App (^F "f2" 0) (^BVT 1)) (^BVT 0)))
|
||
(^FT "B" 0) [< Zero],
|
||
testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
|
||
infer_ (ctx [< ("x", ^And (^FT "A" 0) (^FT "A" 0))]) sone
|
||
(^CasePair Zero (^BV 0) (SN $ ^FT "B" 0)
|
||
(SY [< "l", "r"] $ E $ ^App (^App (^F "f2" 0) (^BVT 1)) (^BVT 0))),
|
||
testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
|
||
inferAsQ (ctx [< ("x", ^And (^FT "A" 0) (^FT "B" 0))]) sone
|
||
(^CasePair Any (^BV 0) (SN $ ^FT "A" 0)
|
||
(SY [< "l", "r"] $ ^BVT 1))
|
||
(^FT "A" 0) [< Any],
|
||
testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
|
||
inferAsQ (ctx [< ("x", ^And (^FT "A" 0) (^FT "B" 0))]) szero
|
||
(^CasePair One (^BV 0) (SN $ ^FT "A" 0)
|
||
(SY [< "l", "r"] $ ^BVT 1))
|
||
(^FT "A" 0) [< Zero],
|
||
testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
|
||
infer_ (ctx [< ("x", ^And (^FT "A" 0) (^FT "B" 0))]) sone
|
||
(^CasePair One (^BV 0) (SN $ ^FT "A" 0)
|
||
(SY [< "l", "r"] $ ^BVT 1)),
|
||
note "fst : 0.(A : ★₀) → 0.(B : ω.A → ★₀) → ω.((x : A) × B x) → A",
|
||
note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
|
||
testTC "0 · ‹type of fst› ⇐ ★₁" $
|
||
check_ empty szero fstTy (^TYPE 1),
|
||
testTC "1 · ‹def of fst› ⇐ ‹type of fst›" $
|
||
check_ empty sone fstDef fstTy,
|
||
note "snd : 0.(A : ★₀) → 0.(B : A ↠ ★₀) → ω.(p : (x : A) × B x) → B (fst A B p)",
|
||
note " ≔ (λ A B p ⇒ caseω p return p ⇒ B (fst A B p) of (x, y) ⇒ y)",
|
||
testTC "0 · ‹type of snd› ⇐ ★₁" $
|
||
check_ empty szero sndTy (^TYPE 1),
|
||
testTC "1 · ‹def of snd› ⇐ ‹type of snd›" $
|
||
check_ empty sone sndDef sndTy,
|
||
testTC "0 · snd A P ⇒ ω.(p : (x : A) × P x) → P (fst A P p)" $
|
||
inferAs empty szero
|
||
(^App (^App (^F "snd" 0) (^FT "A" 0)) (^FT "P" 0))
|
||
(^PiY Any "p" (^SigY "x" (^FT "A" 0) (E $ ^App (^F "P" 0) (^BVT 0)))
|
||
(E $ ^App (^F "P" 0)
|
||
(E $ apps (^F "fst" 0) [^FT "A" 0, ^FT "P" 0, ^BVT 0]))),
|
||
testTC "1 · fst A (λ _ ⇒ B) (a, b) ⇒ A" $
|
||
inferAs empty sone
|
||
(apps (^F "fst" 0)
|
||
[^FT "A" 0, ^LamN (^FT "B" 0), ^Pair (^FT "a" 0) (^FT "b" 0)])
|
||
(^FT "A" 0),
|
||
testTC "1 · fst¹ A (λ _ ⇒ B) (a, b) ⇒ A" $
|
||
inferAs empty sone
|
||
(apps (^F "fst" 1)
|
||
[^FT "A" 0, ^LamN (^FT "B" 0), ^Pair (^FT "a" 0) (^FT "b" 0)])
|
||
(^FT "A" 0),
|
||
testTCFail "1 · fst ★⁰ (λ _ ⇒ ★⁰) (A, B) ⇏" $
|
||
infer_ empty sone
|
||
(apps (^F "fst" 0)
|
||
[^TYPE 0, ^LamN (^TYPE 0), ^Pair (^FT "A" 0) (^FT "B" 0)]),
|
||
testTC "0 · fst¹ ★⁰ (λ _ ⇒ ★⁰) (A, B) ⇒ ★⁰" $
|
||
inferAs empty szero
|
||
(apps (^F "fst" 1)
|
||
[^TYPE 0, ^LamN (^TYPE 0), ^Pair (^FT "A" 0) (^FT "B" 0)])
|
||
(^TYPE 0)
|
||
],
|
||
|
||
"enums" :- [
|
||
testTC "1 · 'a ⇐ {a}" $
|
||
check_ empty sone (^Tag "a") (^enum ["a"]),
|
||
testTC "1 · 'a ⇐ {a, b, c}" $
|
||
check_ empty sone (^Tag "a") (^enum ["a", "b", "c"]),
|
||
testTCFail "1 · 'a ⇍ {b, c}" $
|
||
check_ empty sone (^Tag "a") (^enum ["b", "c"]),
|
||
testTC "0=1 ⊢ 1 · 'a ⇐ {b, c}" $
|
||
check_ empty01 sone (^Tag "a") (^enum ["b", "c"])
|
||
],
|
||
|
||
"enum matching" :- [
|
||
testTC "ω.x : {tt} ⊢ 1 · case1 x return {tt} of { 'tt ⇒ 'tt } ⇒ {tt}" $
|
||
inferAs (ctx [< ("x", ^enum ["tt"])]) sone
|
||
(^CaseEnum One (^BV 0) (SN (^enum ["tt"]))
|
||
(singleton "tt" (^Tag "tt")))
|
||
(^enum ["tt"]),
|
||
testTCFail "ω.x : {tt} ⊢ 1 · case1 x return {tt} of { 'ff ⇒ 'tt } ⇏" $
|
||
infer_ (ctx [< ("x", ^enum ["tt"])]) sone
|
||
(^CaseEnum One (^BV 0) (SN (^enum ["tt"]))
|
||
(singleton "ff" (^Tag "tt")))
|
||
],
|
||
|
||
"equality types" :- [
|
||
testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ Type" $
|
||
checkType_ empty (^Eq0 (^TYPE 0) nat nat) Nothing,
|
||
testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ ★₁" $
|
||
check_ empty szero (^Eq0 (^TYPE 0) nat nat) (^TYPE 1),
|
||
testTCFail "1 · ℕ ≡ ℕ : ★₀ ⇍ ★₁" $
|
||
check_ empty sone (^Eq0 (^TYPE 0) nat nat) (^TYPE 1),
|
||
testTC "0 · ℕ ≡ ℕ : ★₀ ⇐ ★₂" $
|
||
check_ empty szero (^Eq0 (^TYPE 0) nat nat) (^TYPE 2),
|
||
testTC "0 · ℕ ≡ ℕ : ★₁ ⇐ ★₂" $
|
||
check_ empty szero (^Eq0 (^TYPE 1) nat nat) (^TYPE 2),
|
||
testTCFail "0 · ℕ ≡ ℕ : ★₁ ⇍ ★₁" $
|
||
check_ empty szero (^Eq0 (^TYPE 1) nat nat) (^TYPE 1),
|
||
testTCFail "0 ≡ 'beep : {beep} ⇍ Type" $
|
||
checkType_ empty
|
||
(^Eq0 (^enum ["beep"]) (^Zero) (^Tag "beep"))
|
||
Nothing,
|
||
testTC "ab : A ≡ B : ★₀, x : A, y : B ⊢ 0 · Eq [i ⇒ ab i] x y ⇐ ★₀" $
|
||
check_ (ctx [< ("ab", ^Eq0 (^TYPE 0) (^FT "A" 0) (^FT "B" 0)),
|
||
("x", ^FT "A" 0), ("y", ^FT "B" 0)]) szero
|
||
(^EqY "i" (E $ ^DApp (^BV 2) (^BV 0)) (^BVT 1) (^BVT 0))
|
||
(^TYPE 0),
|
||
testTCFail "ab : A ≡ B : ★₀, x : A, y : B ⊢ Eq [i ⇒ ab i] y x ⇍ Type" $
|
||
check_ (ctx [< ("ab", ^Eq0 (^TYPE 0) (^FT "A" 0) (^FT "B" 0)),
|
||
("x", ^FT "A" 0), ("y", ^FT "B" 0)]) szero
|
||
(^EqY "i" (E $ ^DApp (^BV 2) (^BV 0)) (^BVT 0) (^BVT 1))
|
||
(^TYPE 0)
|
||
],
|
||
|
||
"equalities" :- [
|
||
testTC "1 · (δ i ⇒ a) ⇐ a ≡ a" $
|
||
check_ empty sone (^DLamN (^FT "a" 0))
|
||
(^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0)),
|
||
testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q # uip" $
|
||
check_ empty szero
|
||
(^LamY "p" (^LamY "q" (^DLamN (^BVT 1))))
|
||
(^PiY Any "p" (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^PiY Any "q" (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^Eq0 (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^BVT 1) (^BVT 0)))),
|
||
testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q # uip(2)" $
|
||
check_ empty szero
|
||
(^LamY "p" (^LamY "q" (^DLamN (^BVT 0))))
|
||
(^PiY Any "p" (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^PiY Any "q" (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^Eq0 (^Eq0 (^FT "A" 0) (^FT "a" 0) (^FT "a" 0))
|
||
(^BVT 1) (^BVT 0))))
|
||
],
|
||
|
||
"natural numbers" :- [
|
||
testTC "0 · ℕ ⇐ ★₀" $ check_ empty szero nat (^TYPE 0),
|
||
testTC "0 · ℕ ⇐ ★₇" $ check_ empty szero nat (^TYPE 7),
|
||
testTCFail "1 · ℕ ⇍ ★₀" $ check_ empty sone nat (^TYPE 0),
|
||
testTC "1 · zero ⇐ ℕ" $ check_ empty sone (^Zero) nat,
|
||
testTCFail "1 · zero ⇍ ℕ×ℕ" $ check_ empty sone (^Zero) (^And nat nat),
|
||
testTC "ω·n : ℕ ⊢ 1 · succ n ⇐ ℕ" $
|
||
check_ (ctx [< ("n", nat)]) sone (^Succ (^BVT 0)) nat,
|
||
testTC "1 · λ n ⇒ succ n ⇐ 1.ℕ → ℕ" $
|
||
check_ empty sone
|
||
(^LamY "n" (^Succ (^BVT 0)))
|
||
(^Arr One nat nat)
|
||
],
|
||
|
||
"natural elim" :- [
|
||
note "1 · λ n ⇒ case1 n return ℕ of { zero ⇒ 0; succ n ⇒ n }",
|
||
note " ⇐ 1.ℕ → ℕ",
|
||
testTC "pred" $
|
||
check_ empty sone
|
||
(^LamY "n" (E $
|
||
^CaseNat One Zero (^BV 0) (SN nat)
|
||
(^Zero) (SY [< "n", ^BN Unused] $ ^BVT 1)))
|
||
(^Arr One nat nat),
|
||
note "1 · λ m n ⇒ case1 m return ℕ of { zero ⇒ n; succ _, 1.p ⇒ succ p }",
|
||
note " ⇐ 1.ℕ → 1.ℕ → 1.ℕ",
|
||
testTC "plus" $
|
||
check_ empty sone
|
||
(^LamY "m" (^LamY "n" (E $
|
||
^CaseNat One One (^BV 1) (SN nat)
|
||
(^BVT 0)
|
||
(SY [< ^BN Unused, "p"] $ ^Succ (^BVT 0)))))
|
||
(^Arr One nat (^Arr One nat nat))
|
||
],
|
||
|
||
"box types" :- [
|
||
testTC "0 · [0.ℕ] ⇐ ★₀" $
|
||
check_ empty szero (^BOX Zero nat) (^TYPE 0),
|
||
testTC "0 · [0.★₀] ⇐ ★₁" $
|
||
check_ empty szero (^BOX Zero (^TYPE 0)) (^TYPE 1),
|
||
testTCFail "0 · [0.★₀] ⇍ ★₀" $
|
||
check_ empty szero (^BOX Zero (^TYPE 0)) (^TYPE 0)
|
||
],
|
||
|
||
todo "box values",
|
||
todo "box elim",
|
||
|
||
"type-case" :- [
|
||
testTC "0 · type-case ℕ ∷ ★₀ return ★₀ of { _ ⇒ ℕ } ⇒ ★₀" $
|
||
inferAs empty szero
|
||
(^TypeCase (^Ann nat (^TYPE 0)) (^TYPE 0) empty nat)
|
||
(^TYPE 0)
|
||
],
|
||
|
||
todo "add the examples dir to the tests"
|
||
]
|
||
|
||
{-
|
||
"misc" :- [
|
||
note "0·A : Type, 0·P : A → Type, ω·p : (1·x : A) → P x",
|
||
note "⊢",
|
||
note "1 · λ x y xy ⇒ δ i ⇒ p (xy i)",
|
||
note " ⇐ (0·x y : A) → (1·xy : x ≡ y) → Eq [i ⇒ P (xy i)] (p x) (p y)",
|
||
testTC "cong" $
|
||
check_ empty sone
|
||
([< "x", "y", "xy"] :\\ [< "i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||
(PiY Zero "x" (FT "A") $
|
||
PiY Zero "y" (FT "A") $
|
||
PiY One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $
|
||
EqY "i" (E $ F "P" :@ E (BV 0 :% BV 0))
|
||
(E $ F "p" :@ BVT 2) (E $ F "p" :@ BVT 1)),
|
||
note "0·A : Type, 0·P : ω·A → Type,",
|
||
note "ω·p q : (1·x : A) → P x",
|
||
note "⊢",
|
||
note "1 · λ eq ⇒ δ i ⇒ λ x ⇒ eq x i",
|
||
note " ⇐ (1·eq : (1·x : A) → p x ≡ q x) → p ≡ q",
|
||
testTC "funext" $
|
||
check_ empty sone
|
||
([< "eq"] :\\ [< "i"] :\\% [< "x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||
(PiY One "eq"
|
||
(PiY One "x" (FT "A")
|
||
(Eq0 (E $ F "P" :@ BVT 0)
|
||
(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)))
|
||
(Eq0 (PiY Any "x" (FT "A") $ E $ F "P" :@ BVT 0) (FT "p") (FT "q"))),
|
||
todo "absurd (when coerce is in)"
|
||
-- absurd : (`true ≡ `false : {true, false}) ⇾ (0·A : ★₀) → A ≔
|
||
-- λ e ⇒
|
||
-- case coerce [i ⇒ case e @i return ★₀ of {`true ⇒ {tt}; `false ⇒ {}}]
|
||
-- @0 @1 `tt
|
||
-- return A
|
||
-- of { }
|
||
]
|
||
-}
|