use NContext/SnocVect for scope name lists etc
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32f38238ef
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12 changed files with 165 additions and 134 deletions
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@ -41,7 +41,7 @@ reflTy =
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Eq0 (BVT 1) (BVT 0) (BVT 0)
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reflDef : IsQty q => Term q d n
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reflDef = ["A","x"] :\\ ["i"] :\\% BVT 0
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reflDef = [< "A","x"] :\\ [< "i"] :\\% BVT 0
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fstTy : Term Three d n
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@ -52,8 +52,8 @@ fstTy =
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fstDef : Term Three d n
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fstDef =
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(["A","B","p"] :\\
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E (CasePair Any (BV 0) (SN $ BVT 2) (SY ["x","y"] $ BVT 1)))
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([< "A","B","p"] :\\
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E (CasePair Any (BV 0) (SN $ BVT 2) (SY [< "x","y"] $ BVT 1)))
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sndTy : Term Three d n
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sndTy =
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@ -64,10 +64,10 @@ sndTy =
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sndDef : Term Three d n
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sndDef =
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(["A","B","p"] :\\
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([< "A","B","p"] :\\
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E (CasePair Any (BV 0)
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(SY ["p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
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(SY ["x","y"] $ BVT 0)))
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(SY [< "p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
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(SY [< "x","y"] $ BVT 0)))
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defGlobals : Definitions Three
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@ -270,18 +270,18 @@ tests = "typechecker" :- [
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"lambda" :- [
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note "linear & unrestricted identity",
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testTC "1 · (λ x ⇒ x) ⇐ A ⊸ A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr One (FT "A") (FT "A")),
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testTC "1 · (λ x ⇒ x) ⇐ A → A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr Any (FT "A") (FT "A")),
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note "(fail) zero binding used relevantly",
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testTCFail "1 · (λ x ⇒ x) ⇍ A ⇾ A" $
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check_ empty sone (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty sone ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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note "(but ok in overall erased context)",
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testTC "0 · (λ x ⇒ x) ⇐ A ⇾ A" $
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check_ empty szero (["x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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check_ empty szero ([< "x"] :\\ BVT 0) (Arr Zero (FT "A") (FT "A")),
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testTC "1 · (λ A x ⇒ refl A x) ⇐ ⋯ # (type of refl)" $
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check_ empty sone
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(["A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
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([< "A", "x"] :\\ E (F "refl" :@@ [BVT 1, BVT 0]))
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reflTy,
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testTC "1 · (λ A x ⇒ δ i ⇒ x) ⇐ ⋯ # (def. and type of refl)" $
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check_ empty sone reflDef reflTy
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@ -295,7 +295,7 @@ tests = "typechecker" :- [
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(Pair (BVT 0) (BVT 0)) (FT "A" `And` FT "A") [< Any],
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testTC "1 · (a, δ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
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check_ empty sone
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(Pair (FT "a") (["i"] :\\% FT "a"))
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(Pair (FT "a") ([< "i"] :\\% FT "a"))
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(Sig_ "x" (FT "A") $ Eq0 (FT "A") (BVT 0) (FT "a"))
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],
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@ -303,36 +303,36 @@ tests = "typechecker" :- [
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testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair One (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< One],
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testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Any],
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testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
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inferAsQ (ctx [< ("x", FT "A" `And` FT "A")]) szero
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(CasePair Any (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
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(FT "B") [< Zero],
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testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
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infer_ (ctx [< ("x", FT "A" `And` FT "A")]) sone
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(CasePair Zero (BV 0) (SN $ FT "B")
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(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
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(SY [< "l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
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testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
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inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) sone
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(CasePair Any (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1))
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(SY [< "l", "r"] $ BVT 1))
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(FT "A") [< Any],
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testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
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inferAsQ (ctx [< ("x", FT "A" `And` FT "B")]) szero
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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1))
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(SY [< "l", "r"] $ BVT 1))
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(FT "A") [< Zero],
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testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
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infer_ (ctx [< ("x", FT "A" `And` FT "B")]) sone
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(CasePair One (BV 0) (SN $ FT "A")
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(SY ["l", "r"] $ BVT 1)),
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(SY [< "l", "r"] $ BVT 1)),
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note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
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note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
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testTC "0 · ‹type of fst› ⇐ ★₂" $
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@ -347,9 +347,9 @@ tests = "typechecker" :- [
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check_ empty sone sndDef sndTy,
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testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
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inferAs empty szero
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(F "snd" :@@ [TYPE 0, ["x"] :\\ BVT 0])
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(F "snd" :@@ [TYPE 0, [< "x"] :\\ BVT 0])
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(Pi_ Any "A" (Sig_ "A" (TYPE 0) $ BVT 0) $
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(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
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(E $ F "fst" :@@ [TYPE 0, [< "x"] :\\ BVT 0, BVT 0]))
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],
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"enums" :- [
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@ -369,13 +369,13 @@ tests = "typechecker" :- [
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(Eq0 (FT "A") (FT "a") (FT "a")),
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testTC "0 · (λ p q ⇒ δ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ empty szero
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(["p","q"] :\\ ["i"] :\\% BVT 1)
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([< "p","q"] :\\ [< "i"] :\\% BVT 1)
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(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
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testTC "0 · (λ p q ⇒ δ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
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check_ empty szero
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(["p","q"] :\\ ["i"] :\\% BVT 0)
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([< "p","q"] :\\ [< "i"] :\\% BVT 0)
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(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
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Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0))
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@ -388,7 +388,7 @@ tests = "typechecker" :- [
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note " ⇐ (0·x y : A) → (1·xy : x ≡ y) → Eq [i ⇒ P (xy i)] (p x) (p y)",
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testTC "cong" $
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check_ empty sone
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(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
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([< "x", "y", "xy"] :\\ [< "i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
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(Pi_ Zero "x" (FT "A") $
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Pi_ Zero "y" (FT "A") $
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Pi_ One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $
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@ -401,7 +401,7 @@ tests = "typechecker" :- [
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note " ⇐ (1·eq : (1·x : A) → p x ≡ q x) → p ≡ q",
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testTC "funext" $
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check_ empty sone
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(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
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([< "eq"] :\\ [< "i"] :\\% [< "x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
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(Pi_ One "eq"
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(Pi_ One "x" (FT "A")
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(Eq0 (E $ F "P" :@ BVT 0)
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