nicer constructors for ASTs
This commit is contained in:
parent
3d9b730803
commit
302de6266e
3 changed files with 98 additions and 83 deletions
|
|
@ -36,8 +36,8 @@ inj act = do
|
|||
|
||||
reflTy : IsQty q => Term q d n
|
||||
reflTy =
|
||||
Pi zero (TYPE 0) $ S ["A"] $ Y $
|
||||
Pi one (BVT 0) $ S ["x"] $ Y $
|
||||
Pi_ zero "A" (TYPE 0) $
|
||||
Pi_ one "x" (BVT 0) $
|
||||
Eq0 (BVT 1) (BVT 0) (BVT 0)
|
||||
|
||||
reflDef : IsQty q => Term q d n
|
||||
|
|
@ -46,30 +46,28 @@ reflDef = ["A","x"] :\\ ["i"] :\\% BVT 0
|
|||
|
||||
fstTy : Term Three d n
|
||||
fstTy =
|
||||
(Pi Zero (TYPE 1) $ S ["A"] $ Y $
|
||||
Pi Zero (Arr Any (BVT 0) (TYPE 1)) $ S ["B"] $ Y $
|
||||
Arr Any (Sig (BVT 1) $ S ["x"] $ Y $ E $ BV 1 :@ BVT 0)
|
||||
(BVT 1))
|
||||
(Pi_ Zero "A" (TYPE 1) $
|
||||
Pi_ Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
|
||||
Arr Any (Sig_ "x" (BVT 1) $ E $ BV 1 :@ BVT 0) (BVT 1))
|
||||
|
||||
fstDef : Term Three d n
|
||||
fstDef =
|
||||
(["A","B","p"] :\\
|
||||
E (CasePair Any (BV 0) (S ["_"] $ N $ BVT 2)
|
||||
(S ["x","y"] $ Y $ BVT 1)))
|
||||
E (CasePair Any (BV 0) (SN $ BVT 2) (SY ["x","y"] $ BVT 1)))
|
||||
|
||||
sndTy : Term Three d n
|
||||
sndTy =
|
||||
(Pi Zero (TYPE 1) $ S ["A"] $ Y $
|
||||
Pi Zero (Arr Any (BVT 0) (TYPE 1)) $ S ["B"] $ Y $
|
||||
Pi Any (Sig (BVT 1) $ S ["x"] $ Y $ E $ BV 1 :@ BVT 0) $ S ["p"] $ Y $
|
||||
(Pi_ Zero "A" (TYPE 1) $
|
||||
Pi_ Zero "B" (Arr Any (BVT 0) (TYPE 1)) $
|
||||
Pi_ Any "p" (Sig_ "x" (BVT 1) $ E $ BV 1 :@ BVT 0) $
|
||||
E (BV 1 :@ E (F "fst" :@@ [BVT 2, BVT 1, BVT 0])))
|
||||
|
||||
sndDef : Term Three d n
|
||||
sndDef =
|
||||
(["A","B","p"] :\\
|
||||
E (CasePair Any (BV 0)
|
||||
(S ["p"] $ Y $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
|
||||
(S ["x","y"] $ Y $ BVT 0)))
|
||||
(SY ["p"] $ E $ BV 2 :@ E (F "fst" :@@ [BVT 3, BVT 2, BVT 0]))
|
||||
(SY ["x","y"] $ BVT 0)))
|
||||
|
||||
|
||||
defGlobals : Definitions Three
|
||||
|
|
@ -85,8 +83,8 @@ defGlobals = fromList
|
|||
("f", mkAbstract Any $ Arr One (FT "A") (FT "A")),
|
||||
("g", mkAbstract Any $ Arr One (FT "A") (FT "B")),
|
||||
("f2", mkAbstract Any $ Arr One (FT "A") $ Arr One (FT "A") (FT "B")),
|
||||
("p", mkAbstract Any $ Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0),
|
||||
("q", mkAbstract Any $ Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0),
|
||||
("p", mkAbstract Any $ Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0),
|
||||
("q", mkAbstract Any $ Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0),
|
||||
("refl", mkDef Any reflTy reflDef),
|
||||
("fst", mkDef Any fstTy fstDef),
|
||||
("snd", mkDef Any sndTy sndDef)]
|
||||
|
|
@ -180,7 +178,7 @@ tests = "typechecker" :- [
|
|||
check_ (ctx [<]) szero (Arr One (FT "C") (FT "D")) (TYPE 0),
|
||||
testTC "0 · (1·x : A) → P x ⇐ ★₀" $
|
||||
check_ (ctx [<]) szero
|
||||
(Pi One (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0)
|
||||
(Pi_ One "x" (FT "A") $ E $ F "P" :@ BVT 0)
|
||||
(TYPE 0),
|
||||
testTCFail "0 · A ⊸ P ⇍ ★₀" $
|
||||
check_ (ctx [<]) szero (Arr One (FT "A") $ FT "P") (TYPE 0),
|
||||
|
|
@ -196,14 +194,14 @@ tests = "typechecker" :- [
|
|||
check_ (ctx [<]) szero (FT "A" `And` FT "P") (TYPE 0),
|
||||
testTC "0 · (x : A) × P x ⇐ ★₀" $
|
||||
check_ (ctx [<]) szero
|
||||
(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 0),
|
||||
(Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 0),
|
||||
testTC "0 · (x : A) × P x ⇐ ★₁" $
|
||||
check_ (ctx [<]) szero
|
||||
(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 1),
|
||||
(Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 1),
|
||||
testTC "0 · (A : ★₀) × A ⇐ ★₁" $
|
||||
check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 1),
|
||||
check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 1),
|
||||
testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
|
||||
check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 0),
|
||||
check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 0),
|
||||
testTCFail "1 · A × A ⇍ ★₀" $
|
||||
check_ (ctx [<]) sone (FT "A" `And` FT "A") (TYPE 0)
|
||||
],
|
||||
|
|
@ -214,15 +212,13 @@ tests = "typechecker" :- [
|
|||
testTC "0 · {a,b,c} ⇐ ★₀" $
|
||||
check_ (ctx [<]) szero (enum ["a", "b", "c"]) (TYPE 0),
|
||||
testTC "0 · {a,b,c} ⇐ ★₃" $
|
||||
check_ (ctx [<]) szero
|
||||
(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 0),
|
||||
check_ (ctx [<]) szero (Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 0),
|
||||
testTC "0 · (x : A) × P x ⇐ ★₁" $
|
||||
check_ (ctx [<]) szero
|
||||
(Sig (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0) (TYPE 1),
|
||||
check_ (ctx [<]) szero (Sig_ "x" (FT "A") $ E $ F "P" :@ BVT 0) (TYPE 1),
|
||||
testTC "0 · (A : ★₀) × A ⇐ ★₁" $
|
||||
check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 1),
|
||||
check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 1),
|
||||
testTCFail "0 · (A : ★₀) × A ⇍ ★₀" $
|
||||
check_ (ctx [<]) szero (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) (TYPE 0),
|
||||
check_ (ctx [<]) szero (Sig_ "A" (TYPE 0) $ BVT 0) (TYPE 0),
|
||||
testTCFail "1 · A × A ⇍ ★₀" $
|
||||
check_ (ctx [<]) sone (FT "A" `And` FT "A") (TYPE 0)
|
||||
],
|
||||
|
|
@ -251,7 +247,7 @@ tests = "typechecker" :- [
|
|||
testTCFail "1 · A ⇏ ★₀" $
|
||||
infer_ (ctx [<]) sone (F "A"),
|
||||
note "refl : (0·A : ★₀) → (1·x : A) → (x ≡ x : A) ≔ (λ A x ⇒ λᴰ _ ⇒ x)",
|
||||
testTC "1 · refl ⇒ ⋯" $ inferAs (ctx [<]) sone (F "refl") reflTy,
|
||||
testTC "1 · refl ⇒ ⋯" $ inferAs (ctx [<]) sone (F "refl") reflTy,
|
||||
testTC "1 · [refl] ⇐ ⋯" $ check_ (ctx [<]) sone (FT "refl") reflTy
|
||||
],
|
||||
|
||||
|
|
@ -296,51 +292,43 @@ tests = "typechecker" :- [
|
|||
testTC "1 · (a, λᴰ i ⇒ a) ⇐ (x : A) × (x ≡ a)" $
|
||||
check_ (ctx [<]) sone
|
||||
(Pair (FT "a") (["i"] :\\% FT "a"))
|
||||
(Sig (FT "A") $ S ["x"] $ Y $
|
||||
Eq0 (FT "A") (BVT 0) (FT "a"))
|
||||
(Sig_ "x" (FT "A") $ Eq0 (FT "A") (BVT 0) (FT "a"))
|
||||
],
|
||||
|
||||
"unpairing" :- [
|
||||
testTC "x : A × A ⊢ 1 · (case1 x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 1·x" $
|
||||
inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
|
||||
(CasePair One (BV 0)
|
||||
(S ["_"] $ N $ FT "B")
|
||||
(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(CasePair One (BV 0) (SN $ FT "B")
|
||||
(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(FT "B") [< One],
|
||||
testTC "x : A × A ⊢ 1 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ ω·x" $
|
||||
inferAsQ (ctx [< FT "A" `And` FT "A"]) sone
|
||||
(CasePair Any (BV 0)
|
||||
(S ["_"] $ N $ FT "B")
|
||||
(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(CasePair Any (BV 0) (SN $ FT "B")
|
||||
(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(FT "B") [< Any],
|
||||
testTC "x : A × A ⊢ 0 · (caseω x return B of (l,r) ⇒ f2 l r) ⇒ B ⊳ 0·x" $
|
||||
inferAsQ (ctx [< FT "A" `And` FT "A"]) szero
|
||||
(CasePair Any (BV 0)
|
||||
(S ["_"] $ N $ FT "B")
|
||||
(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(CasePair Any (BV 0) (SN $ FT "B")
|
||||
(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0]))
|
||||
(FT "B") [< Zero],
|
||||
testTCFail "x : A × A ⊢ 1 · (case0 x return B of (l,r) ⇒ f2 l r) ⇏" $
|
||||
infer_ (ctx [< FT "A" `And` FT "A"]) sone
|
||||
(CasePair Zero (BV 0)
|
||||
(S ["_"] $ N $ FT "B")
|
||||
(S ["l", "r"] $ Y $ E $ F "f2" :@@ [BVT 1, BVT 0])),
|
||||
(CasePair Zero (BV 0) (SN $ FT "B")
|
||||
(SY ["l", "r"] $ E $ F "f2" :@@ [BVT 1, BVT 0])),
|
||||
testTC "x : A × B ⊢ 1 · (caseω x return A of (l,r) ⇒ l) ⇒ A ⊳ ω·x" $
|
||||
inferAsQ (ctx [< FT "A" `And` FT "B"]) sone
|
||||
(CasePair Any (BV 0)
|
||||
(S ["_"] $ N $ FT "A")
|
||||
(S ["l", "r"] $ Y $ BVT 1))
|
||||
(CasePair Any (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1))
|
||||
(FT "A") [< Any],
|
||||
testTC "x : A × B ⊢ 0 · (case1 x return A of (l,r) ⇒ l) ⇒ A ⊳ 0·x" $
|
||||
inferAsQ (ctx [< FT "A" `And` FT "B"]) szero
|
||||
(CasePair One (BV 0)
|
||||
(S ["_"] $ N $ FT "A")
|
||||
(S ["l", "r"] $ Y $ BVT 1))
|
||||
(CasePair One (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1))
|
||||
(FT "A") [< Zero],
|
||||
testTCFail "x : A × B ⊢ 1 · (case1 x return A of (l,r) ⇒ l) ⇏" $
|
||||
infer_ (ctx [< FT "A" `And` FT "B"]) sone
|
||||
(CasePair One (BV 0)
|
||||
(S ["_"] $ N $ FT "A")
|
||||
(S ["l", "r"] $ Y $ BVT 1)),
|
||||
(CasePair One (BV 0) (SN $ FT "A")
|
||||
(SY ["l", "r"] $ BVT 1)),
|
||||
note "fst : (0·A : ★₁) → (0·B : A ↠ ★₁) → ((x : A) × B x) ↠ A",
|
||||
note " ≔ (λ A B p ⇒ caseω p return A of (x, y) ⇒ x)",
|
||||
testTC "0 · ‹type of fst› ⇐ ★₂" $
|
||||
|
|
@ -356,7 +344,7 @@ tests = "typechecker" :- [
|
|||
testTC "0 · snd ★₀ (λ x ⇒ x) ⇒ (ω·p : (A : ★₀) × A) → fst ★₀ (λ x ⇒ x) p" $
|
||||
inferAs (ctx [<]) szero
|
||||
(F "snd" :@@ [TYPE 0, ["x"] :\\ BVT 0])
|
||||
(Pi Any (Sig (TYPE 0) $ S ["A"] $ Y $ BVT 0) $ S ["p"] $ Y $
|
||||
(Pi_ Any "A" (Sig_ "A" (TYPE 0) $ BVT 0) $
|
||||
(E $ F "fst" :@@ [TYPE 0, ["x"] :\\ BVT 0, BVT 0]))
|
||||
],
|
||||
|
||||
|
|
@ -373,20 +361,19 @@ tests = "typechecker" :- [
|
|||
|
||||
"equalities" :- [
|
||||
testTC "1 · (λᴰ i ⇒ a) ⇐ a ≡ a" $
|
||||
check_ (ctx [<]) sone (DLam $ S ["i"] $ N $ FT "a")
|
||||
check_ (ctx [<]) sone (DLam $ SN $ FT "a")
|
||||
(Eq0 (FT "A") (FT "a") (FT "a")),
|
||||
testTC "0 · (λ p q ⇒ λᴰ i ⇒ p) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
|
||||
check_ (ctx [<]) szero
|
||||
(Lam $ S ["p"] $ Y $ Lam $ S ["q"] $ N $ DLam $ S ["i"] $ N $ BVT 0)
|
||||
(Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["p"] $ Y $
|
||||
Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["q"] $ Y $
|
||||
(["p","q"] :\\ ["i"] :\\% BVT 1)
|
||||
(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0)),
|
||||
testTC "0 · (λ p q ⇒ λᴰ i ⇒ q) ⇐ (ω·p q : a ≡ a') → p ≡ q" $
|
||||
check_ (ctx [<]) szero
|
||||
(Lam $ S ["p"] $ N $ Lam $ S ["q"] $ Y $
|
||||
DLam $ S ["i"] $ N $ BVT 0)
|
||||
(Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["p"] $ Y $
|
||||
Pi Any (Eq0 (FT "A") (FT "a") (FT "a")) $ S ["q"] $ Y $
|
||||
(["p","q"] :\\ ["i"] :\\% BVT 0)
|
||||
(Pi_ Any "p" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Pi_ Any "q" (Eq0 (FT "A") (FT "a") (FT "a")) $
|
||||
Eq0 (Eq0 (FT "A") (FT "a") (FT "a")) (BVT 1) (BVT 0))
|
||||
],
|
||||
|
||||
|
|
@ -398,11 +385,11 @@ tests = "typechecker" :- [
|
|||
testTC "cong" $
|
||||
check_ (ctx [<]) sone
|
||||
(["x", "y", "xy"] :\\ ["i"] :\\% E (F "p" :@ E (BV 0 :% BV 0)))
|
||||
(Pi Zero (FT "A") $ S ["x"] $ Y $
|
||||
Pi Zero (FT "A") $ S ["y"] $ Y $
|
||||
Pi One (Eq0 (FT "A") (BVT 1) (BVT 0)) $ S ["xy"] $ Y $
|
||||
Eq (S ["i"] $ Y $ E $ F "P" :@ E (BV 0 :% BV 0))
|
||||
(E $ F "p" :@ BVT 2) (E $ F "p" :@ BVT 1)),
|
||||
(Pi_ Zero "x" (FT "A") $
|
||||
Pi_ Zero "y" (FT "A") $
|
||||
Pi_ One "xy" (Eq0 (FT "A") (BVT 1) (BVT 0)) $
|
||||
Eq_ "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 "⊢",
|
||||
|
|
@ -411,12 +398,10 @@ tests = "typechecker" :- [
|
|||
testTC "funext" $
|
||||
check_ (ctx [<]) sone
|
||||
(["eq"] :\\ ["i"] :\\% ["x"] :\\ E (BV 1 :@ BVT 0 :% BV 0))
|
||||
(Pi One
|
||||
(Pi One (FT "A") $ S ["x"] $ Y $
|
||||
Eq0 (E $ F "P" :@ BVT 0)
|
||||
(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)) $
|
||||
S ["eq"] $ Y $
|
||||
Eq0 (Pi Any (FT "A") $ S ["x"] $ Y $ E $ F "P" :@ BVT 0)
|
||||
(FT "p") (FT "q"))
|
||||
(Pi_ One "eq"
|
||||
(Pi_ One "x" (FT "A")
|
||||
(Eq0 (E $ F "P" :@ BVT 0)
|
||||
(E $ F "p" :@ BVT 0) (E $ F "q" :@ BVT 0)))
|
||||
(Eq0 (Pi_ Any "x" (FT "A") $ E $ F "P" :@ BVT 0) (FT "p") (FT "q")))
|
||||
]
|
||||
]
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue