refactor core syntax slightly to derive Eq/Show
add a new `WithSubst tm env to` record that packages a `tm from` with a `Subst env from to`, and write instances for just that. the rest of the AST can be derived
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13 changed files with 184 additions and 269 deletions
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@ -1,158 +0,0 @@
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module TermImpls
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import Quox.Syntax
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import public Quox.Pretty
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private
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eqShiftLen : Shift from1 to -> Shift from2 to -> Maybe (from1 = from2)
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eqShiftLen SZ SZ = Just Refl
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eqShiftLen (SS by) (SS bz) = eqShiftLen by bz
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eqShiftLen _ _ = Nothing
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private
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eqSubstLen : Subst tm1 from1 to -> Subst tm2 from2 to -> Maybe (from1 = from2)
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eqSubstLen (Shift by) (Shift bz) = eqShiftLen by bz
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eqSubstLen (_ ::: th) (_ ::: ph) = cong S <$> eqSubstLen th ph
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eqSubstLen _ _ = Nothing
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-- maybe from1 = from2 in the last case, but this is for
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-- (==), and the substs aren't equal, so who cares
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mutual
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export covering
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Eq (Term d n) where
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TYPE k == TYPE l = k == l
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TYPE _ == _ = False
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Pi qty1 arg1 res1 == Pi qty2 arg2 res2 =
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qty1 == qty2 && arg1 == arg2 && res1 == res2
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Pi {} == _ = False
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Lam body1 == Lam body2 = body1 == body2
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Lam {} == _ = False
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Sig fst1 snd1 == Sig fst2 snd2 =
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fst1 == fst2 && snd1 == snd2
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Sig {} == _ = False
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Pair fst1 snd1 == Pair fst2 snd2 = fst1 == fst2 && snd1 == snd2
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Pair {} == _ = False
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Enum ts1 == Enum ts2 = ts1 == ts2
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Enum _ == _ = False
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Tag t1 == Tag t2 = t1 == t2
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Tag _ == _ = False
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Eq ty1 l1 r1 == Eq ty2 l2 r2 =
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ty1 == ty2 && l1 == l2 && r1 == r2
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Eq {} == _ = False
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DLam body1 == DLam body2 = body1 == body2
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DLam {} == _ = False
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Nat == Nat = True
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Nat == _ = False
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Zero == Zero = True
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Zero == _ = False
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Succ m == Succ n = m == n
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Succ _ == _ = False
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BOX q1 ty1 == BOX q2 ty2 = q1 == q2 && ty1 == ty2
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BOX {} == _ = False
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Box val1 == Box val2 = val1 == val2
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Box _ == _ = False
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E e == E f = e == f
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E _ == _ = False
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CloT tm1 th1 == CloT tm2 th2 =
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case eqSubstLen th1 th2 of
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Just Refl => tm1 == tm2 && th1 == th2
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Nothing => False
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CloT {} == _ = False
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DCloT tm1 th1 == DCloT tm2 th2 =
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case eqSubstLen th1 th2 of
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Just Refl => tm1 == tm2 && th1 == th2
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Nothing => False
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DCloT {} == _ = False
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export covering
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Eq (Elim d n) where
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F x == F y = x == y
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F _ == _ = False
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B i == B j = i == j
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B _ == _ = False
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(fun1 :@ arg1) == (fun2 :@ arg2) = fun1 == fun2 && arg1 == arg2
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(_ :@ _) == _ = False
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CasePair q1 p1 r1 b1 == CasePair q2 p2 r2 b2 =
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q1 == q2 && p1 == p2 && r1 == r2 && b1 == b2
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CasePair {} == _ = False
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CaseEnum q1 t1 r1 a1 == CaseEnum q2 t2 r2 a2 =
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q1 == q2 && t1 == t2 && r1 == r2 && a1 == a2
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CaseEnum {} == _ = False
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CaseNat q1 q1' n1 r1 z1 s1 == CaseNat q2 q2' n2 r2 z2 s2 =
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q1 == q2 && q1' == q2' && n1 == n2 &&
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r1 == r2 && z1 == z2 && s1 == s2
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CaseNat {} == _ = False
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CaseBox q1 x1 r1 b1 == CaseBox q2 x2 r2 b2 =
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q1 == q2 && x1 == x2 && r1 == r2 && b1 == b2
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CaseBox {} == _ = False
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(fun1 :% dim1) == (fun2 :% dim2) = fun1 == fun2 && dim1 == dim2
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(_ :% _) == _ = False
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(tm1 :# ty1) == (tm2 :# ty2) = tm1 == tm2 && ty1 == ty2
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(_ :# _) == _ = False
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Coe ty1 p1 q1 val1 == Coe ty2 p2 q2 val2 =
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ty1 == ty2 && p1 == p2 && q1 == q2 && val1 == val2
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Coe {} == _ = False
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Comp ty1 p1 q1 val1 r1 zero1 one1 == Comp ty2 p2 q2 val2 r2 zero2 one2 =
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ty1 == ty2 && p1 == p2 && q1 == q2 &&
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val1 == val2 && r1 == r2 && zero1 == zero2 && one1 == one2
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Comp {} == _ = False
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TypeCase ty1 ret1 arms1 def1 == TypeCase ty2 ret2 arms2 def2 =
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ty1 == ty2 && ret1 == ret2 &&
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arms1 == arms2 && def1 == def2
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TypeCase {} == _ = False
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CloE el1 th1 == CloE el2 th2 =
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case eqSubstLen th1 th2 of
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Just Refl => el1 == el2 && th1 == th2
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Nothing => False
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CloE {} == _ = False
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DCloE el1 th1 == DCloE el2 th2 =
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case eqSubstLen th1 th2 of
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Just Refl => el1 == el2 && th1 == th2
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Nothing => False
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DCloE {} == _ = False
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export covering
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{s : Nat} -> Eq (ScopeTermN s d n) where
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b1 == b2 = b1.term == b2.term
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export covering
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{s : Nat} -> Eq (DScopeTermN s d n) where
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b1 == b2 = b1.term == b2.term
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export covering
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Show (Term d n) where
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showPrec d t = showParens (d /= Open) $ prettyStr True t
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export covering
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Show (Elim d n) where
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showPrec d e = showParens (d /= Open) $ prettyStr True e
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@ -237,27 +237,27 @@ tests = "equality & subtyping" :- [
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testEq "[#0]{} = [#0] : A" $
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equalT (extendTy Any "x" (FT "A") empty)
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(FT "A")
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(CloT (BVT 0) id)
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(CloT (Sub (BVT 0) id))
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(BVT 0),
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testEq "[#0]{a} = [a] : A" $
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equalT empty (FT "A")
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(CloT (BVT 0) (F "a" ::: id))
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(CloT (Sub (BVT 0) (F "a" ::: id)))
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(FT "a"),
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testEq "[#0]{a,b} = [a] : A" $
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equalT empty (FT "A")
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(CloT (BVT 0) (F "a" ::: F "b" ::: id))
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(CloT (Sub (BVT 0) (F "a" ::: F "b" ::: id)))
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(FT "a"),
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testEq "[#1]{a,b} = [b] : A" $
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equalT empty (FT "A")
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(CloT (BVT 1) (F "a" ::: F "b" ::: id))
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(CloT (Sub (BVT 1) (F "a" ::: F "b" ::: id)))
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(FT "b"),
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testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A (N)" $
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(CloT (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id))
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(CloT (Sub (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id)))
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(Lam $ S [< "y"] $ N $ FT "a"),
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testEq "(λy ⇒ [#1]){a} = λy ⇒ [a] : B ⇾ A (Y)" $
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equalT empty (Arr Zero (FT "B") (FT "A"))
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(CloT ([< "y"] :\\ BVT 1) (F "a" ::: id))
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(CloT (Sub ([< "y"] :\\ BVT 1) (F "a" ::: id)))
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([< "y"] :\\ FT "a")
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],
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@ -265,12 +265,12 @@ tests = "equality & subtyping" :- [
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testEq "★₀‹𝟎› = ★₀ : ★₁" $
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equalTD 1
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(extendDim "𝑗" empty)
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(TYPE 1) (DCloT (TYPE 0) (K Zero ::: id)) (TYPE 0),
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(TYPE 1) (DCloT (Sub (TYPE 0) (K Zero ::: id))) (TYPE 0),
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testEq "(δ i ⇒ a)‹𝟎› = (δ i ⇒ a) : (a ≡ a : A)" $
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equalTD 1
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(extendDim "𝑗" empty)
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(Eq0 (FT "A") (FT "a") (FT "a"))
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(DCloT ([< "i"] :\\% FT "a") (K Zero ::: id))
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(DCloT (Sub ([< "i"] :\\% FT "a") (K Zero ::: id)))
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([< "i"] :\\% FT "a"),
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note "it is hard to think of well-typed terms with big dctxs"
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],
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@ -504,10 +504,10 @@ tests = "equality & subtyping" :- [
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"elim closure" :- [
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testEq "#0{a} = a" $
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equalE empty (CloE (BV 0) (F "a" ::: id)) (F "a"),
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equalE empty (CloE (Sub (BV 0) (F "a" ::: id))) (F "a"),
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testEq "#1{a} = #0" $
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equalE (extendTy Any "x" (FT "A") empty)
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(CloE (BV 1) (F "a" ::: id)) (BV 0)
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(CloE (Sub (BV 1) (F "a" ::: id))) (BV 0)
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],
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"elim d-closure" :- [
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@ -515,41 +515,42 @@ tests = "equality & subtyping" :- [
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testEq "(eq-AB #0)‹𝟎› = eq-AB 𝟎" $
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equalED 1
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(extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (K Zero ::: id))
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(DCloE (Sub (F "eq-AB" :% BV 0) (K Zero ::: id)))
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(F "eq-AB" :% K Zero),
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testEq "(eq-AB #0)‹𝟎› = A" $
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equalED 1
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(extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (K Zero ::: id)) (F "A"),
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(DCloE (Sub (F "eq-AB" :% BV 0) (K Zero ::: id))) (F "A"),
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testEq "(eq-AB #0)‹𝟏› = B" $
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equalED 1
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(extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (K One ::: id)) (F "B"),
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(DCloE (Sub (F "eq-AB" :% BV 0) (K One ::: id))) (F "B"),
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testNeq "(eq-AB #0)‹𝟏› ≠ A" $
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equalED 1
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(extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (K One ::: id)) (F "A"),
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(DCloE (Sub (F "eq-AB" :% BV 0) (K One ::: id))) (F "A"),
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testEq "(eq-AB #0)‹#0,𝟎› = (eq-AB #0)" $
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equalED 2
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(extendDim "𝑗" $ extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id))
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(DCloE (Sub (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id)))
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(F "eq-AB" :% BV 0),
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testNeq "(eq-AB #0)‹𝟎› ≠ (eq-AB 𝟎)" $
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equalED 2
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(extendDim "𝑗" $ extendDim "𝑖" empty)
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(DCloE (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id))
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(DCloE (Sub (F "eq-AB" :% BV 0) (BV 0 ::: K Zero ::: id)))
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(F "eq-AB" :% K Zero),
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testEq "#0‹𝟎› = #0 # term and dim vars distinct" $
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equalED 1
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(extendTy Any "x" (FT "A") $ extendDim "𝑖" empty)
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(DCloE (BV 0) (K Zero ::: id)) (BV 0),
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(DCloE (Sub (BV 0) (K Zero ::: id))) (BV 0),
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testEq "a‹𝟎› = a" $
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equalED 1 (extendDim "𝑖" empty) (DCloE (F "a") (K Zero ::: id)) (F "a"),
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equalED 1 (extendDim "𝑖" empty)
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(DCloE (Sub (F "a") (K Zero ::: id))) (F "a"),
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testEq "(f [a])‹𝟎› = f‹𝟎› [a]‹𝟎›" $
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let th = K Zero ::: id in
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equalED 1 (extendDim "𝑖" empty)
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(DCloE (F "f" :@ FT "a") th)
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(DCloE (F "f") th :@ DCloT (FT "a") th)
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(DCloE (Sub (F "f" :@ FT "a") th))
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(DCloE (Sub (F "f") th) :@ DCloT (Sub (FT "a") th))
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],
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"clashes" :- [
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@ -2,7 +2,6 @@ module Tests.FromPTerm
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import Quox.Parser.FromParser
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import Quox.Parser
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import TermImpls
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import TypingImpls
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import Tests.Parser as TParser
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import TAP
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@ -2,7 +2,6 @@ module Tests.Reduce
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import Quox.Syntax as Lib
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import Quox.Equal
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import TermImpls
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import TypingImpls
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import TAP
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@ -67,34 +66,34 @@ tests = "whnf" :- [
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"elim closure" :- [
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testWhnf "x{}" (ctx [< ("A", Nat)])
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(CloE (BV 0) id)
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(CloE (Sub (BV 0) id))
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(BV 0),
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testWhnf "x{a/x}" empty
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(CloE (BV 0) (F "a" ::: id))
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(CloE (Sub (BV 0) (F "a" ::: id)))
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(F "a"),
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testWhnf "x{x/x,a/y}" (ctx [< ("A", Nat)])
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(CloE (BV 0) (BV 0 ::: F "a" ::: id))
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(CloE (Sub (BV 0) (BV 0 ::: F "a" ::: id)))
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(BV 0),
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testWhnf "x{(y{a/y})/x}" empty
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(CloE (BV 0) ((CloE (BV 0) (F "a" ::: id)) ::: id))
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(CloE (Sub (BV 0) ((CloE (Sub (BV 0) (F "a" ::: id))) ::: id)))
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(F "a"),
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testWhnf "(x y){f/x,a/y}" empty
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(CloE (BV 0 :@ BVT 1) (F "f" ::: F "a" ::: id))
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(CloE (Sub (BV 0 :@ BVT 1) (F "f" ::: F "a" ::: id)))
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(F "f" :@ FT "a"),
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testWhnf "([y] ∷ [x]){A/x}" (ctx [< ("A", Nat)])
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(CloE (BVT 1 :# BVT 0) (F "A" ::: id))
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(CloE (Sub (BVT 1 :# BVT 0) (F "A" ::: id)))
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(BV 0),
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testWhnf "([y] ∷ [x]){A/x,a/y}" empty
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(CloE (BVT 1 :# BVT 0) (F "A" ::: F "a" ::: id))
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(CloE (Sub (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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testWhnf "(λy. x){a/x}" empty
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(CloT (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id))
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(CloT (Sub (Lam $ S [< "y"] $ N $ BVT 0) (F "a" ::: id)))
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(Lam $ S [< "y"] $ N $ FT "a"),
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testWhnf "(λy. y){a/x}" empty
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(CloT ([< "y"] :\\ BVT 0) (F "a" ::: id))
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(CloT (Sub ([< "y"] :\\ BVT 0) (F "a" ::: id)))
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([< "y"] :\\ BVT 0)
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],
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@ -112,8 +111,8 @@ tests = "whnf" :- [
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F "a" :@
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E ((([< "x"] :\\ BVT 0) :# Arr One (FT "A") (FT "A")) :@ FT "a"),
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testNoStep "λx. [y [x]]{x/x,a/y}" (ctx [< ("A", Nat)]) $
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[< "x"] :\\ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id),
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[< "x"] :\\ CloT (Sub (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)),
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testNoStep "f ([y [x]]{x/x,a/y})" (ctx [< ("A", Nat)]) $
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F "f" :@ CloT (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id)
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F "f" :@ CloT (Sub (E $ BV 1 :@ BVT 0) (BV 0 ::: F "a" ::: id))
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]
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]
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@ -3,7 +3,6 @@ module TypingImpls
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import TAP
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import public Quox.Typing
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import public Quox.Pretty
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import public TermImpls
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import Derive.Prelude
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%language ElabReflection
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@ -5,7 +5,6 @@ depends = base, contrib, elab-util, snocvect, quox-lib, tap, eff
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executable = quox-tests
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main = Tests
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modules =
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TermImpls,
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TypingImpls,
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PrettyExtra,
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Tests.DimEq,
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