Remove some ambiguities in parsing
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@@ -3,7 +3,6 @@ module Tree
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-- adapted from Conor McBride's 2-3 tree example
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-- youtube video: https://youtu.be/v2yXrOkzt5w?t=3013
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data Nat : U where
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Z : Nat
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S : Nat -> Nat
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@@ -16,8 +15,8 @@ data Void : U where
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infixl 4 _+_
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data _+_ : U -> U -> U where
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inl : {A B} -> A -> A + B
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inr : {A B} -> B -> A + B
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inl : ∀ a b. a -> a + b
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inr : ∀ a b. b -> a + b
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infix 4 _<=_
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@@ -47,14 +46,14 @@ _ <<= Top = Unit
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_ <<= _ = Void
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data Intv : Bnd -> Bnd -> U where
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intv : {l u} (x : Nat) (lx : l <<= N x) (xu : N x <<= u) -> Intv l u
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intv : ∀ l u. (x : Nat) (lx : l <<= N x) (xu : N x <<= u) -> Intv l u
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data T23 : Bnd -> Bnd -> Nat -> U where
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leaf : {l u} (lu : l <<= u) -> T23 l u Z
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node2 : {l u h} (x : _)
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leaf : ∀ l u. (lu : l <<= u) -> T23 l u Z
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node2 : ∀ l u h. (x : _)
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(tlx : T23 l (N x) h) (txu : T23 (N x) u h) ->
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T23 l u (S h)
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node3 : {l u h} (x y : _)
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node3 : ∀ l u h. (x y : _)
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(tlx : T23 l (N x) h) (txy : T23 (N x) (N y) h) (tyu : T23 (N y) u h) ->
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T23 l u (S h)
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@@ -66,12 +65,12 @@ data Sg : (A : U) -> (A -> U) -> U where
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_,_ : {A : U} {B : A -> U} -> (a : A) -> B a -> Sg A B
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_*_ : U -> U -> U
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A * B = Sg A (\ _ => B)
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a * b = Sg a (\ _ => b)
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TooBig : Bnd -> Bnd -> Nat -> U
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TooBig l u h = Sg Nat (\ x => T23 l (N x) h * T23 (N x) u h)
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insert : {l u h} -> Intv l u -> T23 l u h -> TooBig l u h + T23 l u h
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insert : ∀ l u h. Intv l u -> T23 l u h -> TooBig l u h + T23 l u h
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insert (intv x lx xu) (leaf lu) = inl (x , (leaf lx , leaf xu))
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insert (intv x lx xu) (node2 y tly tyu) = case cmp x y of
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-- u := N y is not solved at this time
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