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update docs and a test

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This commit is contained in:
Steve Dunham
2024-10-30 08:21:33 -07:00
parent 30648c8e9c
commit e6502abeed
3 changed files with 15 additions and 132 deletions
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32
tests/black/Tree.newt
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@@ -1,6 +1,8 @@
module Tree
-- https://youtu.be/v2yXrOkzt5w?t=3013
-- adapted from Conor McBride's 2-3 tree example
-- youtube video: https://youtu.be/v2yXrOkzt5w?t=3013
data Nat : U where
Z : Nat
@@ -60,43 +62,35 @@ data T23 : Bnd -> Bnd -> Nat -> U where
infixl 5 _*_
infixr 1 _,_
infixr 1 _**_
data Sg : (A : U) -> (A -> U) -> U where
_**_ : {A : U} {B : A -> U} -> (a : A) -> B a -> Sg A B
_,_ : {A : U} {B : A -> U} -> (a : A) -> B a -> Sg A B
-- Accidentally defined this as a separate data because I was
-- guessing the def behind _*_. I get an unsolved meta below if
-- I define in terms of Sg.
-- _*_ : U -> U -> U
-- A * B = Sg A (\ _ => B)
data _*_ : (A B : U) -> U where
_,_ : {A B : U} -> A -> B -> A * B
_*_ : U -> U -> U
A * B = Sg A (\ _ => B)
TooBig : Bnd -> Bnd -> Nat -> U
TooBig l u h = Sg Nat (\ x => T23 l (N x) h * T23 (N x) u h)
insert : {h : Nat} {l u : Bnd} -> Intv l u -> T23 l u h -> TooBig l u h + T23 l u h
-- Agda is yellow here, needs h = x on each leaf
insert (intv x lx xu) (leaf lu) = inl (x ** (leaf {_} {_} {x} lx , leaf {_} {_} {x} xu))
-- The second arg to the second _,_ is unsolved and pi-typed
insert (intv x lx xu) (leaf lu) = inl (x , (leaf {_} {_} {x} lx , leaf {_} {_} {x} xu))
insert (intv x lx xu) (node2 y tly tyu) = case cmp x y of
-- u := N y is not solved at this time
inl xy => case insert (intv {_} {N y} x lx xy) tly of
inl (z ** (tlz, tzy)) => inr (node3 z y tlz tzy tyu)
inl (z , (tlz , tzy)) => inr (node3 z y tlz tzy tyu)
inr tly' => inr (node2 y tly' tyu)
inr yx => case insert (intv {N y} x yx xu) tyu of
inl (z ** (tyz, tzu)) => inr (node3 y z tly tyz tzu)
inl (z , (tyz , tzu)) => inr (node3 y z tly tyz tzu)
inr tyu' => inr (node2 y tly tyu')
insert (intv x lx xu) (node3 y z tly tyz tzu) = case cmp x y of
inl xy => case insert (intv {_} {N y} x lx xy) tly of
inl (v ** (tlv , tvy)) => inl (y ** (node2 v tlv tvy, node2 z tyz tzu))
inl (v , (tlv , tvy)) => inl (y , (node2 v tlv tvy , node2 z tyz tzu))
inr tly' => inr (node3 y z tly' tyz tzu)
inr yx => case cmp x z of
inl xz => case insert (intv {N y} {N z} x yx xz) tyz of
inl (w ** (tyw , twz)) => inl (w ** (node2 y tly tyw, node2 z twz tzu))
inl (w , (tyw , twz)) => inl (w , (node2 y tly tyw , node2 z twz tzu))
inr tyz' => inr (node3 y z tly tyz' tzu)
inr zx => case insert (intv {N z} x zx xu) tzu of
inl (w ** (tzw, twu)) => inl (z ** (node2 y tly tyz, node2 w tzw twu))
inl (w , (tzw , twu)) => inl (z , (node2 y tly tyz , node2 w tzw twu))
inr tzu' => inr (node3 y z tly tyz tzu')