Improvements to grammar

This commit is contained in:
2024-11-09 21:39:45 -08:00
parent bb749a917a
commit 6abd97ee85
9 changed files with 80 additions and 80 deletions

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@@ -16,8 +16,8 @@ data Void : U where
infixl 4 _+_
data _+_ : U -> U -> U where
inl : {A B : U} -> A -> A + B
inr : {A B : U} -> B -> A + B
inl : {A B} -> A -> A + B
inr : {A B} -> B -> A + B
infix 4 _<=_
@@ -47,14 +47,14 @@ _ <<= Top = Unit
_ <<= _ = Void
data Intv : Bnd -> Bnd -> U where
intv : {l u : Bnd} (x : Nat) (lx : l <<= N x) (xu : N x <<= u) -> Intv l u
intv : {l u} (x : Nat) (lx : l <<= N x) (xu : N x <<= u) -> Intv l u
data T23 : Bnd -> Bnd -> Nat -> U where
leaf : {l u : Bnd} {h : Nat} (lu : l <<= u) -> T23 l u Z
node2 : {l u : Bnd} {h : Nat} (x : _)
leaf : {l u} (lu : l <<= u) -> T23 l u Z
node2 : {l u h} (x : _)
(tlx : T23 l (N x) h) (txu : T23 (N x) u h) ->
T23 l u (S h)
node3 : {l u : Bnd} {h : Nat} (x y : _)
node3 : {l u h} (x y : _)
(tlx : T23 l (N x) h) (txy : T23 (N x) (N y) h) (tyu : T23 (N y) u h) ->
T23 l u (S h)
@@ -71,10 +71,8 @@ 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
-- 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 : {l u h} -> Intv l u -> T23 l u h -> TooBig l u h + T23 l u h
insert (intv x lx xu) (leaf lu) = inl (x , (leaf lx , leaf 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