Improvements to grammar
This commit is contained in:
@@ -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
|
||||
|
||||
@@ -3,35 +3,35 @@ module TypeClass
|
||||
data Monad : (U -> U) -> U where
|
||||
MkMonad : { M : U -> U } ->
|
||||
(bind : {A B : U} -> (M A) -> (A -> M B) -> M B) ->
|
||||
(pure : {A : U} -> A -> M A) ->
|
||||
(pure : ∀ A. A -> M A) ->
|
||||
Monad M
|
||||
|
||||
infixl 1 _>>=_ _>>_
|
||||
_>>=_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> (m a) -> (a -> m b) -> m b
|
||||
_>>=_ {a} {b} {m} {{MkMonad bind' _}} ma amb = bind' {a} {b} ma amb
|
||||
_>>=_ : ∀ m a b. {{Monad m}} -> (m a) -> (a -> m b) -> m b
|
||||
_>>=_ {{MkMonad bind' _}} ma amb = bind' ma amb
|
||||
|
||||
_>>_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> m a -> m b -> m b
|
||||
_>>_ : ∀ m a b. {{Monad m}} -> m a -> m b -> m b
|
||||
ma >> mb = mb
|
||||
|
||||
pure : {a : U} {m : U -> U} {{_ : Monad m}} -> a -> m a
|
||||
pure {_} {_} {{MkMonad _ pure'}} a = pure' a
|
||||
pure : ∀ m a. {{Monad m}} -> a -> m a
|
||||
pure {{MkMonad _ pure'}} a = pure' a
|
||||
|
||||
data Either : U -> U -> U where
|
||||
Left : {A B : U} -> A -> Either A B
|
||||
Right : {A B : U} -> B -> Either A B
|
||||
Left : ∀ A B. A -> Either A B
|
||||
Right : ∀ A B. B -> Either A B
|
||||
|
||||
bindEither : {A B C : U} -> (Either A B) -> (B -> Either A C) -> Either A C
|
||||
bindEither : ∀ A B C. (Either A B) -> (B -> Either A C) -> Either A C
|
||||
bindEither (Left a) amb = Left a
|
||||
bindEither (Right b) amb = amb b
|
||||
|
||||
EitherMonad : {A : U} -> Monad (Either A)
|
||||
EitherMonad : ∀ A. Monad (Either A)
|
||||
EitherMonad = MkMonad {Either A} bindEither Right
|
||||
|
||||
data Maybe : U -> U where
|
||||
Just : {A : U} -> A -> Maybe A
|
||||
Nothing : {A : U} -> Maybe A
|
||||
Just : ∀ A. A -> Maybe A
|
||||
Nothing : ∀ A. Maybe A
|
||||
|
||||
bindMaybe : {A B : U} -> Maybe A -> (A -> Maybe B) -> Maybe B
|
||||
bindMaybe : ∀ A B. Maybe A -> (A -> Maybe B) -> Maybe B
|
||||
bindMaybe Nothing amb = Nothing
|
||||
bindMaybe (Just a) amb = amb a
|
||||
|
||||
@@ -40,19 +40,19 @@ MaybeMonad = MkMonad bindMaybe Just
|
||||
|
||||
infixr 7 _::_
|
||||
data List : U -> U where
|
||||
Nil : {A : U} -> List A
|
||||
_::_ : {A : U} -> A -> List A -> List A
|
||||
Nil : ∀ A. List A
|
||||
_::_ : ∀ A. A -> List A -> List A
|
||||
|
||||
infixl 7 _++_
|
||||
_++_ : {A : U} -> List A -> List A -> List A
|
||||
_++_ : ∀ A. List A -> List A -> List A
|
||||
Nil ++ ys = ys
|
||||
(x :: xs) ++ ys = x :: (xs ++ ys)
|
||||
|
||||
bindList : {A B : U} -> List A -> (A -> List B) -> List B
|
||||
bindList : ∀ A B. List A -> (A -> List B) -> List B
|
||||
bindList Nil f = Nil
|
||||
bindList (x :: xs) f = f x ++ bindList xs f
|
||||
|
||||
singleton : {A : U} -> A -> List A
|
||||
singleton : ∀ A. A -> List A
|
||||
singleton a = a :: Nil
|
||||
|
||||
-- TODO need better error when the monad is not defined
|
||||
@@ -61,7 +61,7 @@ ListMonad = MkMonad bindList singleton
|
||||
|
||||
infixr 1 _,_
|
||||
data Pair : U -> U -> U where
|
||||
_,_ : {A B : U} -> A -> B -> Pair A B
|
||||
_,_ : ∀ A B. A -> B -> Pair A B
|
||||
|
||||
ptype Int
|
||||
|
||||
@@ -69,7 +69,7 @@ test : Maybe Int
|
||||
test = pure 10
|
||||
|
||||
foo : Int -> Maybe Int
|
||||
foo x = Just 42 >> Just x >>= (\ x => pure {_} {Maybe} 10)
|
||||
foo x = Just 42 >> Just x >>= (\ x => pure 10)
|
||||
|
||||
bar : Int -> Maybe Int
|
||||
bar x = do
|
||||
@@ -77,7 +77,7 @@ bar x = do
|
||||
z <- Just x
|
||||
pure z
|
||||
|
||||
baz : {A B : U} -> List A -> List B -> List (Pair A B)
|
||||
baz : ∀ A B. List A -> List B -> List (Pair A B)
|
||||
baz xs ys = do
|
||||
x <- xs
|
||||
y <- ys
|
||||
|
||||
Reference in New Issue
Block a user