--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/variant.ur	Tue Dec 14 10:33:24 2010 -0500
@@ -0,0 +1,95 @@
+fun read [r ::: {Unit}] [t ::: Type] (fl : folder r) (r : $(mapU t r)) (v : variant (mapU {} r)) : t =
+    match v
+    (@fold [fn r => r' :: {Unit} -> [r ~ r'] => $(mapU t (r ++ r')) -> $(mapU ({} -> t) r)]
+     (fn [nm :: Name] [u::_] [us::_] [[nm] ~ us] (cs : r' :: {Unit} -> [us ~ r'] => $(mapU t (us ++ r')) -> _) [r'::_] [[nm = u] ++ us ~ r'] r =>
+         {nm = fn () => r.nm} ++ cs [[nm = u] ++ r'] ! r)
+     (fn [r'::_] [[] ~ r'] _ => {}) fl [[]] ! r)
+
+fun write [r ::: {Unit}] [t ::: Type] (fl : folder r) (r : $(mapU t r)) (v : variant (mapU {} r)) (x : t) : $(mapU t r) =
+    match v
+    (@fold [fn r => r' :: {Unit} -> [r ~ r'] => $(mapU t (r ++ r')) -> $(mapU ({} -> $(mapU t (r ++ r'))) r)]
+      (fn [nm :: Name] [u::_] [us::_] [[nm] ~ us]
+          (cs : r' :: {Unit} -> [us ~ r'] => $(mapU t (us ++ r')) -> $(mapU ({} -> $(mapU t (us ++ r'))) us))
+          [r'::_] [[nm = u] ++ us ~ r'] r =>
+          {nm = fn () => r -- nm ++ {nm = x}} ++ cs [[nm = u] ++ r'] ! r)
+      (fn [r'::_] [[] ~ r'] _ => {}) fl [[]] ! r)
+
+fun search [r] [t] (f : variant (mapU {} r) -> option t) (fl : folder r) : option t =
+    @fold [fn r => r' :: {Unit} -> [r ~ r'] => (variant (mapU {} (r ++ r')) -> option t) -> option t]
+    (fn [nm :: Name] [u ::_] [r ::_] [[nm] ~ r]
+                     (acc : r' :: {Unit} -> [r ~ r'] => (variant (mapU {} (r ++ r')) -> option t) -> option t)
+                     [r' ::_] [[nm] ++ r ~ r'] f' =>
+        case f' (make [nm] {}) of
+            None => acc [[nm] ++ r'] ! f'
+          | v => v)
+    (fn [r' ::_] [[] ~ r'] _ => None) fl [[]] ! f
+
+fun find [r] (f : variant (mapU {} r) -> bool) (fl : folder r) : option (variant (mapU {} r)) =
+    @search (fn v => if f v then Some v else None) fl
+
+fun test [nm :: Name] [t ::: Type] [ts ::: {Type}] [[nm] ~ ts] (fl : folder ([nm = t] ++ ts))
+          (v : variant ([nm = t] ++ ts)) : option t =
+    match v ({nm = Some}
+                 ++ (@map0 [fn t' => t' -> option t] (fn [t' :: Type] _ => None) fl -- nm))
+
+fun testLess [nm :: Name] [t ::: Type] [ts ::: {Type}] [[nm] ~ ts] (fl : folder ts) (v : variant ([nm = t] ++ ts)) : option t =
+    match v ({nm = Some}
+                 ++ @map0 [fn t' => t' -> option t] (fn [t' :: Type] _ => None) fl)
+
+fun eq [r] (fl : folder r) (v1 : variant (mapU {} r)) (v2 : variant (mapU {} r)) : bool =
+    match v1
+    (@fold [fn r => r' :: {Unit} -> [r ~ r'] => folder (r ++ r') -> variant (mapU {} (r ++ r')) -> $(mapU ({} -> bool) r)]
+     (fn [nm ::_] [u ::_] [r ::_] [[nm] ~ r]
+         (acc : r' :: {Unit} -> [r ~ r'] => folder (r ++ r') -> variant (mapU {} (r ++ r')) -> $(mapU ({} -> bool) r))
+         [r' ::_] [[nm] ++ r ~ r'] (fl' : folder ([nm] ++ r ++ r')) v =>
+         {nm = fn () => Option.isSome (@test [nm] ! (@Folder.mp fl') v)}
+             ++ acc [[nm] ++ r'] ! fl' v)
+     (fn [r' ::_] [[] ~ r'] _ _ => {}) fl [[]] ! fl v2)
+
+fun fold [r] [t] (fl : folder r) (f : variant (mapU {} r) -> t -> t) : t -> t =
+    @Top.fold [fn r => r' :: {Unit} -> [r ~ r'] => (variant (mapU {} (r ++ r')) -> t -> t) -> t -> t]
+    (fn [nm :: Name] [u ::_] [r ::_] [[nm] ~ r]
+                     (acc : r' :: {Unit} -> [r ~ r'] => (variant (mapU {} (r ++ r')) -> t -> t) -> t -> t)
+                     [r' ::_] [[nm] ++ r ~ r'] f' acc' =>
+        f' (make [nm] {}) (acc [[nm] ++ r'] ! f' acc'))
+    (fn [r' ::_] [[] ~ r'] _ x => x) fl [[]] ! f
+
+fun destrR [K] [f :: K -> Type] [fr :: K -> Type] [t ::: Type]
+    (f : p :: K -> f p -> fr p -> t)
+    [r ::: {K}] (fl : folder r) (v : variant (map f r)) (r : $(map fr r)) : t =
+    match v
+    (@Top.mp [fr] [fn p => f p -> t]
+     (fn [p] (m : fr p) (v : f p) => f [p] v m)
+     fl r)
+
+fun destr2R [K] [f1 :: K -> Type] [f2 :: K -> Type] [fr :: K -> Type] [t ::: Type]
+    (f : p :: K -> f1 p -> f2 p -> fr p -> t)
+    [r ::: {K}] (fl : folder r) (v1 : variant (map f1 r)) (v2 : variant (map f2 r)) (r : $(map fr r)) : option t =
+    match v1
+    (@foldR [fr] [fn r => others :: {K} -> [others ~ r] =>
+                     folder (r ++ others)
+                     -> variant (map f2 (r ++ others))
+                     -> $(map (fn p => f1 p -> option t) r)]
+     (fn [nm ::_] [p ::_] [r ::_] [[nm] ~ r] (meta : fr p)
+         (acc : others :: {K} -> [others ~ r] =>
+          folder (r ++ others)
+          -> variant (map f2 (r ++ others))
+          -> $(map (fn p => f1 p -> option t) r))
+         [others :: {K}] [others ~ [nm = p] ++ r]
+         (fl : folder ([nm = p] ++ r ++ others))
+         (v2 : variant (map f2 ([nm = p] ++ r ++ others))) =>
+         {nm = fn x1 => match v2
+                        ({nm = fn x2 => Some (f [p] x1 x2 meta)}
+                             ++ (@map0 [fn p => f2 p -> option t] (fn [p' ::_] _ => None) fl -- nm))}
+             ++ acc [[nm = p] ++ others] ! fl v2)
+     (fn [others ::_] [others ~ []] _ _ => {})
+     fl r [[]] ! fl v2)
+
+fun testEq [K] [f :: K -> Type] [nm :: Name] [t ::: K] [ts ::: {K}] [r ::: {K}] [[nm] ~ ts]
+    (pf : Eq.eq r ([nm = t] ++ ts)) (fl : folder r) (v : variant (map f r)) : option (f t) =
+  @test [nm] ! (@Folder.mp (@Eq.cast pf [folder] fl))
+   (Eq.cast pf [fn r => variant (map f r)] v)
+
+fun makeEq [K] [f :: K -> Type] [nm :: Name] [t ::: K] [ts ::: {K}] [r ::: {K}] [[nm] ~ ts]
+    (pf : Eq.eq r ([nm = t] ++ ts)) (x : f t) : variant (map f r) =
+  Eq.cast (Eq.sym pf) [fn r => variant (map f r)] (make [nm] x)