From efd5f75c0672773341b5ca1c1d4b2ad0c0d09daa Mon Sep 17 00:00:00 2001
From: Ohad Kammar <ohad.kammar@ed.ac.uk>
Date: Sun, 7 Aug 2022 18:23:04 +0100
Subject: Initial version

---
 src/Data/Fun/Nary.idr | 51 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 src/Data/Fun/Nary.idr

(limited to 'src/Data/Fun')

diff --git a/src/Data/Fun/Nary.idr b/src/Data/Fun/Nary.idr
new file mode 100644
index 0000000..21a684b
--- /dev/null
+++ b/src/Data/Fun/Nary.idr
@@ -0,0 +1,51 @@
+module Data.Fun.Nary
+
+import Data.Vect
+
+%default total
+
+public export
+data Visibility = Visible | Hidden | Auto
+
+public export
+Pi : Visibility -> (a : Type) -> (a -> Type) -> Type
+Pi Visible a b = (x : a) -> b x
+Pi Hidden  a b = {x : a} -> b x
+Pi Auto    a b = {auto x : a} -> b x
+
+public export
+lam : (vis : Visibility) -> (0 b : a -> Type) ->
+      ((x : a) -> b x) -> Pi vis a b
+lam Visible b f = f
+lam Hidden  b f = f _
+lam Auto    b f = f %search
+
+public export
+app : (vis : Visibility) -> (0 b : a -> Type) ->
+      Pi vis a b -> ((x : a) -> b x)
+app Visible b f x = f x
+app Hidden  b f x = f
+app Auto    b f x = f
+
+public export
+PI : (n : Nat) -> Visibility -> (a : Type) -> (Vect n a -> Type) -> Type
+PI Z     vis a b = b []
+PI (S n) vis a b = Pi vis a (\ x => PI n vis a (b . (x ::)))
+
+public export
+curry : (n : Nat) -> (vis : Visibility) ->
+        (0 b : Vect n a -> Type) ->
+        ((as : Vect n a) -> b as) ->
+        PI n vis a b
+curry 0 vis b f = f []
+curry (S n) vis b f
+  = lam vis _ $ \ x => curry n vis (b . (x ::)) (\ xs => f (x :: xs))
+
+public export
+uncurry : (n : Nat) -> (vis : Visibility) ->
+          (0 b : Vect n a -> Type) ->
+          PI n vis a b ->
+          (as : Vect n a) -> b as
+uncurry 0 vis b f [] = f
+uncurry (S n) vis b f (x :: xs)
+  = uncurry n vis (b . (x ::)) (app vis _ f x) xs
-- 
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