Added instances for Add, Mul, and VSpace of functions.

lib/prelude.dx

@@ -152,6 +152,11 @@ instance Add Unit
   sub = \x y. ()
   zero = ()
 
+instance [Add a] Add (n->a)
+  add = \f g. \x. (f x) + (g x)
+  sub = \f g. \x. (f x) - (g x)
+  zero = \x. zero
+
 '#### Mul
 Things that can be multiplied.
 This defines the `Mul` [Monoid](https://en.wikipedia.org/wiki/Monoid), and its operator.
@@ -186,6 +191,10 @@ instance Mul Unit
   mul = \x y. ()
   one = ()
 
+instance [Mul a] Mul (n->a)
+  mul = \f g. \x. (f x) * (g x)
+  one = \x. one
+
 '#### Integral
 Integer-like things.
 
@@ -348,6 +357,9 @@ instance VSpace Float
 instance {a n} [VSpace a] VSpace (n=>a)
   scaleVec = \s xs. for i. s .* xs.i
 
+instance [VSpace a] VSpace (n->a)
+  scaleVec = \s f. \x. s .* (f x)
+
 instance VSpace Unit
   scaleVec = \_ _. ()
 
@@ -1715,6 +1727,9 @@ Type class for generating example values
 interface Arbitrary a
   arb : Key -> a
 
+instance Arbitrary Bool
+  arb = \key. rand key < 0.5
+
 instance Arbitrary Float32
   arb = randn
 

tests/type-tests.dx

@@ -433,3 +433,16 @@ def q (n : Int) : (Fin n)=>Int =
 
 q 5
 > [0, 2, 4, 6, 8]
+
+'### Tests for function VSpace
+
+:p (sin + cos) 5.0 ~~ (\x. sin x + cos x) 5.0
+> True
+:p (sin * cos) 5.0 ~~ (\x. sin x * cos x) 5.0
+> True
+:p (2.8 .* sin) 5.0 ~~ (\x. 2.8 * sin x) 5.0
+> True
+
+xbool : Bool = arb $ newKey 0
+:p xbool
+> True