n-ary nodes

bar.hvmc

@@ -0,0 +1,3 @@
+
+@bar = (?<#0 #1 R> R)
+@main = R & @bar ~ (#123 R)

examples/sort/bitonic/bitonic_sort_ctr.hvm1

@@ -1,9 +1,9 @@
 // Atomic Swapper (HVM builtin)
-//(Data.U60.swap 0 a b) = (Both a b)
-//(Data.U60.swap n a b) = (Both b a)
+//(U60.swap 0 a b) = (Both a b)
+//(U60.swap n a b) = (Both b a)
 
 // Swaps distant values in parallel; corresponds to a Red Box
-(Warp s (Leaf a)   (Leaf b))   = (Data.U60.swap (^ (> a b) s) (Leaf a) (Leaf b))
+(Warp s (Leaf a)   (Leaf b))   = (U60.swap (^ (> a b) s) (Leaf a) (Leaf b))
 (Warp s (Both a b) (Both c d)) = (Join (Warp s a c) (Warp s b d))
 
 // Rebuilds the warped tree in the original order
@@ -33,4 +33,4 @@
 (Sum (Leaf x))   = x
 (Sum (Both a b)) = (+ (Sum a) (Sum b))
 
-Main = (Sum (Sort 0 (Rev (Gen 18 0))))
+Main = (Sum (Sort 0 (Rev (Gen 19 0))))

examples/sort/bitonic/bitonic_sort_ctr.hvm2

@@ -0,0 +1,40 @@
+
+data Tree = (Leaf a) | (Both a b)
+
+(U60.swap 0 a b) = (Both a b)
+(U60.swap n a b) = (Both b a)
+
+// Swaps distant values in parallel; corresponds to a Red Box
+(Warp s (Leaf a)   (Leaf b))   = (U60.swap (^ (> a b) s) (Leaf a) (Leaf b))
+(Warp s (Both a b) (Both c d)) = (Join (Warp s a c) (Warp s b d))
+(Warp s * *) = *
+
+// Rebuilds the warped tree in the original order
+(Join (Both a b) (Both c d)) = (Both (Both a c) (Both b d))
+(Join * *) = *
+
+// Recursively warps each sub-tree; corresponds to a Blue/Green Box
+(Flow s (Leaf a))   = (Leaf a)
+(Flow s (Both a b)) = (Down s (Warp s a b))
+
+// Propagates Flow downwards
+(Down s (Leaf a))   = (Leaf a)
+(Down s (Both a b)) = (Both (Flow s a) (Flow s b))
+
+// Bitonic Sort
+(Sort s (Leaf a))   = (Leaf a)
+(Sort s (Both a b)) = (Flow s (Both (Sort 0 a) (Sort 1 b)))
+
+// Generates a tree of depth `n`
+(Gen 0 x) = (Leaf x)
+(Gen n x) = let m = (- n 1); (Both (Gen m (* x 2)) (Gen m (+ (* x 2) 1)))
+
+// Reverses a tree
+(Rev (Leaf x))   = (Leaf x)
+(Rev (Both a b)) = (Both (Rev b) (Rev a))
+
+// Sums a tree
+(Sum (Leaf x))   = x
+(Sum (Both a b)) = (+ (Sum a) (Sum b))
+
+Main = (Sum (Sort 0 (Rev (Gen 20 0))))

examples/sort/bitonic/bitonic_sort_ctr.hvmc

@@ -0,0 +1,87 @@
+@Both = (a (b (* ((a (b c)) c))))
+@Down = (a ((@Down$C0 (@Down$C1 (a b))) b))
+@Down$C0 = (a (* b))
+& @Leaf ~ (a b)
+@Down$C1 = (a (b ({3 c d} e)))
+& @Both ~ (f (g e))
+& @Flow ~ (d (b g))
+& @Flow ~ (c (a f))
+@Flow = (a ((@Flow$C0 (@Flow$C1 (a b))) b))
+@Flow$C0 = (a (* b))
+& @Leaf ~ (a b)
+@Flow$C1 = (a (b ({5 c d} e)))
+& @Down ~ (c (f e))
+& @Warp ~ (d (a (b f)))
+@Gen = (?<@Gen$C0 @Gen$C1 (a b)> (a b))
+@Gen$C0 = (a b)
+& @Leaf ~ (a b)
+@Gen$C1 = (<+ #1 <- #1 {9 a b}>> ({7 <* #2 c> <* #2 <+ #1 d>>} e))
+& @Both ~ (f (g e))
+& @Gen ~ (b (d g))
+& @Gen ~ (a (c f))
+@Join = ((@Join$C1 (@Join$C6 (a b))) (a b))
+@Join$C0 = (* *)
+@Join$C1 = (* @Join$C0)
+@Join$C2 = (* *)
+@Join$C3 = (* @Join$C2)
+@Join$C4 = (* @Join$C3)
+@Join$C5 = (a (b (c (d e))))
+& @Both ~ (f (g e))
+& @Both ~ (d (b g))
+& @Both ~ (c (a f))
+@Join$C6 = (a (b ((@Join$C4 (@Join$C5 (a (b c)))) c)))
+@Leaf = (a ((a b) (* b)))
+@Rev = ((@Rev$C0 (@Rev$C1 a)) a)
+@Rev$C0 = (a b)
+& @Leaf ~ (a b)
+@Rev$C1 = (a (b c))
+& @Both ~ (d (e c))
+& @Rev ~ (a e)
+& @Rev ~ (b d)
+@Sort = (a ((@Sort$C0 (@Sort$C3 (a b))) b))
+@Sort$C0 = (a (* b))
+& @Leaf ~ (a b)
+@Sort$C1 = a
+& @Sort ~ (#0 a)
+@Sort$C2 = a
+& @Sort ~ (#1 a)
+@Sort$C3 = (a (b (c d)))
+& @Flow ~ (c (e d))
+& @Both ~ (f (g e))
+& @Sort$C2 ~ (b g)
+& @Sort$C1 ~ (a f)
+@Sum = (((a a) (@Sum$C0 b)) b)
+@Sum$C0 = (a (b c))
+& @Sum ~ (a <+ d c>)
+& @Sum ~ (b d)
+@U60.swap = (?<@U60.swap$C0 @U60.swap$C2 (a (b c))> (a (b c)))
+@U60.swap$C0 = (a (b c))
+& @Both ~ (a (b c))
+@U60.swap$C1 = (a (b c))
+& @Both ~ (b (a c))
+@U60.swap$C2 = (* @U60.swap$C1)
+@Warp = (a ((@Warp$C5 (@Warp$C11 (a (b c)))) (b c)))
+@Warp$C0 = ({11 a b} (c ({13 <> a <^ c d>> e} f)))
+& @U60.swap ~ (d (g (h f)))
+& @Leaf ~ (b h)
+& @Leaf ~ (e g)
+@Warp$C1 = (* *)
+@Warp$C10 = (a (b ({15 c d} (e (f g)))))
+& @Join ~ (h (i g))
+& @Warp ~ (d (f (b i)))
+& @Warp ~ (c (e (a h)))
+@Warp$C11 = (a (b (c ((@Warp$C9 (@Warp$C10 (c (a (b d))))) d))))
+@Warp$C2 = (* @Warp$C1)
+@Warp$C3 = (* @Warp$C2)
+@Warp$C4 = (* @Warp$C3)
+@Warp$C5 = (a (b ((@Warp$C0 (@Warp$C4 (b (a c)))) c)))
+@Warp$C6 = (* *)
+@Warp$C7 = (* @Warp$C6)
+@Warp$C8 = (* @Warp$C7)
+@Warp$C9 = (* @Warp$C8)
+@main = a
+& @Sum ~ (b a)
+& @Sort ~ (#0 (c b))
+& @Rev ~ (d c)
+& @Gen ~ (#19 (#0 d))
+

examples/sort/bitonic/bitonic_sort_lam.hvmc

@@ -36,7 +36,7 @@
 & @sum ~ (b a)
 & @sort ~ (c (#0 b))
 & @rev ~ (d c)
-& @gen ~ (#10 (#0 d))
+& @gen ~ (#16 (#0 d))
 @rev = ((@rev$S0 (@rev$S1 a)) a)
 @rev$S0 = (a b)
 & @Leaf ~ (a b)

examples/sort/radix/radix_sort_ctr.hvm1

@@ -26,30 +26,30 @@
 // Radix : U60 -> Map
 (Radix n) =
   let r = Used
-  let r = (Data.U60.swap (& n 1) r Free)
-  let r = (Data.U60.swap (& n 2) r Free)
-  let r = (Data.U60.swap (& n 4) r Free)
-  let r = (Data.U60.swap (& n 8) r Free)
-  let r = (Data.U60.swap (& n 16) r Free)
-  let r = (Data.U60.swap (& n 32) r Free)
-  let r = (Data.U60.swap (& n 64) r Free)
-  let r = (Data.U60.swap (& n 128) r Free)
-  let r = (Data.U60.swap (& n 256) r Free)
-  let r = (Data.U60.swap (& n 512) r Free)
-  let r = (Data.U60.swap (& n 1024) r Free)
-  let r = (Data.U60.swap (& n 2048) r Free)
-  let r = (Data.U60.swap (& n 4096) r Free)
-  let r = (Data.U60.swap (& n 8192) r Free)
-  let r = (Data.U60.swap (& n 16384) r Free)
-  let r = (Data.U60.swap (& n 32768) r Free)
-  let r = (Data.U60.swap (& n 65536) r Free)
-  let r = (Data.U60.swap (& n 131072) r Free)
-  let r = (Data.U60.swap (& n 262144) r Free)
-  let r = (Data.U60.swap (& n 524288) r Free)
-  let r = (Data.U60.swap (& n 1048576) r Free)
-  let r = (Data.U60.swap (& n 2097152) r Free)
-  let r = (Data.U60.swap (& n 4194304) r Free)
-  let r = (Data.U60.swap (& n 8388608) r Free)
+  let r = (U60.swap (& n 1) r Free)
+  let r = (U60.swap (& n 2) r Free)
+  let r = (U60.swap (& n 4) r Free)
+  let r = (U60.swap (& n 8) r Free)
+  let r = (U60.swap (& n 16) r Free)
+  let r = (U60.swap (& n 32) r Free)
+  let r = (U60.swap (& n 64) r Free)
+  let r = (U60.swap (& n 128) r Free)
+  let r = (U60.swap (& n 256) r Free)
+  let r = (U60.swap (& n 512) r Free)
+  let r = (U60.swap (& n 1024) r Free)
+  let r = (U60.swap (& n 2048) r Free)
+  let r = (U60.swap (& n 4096) r Free)
+  let r = (U60.swap (& n 8192) r Free)
+  let r = (U60.swap (& n 16384) r Free)
+  let r = (U60.swap (& n 32768) r Free)
+  let r = (U60.swap (& n 65536) r Free)
+  let r = (U60.swap (& n 131072) r Free)
+  let r = (U60.swap (& n 262144) r Free)
+  let r = (U60.swap (& n 524288) r Free)
+  let r = (U60.swap (& n 1048576) r Free)
+  let r = (U60.swap (& n 2097152) r Free)
+  let r = (U60.swap (& n 4194304) r Free)
+  let r = (U60.swap (& n 8388608) r Free)
   r
 
 // Reverse : Arr -> Arr

examples/sort/radix/radix_sort_ctr.hvmc

@@ -16,7 +16,7 @@
 & @sum ~ (b a)
 & @sort ~ (c b)
 & @rev ~ (d c)
-& @gen ~ (#20 (#0 d))
+& @gen ~ (#18 (#0 d))
 @merge = (((a a) (@merge$C2 (@merge$C7 (b c)))) (b c))
 @merge$C0 = (* *)
 @merge$C1 = (* @merge$C0)

foo.hvmc

@@ -0,0 +1,32 @@
+@S = (a {2 {2 a b} {2 * b}})
+@Z = {2 * {2 a a}}
+@add$C0 = {2 {2 @add$C0 {2 (a a) (b c)}} (b {2 {2 c d} {2 * d}})}
+@era = ({2 @era$C0 {2 @Z a}} a)
+@era$C0 = {2 {2 @era$C0 {2 @Z a}} a}
+@main = a
+& @era ~ (b a)
+& @pow ~ (c b)
+& @S ~ (d c)
+& @S ~ (e d)
+& @S ~ (f e)
+& @S ~ (g f)
+& @S ~ (h g)
+& @S ~ (i h)
+& @S ~ (j i)
+& @S ~ (k j)
+& @S ~ (l k)
+& @S ~ (m l)
+& @S ~ (n m)
+& @S ~ (o n)
+& @S ~ (p o)
+& @S ~ (q p)
+& @S ~ (r q)
+& @S ~ (s r)
+& @S ~ (t s)
+& @S ~ (u t)
+& @S ~ (v u)
+& @S ~ (w v)
+& @S ~ (x w)
+& @S ~ (@Z x)
+@pow = ({2 @pow$C0 {2 {2 {2 @Z a} {2 * a}} b}} b)
+@pow$C0 = {2 {3 {2 @pow$C0 {2 {2 {2 @Z a} {2 * a}} {2 @add$C0 {2 (b b) (c d)}}}} {2 @pow$C0 {2 {2 {2 @Z e} {2 * e}} c}}} d}

foo.hvml

@@ -0,0 +1,28 @@
+data Nat = (S pred) | Z
+
+add = λx λy
+  match x {
+    Z: y
+    S: (S (add x.pred y))
+  }
+
+pow = λx
+  match x {
+    Z: (S Z)
+    S: (add (pow x.pred) (pow x.pred))
+  }
+
+era = λx
+  match x {
+    Z: Z
+    S: (era x.pred)
+  }
+
+main = (era (pow
+  (S (S
+  (S (S (S (S
+  (S (S (S (S
+  (S (S (S (S
+  (S (S (S (S
+  (S (S (S (S
+  Z))))))))))))))))))))))))

radix_opt.hvmc

@@ -0,0 +1,39 @@
+@Node = (a b (:2:3 a b))
+
+@Single = (a (:1:3 a))
+
+@gen = (?<@Single @gen$C1 a> a)
+
+@gen$C1 = ({7 ?<@Single @gen$C1 (a b)> ?<@Single @gen$C1 (c d)>} <<< #1 {9 a <| #1 c>}> (:2:3 b d))
+
+@main = a
+  & @sum ~ (b a)
+  & @sort ~ (c b)
+  & @rev ~ (d c)
+  & @gen ~ (#18 #0 d)
+
+@merge$C2 = (:0:1 (:1:3) (:1:3) *)
+
+@merge$C6 = (a (b ((:0:1) @merge$C2 @merge$C7 a d) ((:0:1) @merge$C2 @merge$C7 b f) (:2:3 d f)))
+
+@merge$C7 = (a b (:0:1 @Node * @merge$C6 a b))
+
+@radix = ({3 <& #8388608 ?<@Node @swap$C2 (a (:0:3) b)>> <& #4194304 ?<@Node @swap$C2 (c (:0:3) a)>> <& #2097152 ?<@Node @swap$C2 (d (:0:3) c)>> <& #1048576 ?<@Node @swap$C2 (e (:0:3) d)>> <& #524288 ?<@Node @swap$C2 (f (:0:3) e)>> {3 <& #262144 ?<@Node @swap$C2 (g (:0:3) f)>> <& #131072 ?<@Node @swap$C2 (h (:0:3) g)>> <& #65536 ?<@Node @swap$C2 (i (:0:3) h)>> <& #32768 ?<@Node @swap$C2 (j (:0:3) i)>> <& #16384 ?<@Node @swap$C2 (k (:0:3) j)>> <& #8192 ?<@Node @swap$C2 (l (:0:3) k)>> {3 <& #4096 ?<@Node @swap$C2 (m (:0:3) l)>> <& #2048 ?<@Node @swap$C2 (n (:0:3) m)>> <& #1024 ?<@Node @swap$C2 (o (:0:3) n)>> <& #512 ?<@Node @swap$C2 (p (:0:3) o)>> <& #256 ?<@Node @swap$C2 (q (:0:3) p)>> <& #128 ?<@Node @swap$C2 (r (:0:3) q)>> {3 <& #64 ?<@Node @swap$C2 (s (:0:3) r)>> <& #32 ?<@Node @swap$C2 (t (:0:3) s)>> <& #16 ?<@Node @swap$C2 (u (:0:3) t)>> <& #8 ?<@Node @swap$C2 (v (:0:3) u)>> <& #4 ?<@Node @swap$C2 (w (:0:3) v)>> <& #2 ?<@Node @swap$C2 (x (:0:3) w)>> <& #1 ?<@Node @swap$C2 ((:1:3) (:0:3) x)>>}}}} b)
+
+@rev = (:0:1 (:0:3) @Single @rev$C1)
+
+@rev$C1 = (((:0:3) @Single @rev$C1 a) ((:0:3) @Single @rev$C1 b) (:2:3 b a))
+
+@sort = (((:0:3) (@radix @to_map$C1 (:1:4) @Single @to_arr$C2 #0 a)) a)
+
+@sum = (:0:1 #0 (:0:1) @sum$C0)
+
+@sum$C0 = ((#0 (:0:1) @sum$C0 <+ b c>) (#0 (:0:1) @sum$C0 b) c)
+
+@swap$C1 = (a b (:2:3 b a))
+
+@swap$C2 = (* @swap$C1)
+
+@to_arr$C2 = (((:1:4) @Single @to_arr$C2 a b) ((:1:4) @Single @to_arr$C2 c d) {5 <* #2 a> <* #2 <+ #1 c>>} (:2:3 b d))
+
+@to_map$C1 = (((:0:3) (@radix @to_map$C1 (:0:1) @merge$C2 @merge$C7 b c)) ((:0:3) @radix @to_map$C1 b) c)

src/compile.rs

@@ -66,7 +66,7 @@ fn compile_def(code: &mut String, host: &Host, name: &str, instr: &[Instruction]
       Instruction::LinkConst { trg, port } => {
         writeln!(code, "net.link_trg({trg}, Trg::port({}));", compile_port(host, port))
       }
-      Instruction::Ctr { lab, trg, lft, rgt } => {
+      Instruction::Ctr2 { lab, trg, lft, rgt } => {
         writeln!(code, "let ({lft}, {rgt}) = net.do_ctr({lab}, {trg});")
       }
       Instruction::Op { op, trg, rhs, out } => {
@@ -75,12 +75,13 @@ fn compile_def(code: &mut String, host: &Host, name: &str, instr: &[Instruction]
       Instruction::OpNum { op, trg, rhs, out } => {
         writeln!(code, "let {out} = net.do_op_num({op:?}, {trg}, {rhs});")
       }
-      Instruction::Mat { trg, lft, rgt } => {
-        writeln!(code, "let ({lft}, {rgt}) = net.do_mat({trg});")
+      Instruction::Mat { trg, zero, succ, out } => {
+        writeln!(code, "let ({zero}, {succ}, {out}) = net.do_mat({trg});")
       }
       Instruction::Wires { av, aw, bv, bw } => {
         writeln!(code, "let ({av}, {aw}, {bv}, {bw}) = net.do_wires();")
       }
+      _ => todo!(),
     }?;
   }
   writeln!(code, "}}")?;