Problems with recursion and numeric constraints

[ramsdell]

I am playing with the new numeric constraints. I'm trying to write a very silly version of copy that uses recursive descent. However, the obvious way of using numeric constraints fails to type check. I tried other permutations of type annotations, but they all failed. Here is the function:

/* Silly recursive copy */

cpy : {n, a} (fin n) => [2 ^^ n]a -> [2 ^^ n]a
cpy a | n == 0 => a
      | n > 1 => cpy`{n - 1} # cpy`{n - 1}

[ramsdell]

The way to write this with without numeric constraints is:

rec : {n, a} (fin n) => [2 ^^ n]a -> [2 ^^ n]a
rec a =
    if `n == 0 then a
    else coerceSize (l' # r')
  where
    l # r = coerceSize a
    l' = rec`{max 1 n - 1} l
    r' = rec`{max 1 n - 1} r

coerceSize : {m, n, a} [m]a -> [n]a
coerceSize xs = [ xs @ i | i <- [0 .. <n]]

[yav]

@ramsdell you are missing the argument to cpy in the recursive calls, you probably meant to write something like this:

cpy : {n, a} (fin n) => [2 ^^ n]a -> [2 ^^ n]a                                   
cpy a                                                                               
  | n == 0 => a                                                                     
  | n > 1  => (cpy`{n - 1} x # cpy`{n - 1} y)                                    
                  where (x # y) = a

This fails because Cryptol doesn't know that 2 * 2 ^^ (n - 1) == 2 ^^ n

#1381 is related to this issule

[weaversa]

Another issue is that you've defined the function for n==0 and n>1, but not for n==1.

[ramsdell]

Yeah, there was a bit of sloppiness last night. Here is the example that works.

/* Silly recursive copy */

cpy : {n, a} (fin n) => [2 ^^ n]a -> [2 ^^ n]a
cpy a | n == 0 => a
      | n > 0 => coerceSize (l' # r')
                 where
                   l # r = coerceSize a
                   l' = cpy`{max 1 n - 1} l
                   r' = cpy`{max 1 n - 1} r

coerceSize : {m, n, a} [m]a -> [n]a
coerceSize xs = [ xs @ i | i <- [0 .. <n]]

[yav]

I am closing this, as we are tracking the exponentiation issues in #1381 and #704