module Repmin where

data Root = Top Tree
data Tree = Bin Tree Tree | Leaf Int

sem_Tree (Leaf val) = sem_Leaf val
sem_Tree (Bin left right) = sem_Bin (sem_Tree left) (sem_Tree right)
sem_Root (Top top) = sem_Top (sem_Tree top)

sem_Leaf val = \lhs_gmin -> 
  let lhs_lmin = val
      lhs_repl = Leaf lhs_gmin
  in (lhs_lmin, lhs_repl)

sem_Bin left right = \lhs_gmin ->
  let (left_lmin, left_repl)    = left lhs_gmin
      (right_lmin, right_repl)  = right lhs_gmin
      lhs_lmin = left_lmin `min` right_lmin
      lhs_repl = Bin left_repl right_repl
  in (lhs_lmin, lhs_repl)

sem_Top top = lhs_repl where
  (top_lmin, top_repl) = top top_gmin
  top_gmin  = top_lmin
  lhs_repl  = top_repl