Janus

Janus is a high level reversible programming language created by Christopher Lutz and Howard Derby [1] as part of a class they taught. It was later discovered and developed further by Yokohama, Gluck et. al [2]. Any program written in it can be run forwards or backwards. A compiler from Janus to PISA was described in [3].

Example

 procedure init(int n, stack list)
  local int q=0
  
  n += 4
  q+=9 push(list,q)
  q+=7 push(list,q)
  q+=1 push(list,q)
  q+=5 push(list,q)
  
  delocal int q=0
 
 procedure makeidperm(int n, stack perm)
  local int i=0
  local int z=0
  
  from  i=0
  do    skip
  loop  push(perm,z)
        perm[i] += i
        i += 1
  until i=n
  i -= n
  
  delocal int z=0
  delocal int i=0
 
 procedure sort(int n, stack list, stack perm)
  local int i=0
  local int j=0
  
  from  i = 0
  do    skip
  loop  j += n-2
        from  j = n-2
        do    skip
        loop  if   list[j] > list[j+1]
              then list[j] <=> list[j+1]
                   perm[j] <=> perm[j+1]
              else skip
              fi   perm[j] > perm[j+1]
              j -= 1
        until j = i-1
        j -= i-1
        i += 1
  until i = n-1
  i -= n-1
  
  delocal int j=0
  delocal int i=0
 
 procedure main(int n, stack list, stack perm)
  call init(n,list)
  call makeidperm(n,perm)
  call sort(n,list,perm)

References

• [1] Janus: a time-reversible language (1986) - The creation of Janus in a Letter from Christopher Lutz to Rolf Landauer.
• JANUS: A TIME-REVERSIBLE LANGUAGE - HTML version of the same letter. (dead link)
• [3] Clean Translation of an Imperative Reversible Programming Language (Axelsen 2011) - Details the compiler from Janus to PISA. (dead link)

• [2] A reversible programming language and its invertible self-interpreter - Tetsuo Yokoyama and Robert Glück. - Defines the term Reversibly-Turing Complete and proves that Janus is including a self interpreter.

External resources

• Program Inversion and Reversible Computation - Modern Janus interpreter in Javascript by Claus Skou Nielsen and Michael Budde.
• An article about Janus on Wikipedia.