// symb ::= 'a' | 't' | 'c' | 'g'

// input : nat -> char -> type   
// output : nat -> char -> type

// dist : nat -> nat -> nat -> type
// dist(i,o,cost) means the edit distance between
//                  input from position i to the end and
//                  output from position o to the end 
//                is cost

// insert costs 100
// delete costs 10
// modify costs 1

// The relation \ttt{ADD(c1,c2,c3)} means that \ttt{c3} is the sum of the
// integers \ttt{c1} and \ttt{c2}.



// TASK:  

// Rule 1: \ttt{i} and \ttt{o} are at the end of the respective strings
//   Use inputdone(?i) and outputdone(?o) to check this.

// Rule 2: The characters at \ttt{i} and \ttt{o} are the same

// Rule 3: The characters at \ttt{i} and \ttt{o} are not the same (use \ttt{?ichar != ?ochar})

// Rule 4: The character at \ttt{i} is deleted

// Rule 5: The character at \ttt{o} is inserted


// ----------------------------------------------------------------------

input(zero(),'a').
input(succ(zero()),'t').
input(succ(succ(zero())),'c').

output(zero(),'a').
output(succ(zero()),'g').
output(succ(succ(zero())),'c').
output(succ(succ(succ(zero()))),'t').

// identifies the end of the input and output strings (should be equal to the length)
outputdone(succ(succ(succ(succ(zero()))))).
inputdone(succ(succ(succ(zero())))).

// SHOULD BE: (101) (102) (103) (211) (210) (212) (320) (321) (430)
?- dist(zero(),zero(),?c).