// 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

dist(?i, ?o, 0) :-
	inputdone(?i),
	outputdone(?o).

dist(?i,?o,?c) :-
	dist(?i,succ(?o),?cost),
	ADD(?cost, 100, ?c).

dist(?i,?o,?c) :-
	dist(succ(?i),?o,?cost),
	ADD(?cost, 10, ?c).

dist(?i,?o,?c) :-
	dist(succ(?i),succ(?o),?cost),
	input(?i,?ichar),
	output(?o,?ochar),
	?ichar != ?ochar,
	ADD(?cost,1,?c).

dist(?i,?o,?c) :-
	dist(succ(?i),succ(?o),?c),
	input(?i,?char),
	output(?o,?char).


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

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())))).

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