I slightly learn Prolog for the design of ATS3.
My opinion is following:
## Variable is useful
```
$ cat family.pl
father(naoyuki, hyogo).
father(saburo, naoyuki).
father(saburo, shinji).
father(yoshihisa, hisako).
mother(hisako, hyogo).
mother(yoko, naoyuki).
mother(yoko, shinji).
mother(nobuko, hisako).
$ swipl
?- [family].
true.
?- father(F, hyogo), father(G, F).
F = naoyuki,
G = saburo.
```
Does ATS2 have such variable to prove something already?
## `spy` is useful
```
$ cat fact.pl
fact(0, 1).
fact(N, F) :-
N > 0,
N1 is N-1,
fact(N1, F1),
F is N*F1.
$ swipl
?- [fact].
true.
?- spy(fact).
% Spy point on fact/2
true.
[debug] ?- fact(10,F).
* Call: (8) fact(10, _828) ? creep
Call: (9) 10>0 ? creep
Exit: (9) 10>0 ? creep
Call: (9) _1052 is 10+ -1 ? creep
Exit: (9) 9 is 10+ -1 ? creep
* Call: (9) fact(9, _1054) ? creep
Call: (10) 9>0 ? creep
Exit: (10) 9>0 ? creep
Call: (10) _1058 is 9+ -1 ? creep
Exit: (10) 8 is 9+ -1 ? creep
* Call: (10) fact(8, _1060) ? creep
Call: (11) 8>0 ? creep
Exit: (11) 8>0 ? creep
Call: (11) _1064 is 8+ -1 ? creep
Exit: (11) 7 is 8+ -1 ? EOF: exit
```
There will be some debugger for proof things of ATS3?
Or symbolic execution such like https://github.com/verifast/verifast
is also useful.
## Compressed description of specification
```
$ cat nat.pl
nat(0).
nat(s(X)) :- nat(X).
plus(0, Y, Y).
plus(s(X), Y, s(Z)) :- plus(X, Y, Z).
le(X, Y) :- plus(X, _, Y).
lt(X, Y) :- le(s(X), Y).
quot(X, Y, 0, X) :- lt(X, Y).
quot(X, Y, s(Q), R) :- plus(Y, X1, X), quot(X1, Y, Q, R).
dnd(M, N) :- quot(N, M, _, s(_)).
df(s(0), _).
df(s(s(M)), N) :- dnd(s(s(M)), N), df(s(M), N).
prime(s(X)) :- df(X, s(X)).
$ swipl
?- [nat].
true.
?- nat(N), prime(N).
N = s(s(0))
```
`nat(N), prime(N).` is very smart description of specification.
Regards,
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