theory Code_Prolog_Examples
imports "~~/src/HOL/Library/Code_Prolog"
begin
section \<open>Example append\<close>
inductive append
where
"append [] ys ys"
| "append xs ys zs ==> append (x # xs) ys (x # zs)"
setup \<open>Code_Prolog.map_code_options (K
{ensure_groundness = false,
limit_globally = NONE,
limited_types = [],
limited_predicates = [],
replacing = [],
manual_reorder = []})\<close>
values_prolog "{(x, y, z). append x y z}"
values_prolog 4 "{(z, x, y). append x y ((1::nat) # (2 # (3 # z)))}"
values_prolog 3 "{(x, y, z). append x y z}"
setup \<open>Code_Prolog.map_code_options (K
{ensure_groundness = false,
limit_globally = NONE,
limited_types = [],
limited_predicates = [],
replacing = [],
manual_reorder = []})\<close>
values_prolog "{(x, y, z). append x y z}"
setup \<open>Code_Prolog.map_code_options (K
{ensure_groundness = false,
limit_globally = NONE,
limited_types = [],
limited_predicates = [],
replacing = [],
manual_reorder = []})\<close>
section \<open>Example queens\<close>
inductive nodiag :: "int => int => int list => bool"
where
"nodiag B D []"
| "D \<noteq> N - B ==> D \<noteq> B - N ==> Da = D + 1 ==> nodiag B Da L ==> nodiag B D (N # L)"
text \<open>
qdelete(A, [A|L], L).
qdelete(X, [A|Z], [A|R]) :-
qdelete(X, Z, R).
\<close>
inductive qdelete :: "int => int list => int list => bool"
where
"qdelete A (A # L) L"
| "qdelete X Z R ==> qdelete X (A # Z) (A # R)"
text \<open>
qperm([], []).
qperm([X|Y], K) :-
qdelete(U, [X|Y], Z),
K = [U|V],
qperm(Z, V).
\<close>
inductive qperm :: "int list => int list => bool"
where
"qperm [] []"
| "qdelete U (X # Y) Z ==> qperm Z V ==> qperm (X # Y) (U # V)"
text \<open>
safe([]).
safe([N|L]) :-
nodiag(N, 1, L),
safe(L).
\<close>
inductive safe :: "int list => bool"
where
"safe []"
| "nodiag N 1 L ==> safe L ==> safe (N # L)"
text \<open>
queen(Data, Out) :-
qperm(Data, Out),
safe(Out)
\<close>
inductive queen :: "int list => int list => bool"
where
"qperm Data Out ==> safe Out ==> queen Data Out"
inductive queen_9
where
"queen [1,2,3,4,5,6,7,8,9] ys ==> queen_9 ys"
values_prolog 10 "{ys. queen_9 ys}"
section \<open>Example symbolic derivation\<close>
hide_const Pow
datatype expr = Log expr | Mult expr expr | Div expr expr | x | Num int | Plus expr expr
| Minus expr expr | Uminus expr | Pow expr int | Exp expr
text \<open>
d(U + V, X, DU + DV) :-
cut,
d(U, X, DU),
d(V, X, DV).
d(U - V, X, DU - DV) :-
cut,
d(U, X, DU),
d(V, X, DV).
d(U * V, X, DU * V + U * DV) :-
cut,
d(U, X, DU),
d(V, X, DV).
d(U / V, X, (DU * V - U * DV) / ^(V, 2)) :-
cut,
d(U, X, DU),
d(V, X, DV).
d(^(U, N), X, DU * num(N) * ^(U, N1)) :-
cut,
N1 is N - 1,
d(U, X, DU).
d(-U, X, -DU) :-
cut,
d(U, X, DU).
d(exp(U), X, exp(U) * DU) :-
cut,
d(U, X, DU).
d(log(U), X, DU / U) :-
cut,
d(U, X, DU).
d(x, X, num(1)) :-
cut.
d(num(_), _, num(0)).
\<close>
inductive d :: "expr => expr => expr => bool"
where
"d U X DU ==> d V X DV ==> d (Plus U V) X (Plus DU DV)"
| "d U X DU ==> d V X DV ==> d (Minus U V) X (Minus DU DV)"
| "d U X DU ==> d V X DV ==> d (Mult U V) X (Plus (Mult DU V) (Mult U DV))"
| "d U X DU ==> d V X DV ==> d (Div U V) X (Div (Minus (Mult DU V) (Mult U DV)) (Pow V 2))"
| "d U X DU ==> N1 = N - 1 ==> d (Pow U N) X (Mult DU (Mult (Num N) (Pow U N1)))"
| "d U X DU ==> d (Uminus U) X (Uminus DU)"
| "d U X DU ==> d (Exp U) X (Mult (Exp U) DU)"
| "d U X DU ==> d (Log U) X (Div DU U)"
| "d x X (Num 1)"
| "d (Num n) X (Num 0)"
text \<open>
ops8(E) :-
d((x + num(1)) * ((^(x, 2) + num(2)) * (^(x, 3) + num(3))), x, E).
divide10(E) :-
d(((((((((x / x) / x) / x) / x) / x) / x) / x) / x) / x, x, E).
log10(E) :-
d(log(log(log(log(log(log(log(log(log(log(x)))))))))), x, E).
times10(E) :-
d(((((((((x * x) * x) * x) * x) * x) * x) * x) * x) * x, x, E)
\<close>
inductive ops8 :: "expr => bool"
where
"d (Mult (Plus x (Num 1)) (Mult (Plus (Pow x 2) (Num 2)) (Plus (Pow x 3) (Num 3)))) x e ==> ops8 e"
inductive divide10
where
"d (Div (Div (Div (Div (Div (Div (Div (Div (Div x x) x) x) x) x) x) x) x) x) x e ==> divide10 e"
inductive log10
where
"d (Log (Log (Log (Log (Log (Log (Log (Log (Log (Log x)))))))))) x e ==> log10 e"
inductive times10
where
"d (Mult (Mult (Mult (Mult (Mult (Mult (Mult (Mult (Mult x x) x) x) x) x) x) x) x) x) x e ==> times10 e"
values_prolog "{e. ops8 e}"
values_prolog "{e. divide10 e}"
values_prolog "{e. log10 e}"
values_prolog "{e. times10 e}"
section \<open>Example negation\<close>
datatype abc = A | B | C
inductive notB :: "abc => bool"
where
"y \<noteq> B \<Longrightarrow> notB y"
setup \<open>Code_Prolog.map_code_options (K
{ensure_groundness = true,
limit_globally = NONE,
limited_types = [],
limited_predicates = [],
replacing = [],
manual_reorder = []})\<close>
values_prolog 2 "{y. notB y}"
inductive notAB :: "abc * abc \<Rightarrow> bool"
where
"y \<noteq> A \<Longrightarrow> z \<noteq> B \<Longrightarrow> notAB (y, z)"
values_prolog 5 "{y. notAB y}"
section \<open>Example prolog conform variable names\<close>
inductive equals :: "abc => abc => bool"
where
"equals y' y'"
values_prolog 1 "{(y, z). equals y z}"
end