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Diffstat (limited to '')
| -rw-r--r-- | sample/nqueenSZ.in | 228 |
1 files changed, 228 insertions, 0 deletions
diff --git a/sample/nqueenSZ.in b/sample/nqueenSZ.in new file mode 100644 index 0000000..af3c97f --- /dev/null +++ b/sample/nqueenSZ.in @@ -0,0 +1,228 @@ +// N-Queen on unary natural numbers +// +// The original is written as a Lisp program in the following file: +// https://www.istc.kobe-u.ac.jp/activity/mage/m27/27_Lisp.pdf + + +// --------------------------------------- +// eq +// equality between unary natural numbers numbers +// r << eq(m, n) +// --------------------------------------- +eq(r,m) >< Z => eqZ(r)~m; +eq(r,m) >< S(x) => eqS(r,x)~m; + +eqZ(r) >< Z => r~True; +eqZ(r) >< S(x) => r~False, Eraser~x; + +eqS(r,x) >< Z => r~False, Eraser~x; +eqS(r,x) >< S(y) => eq(r,y)~x; + + + +// --------------------------------------- +// r, m1, n1 << eq_stream(m,n) +// --------------------------------------- +eq_stream(r,m1,n1, m) >< Z => eqZ_stream(r,m1,n1)~m; +eq_stream(r,m1,n1, m) >< S(n) => n1~S(w), eqS_stream(r,m1,w, n)~m; + +eqZ_stream(r,m1,n1) >< Z => r~True, m1~Z, n1~Z; +eqZ_stream(r,m1,n1) >< S(m) => r~False, m1~S(m), n1~Z; + + +eqS_stream(r,m1,n1, n) >< Z => r~False, m1~Z, n1~n; +eqS_stream(r,m1,n1, n) >< S(m) => m1~S(w), eq_stream(r,w , n1, m)~n; + + + + + +// --------------------------------------- +// member +// r, m1, list1 << member(m, list) +// --------------------------------------- +// fun member x [] = false +// | member x (y::ys) = if x=y then true else (member x ys); + +member(r, m1, list1, m) >< [] => + r~False, m1~m, list1~[]; + +member(r, m1, list1, m) >< n:ys => + eq_result, m2, n2 << eq_stream(m,n), + list1~n2:cnt, + member1(r, m1, cnt, m2, ys) ~ eq_result; + + +member1(r, m1, list1, m2, ys) >< True => + r~True, m1~m2, list1~ys; + +member1(r, m1, list1, m2, ys) >< False => + member(r, m1, list1, m2) ~ys; + + +// member(r,m1,list1, S(Z)) ~ [S(S(Z)), S(Z)]; + + + + +// --------------------------------------- +// len_list (stream version) +// len, done << len_list(list) +// --------------------------------------- + +len_list(len, done) >< [] => + len~Z, done~[]; +len_list(len, done) >< x:xs => + done~x:cnt, + len_list_(len, cnt, S(Z))~xs; + +len_list_(len, done, ct) >< [] => + len~ct, done~[]; +len_list_(len, done, ct) >< x:xs => + done~x:cnt, + len_list_(len, cnt, S(ct)) ~ xs; + + +// --------------------------------------- +// len (non-stream version) +// ret << len(list) +// --------------------------------------- + +len(ret) >< [] => + ret~Z; +len(ret) >< x:xs => + len_list(ret, Eraser)~x:xs; + + + +/** + * threat (stream version) + * check for (0,q) and (k, qpos[col=k]) where k=1... + * http://www.nct9.ne.jp/m_hiroi/func/haskell06.html + 0 1 2 --> + +------------- + 1| . . . . . . + 2| . . . -3. . 5 - 3 = 2 + 3| . . -2. . . 5 - 2 = 3 + 4| . -1. . . . 5 - 1 = 4 + 5| Q . . . . . Q position is 5 + 6| . +1. . . . 5 + 1 = 6 + 7| . . +2. . . 5 + 2 = 7 + 8| . . . +3. . 5 + 2 = 8 + +------------- + * r, board_done << threat(k,m, board) + * return + * r: True if threat conditions are satisfied + * done: the same to `board' + */ +// fun threat k m [] = false +// | threat k m (x::xs) = +// if (k = x-m) orelse (k = x+m) then true +// else (threat (k+1) m xs); + + + +// r << diff(m,n) +diff(r,m) >< Z => r~m; +diff(r,m) >< S(n) => diff_S(r,n)~m; +diff_S(r, n) >< Z => r~S(n); +diff_S(r, n) >< S(m) => diff(r,m)~n; + + + +threat(r, done, k, q) >< [] => + r~False, done~[], Eraser~k, Eraser~q; + +threat(r, done, k, q) >< x:xs => + x1,x2 << Dup(x), + q1,q2 << Dup(q), + diff_xq << diff(x1,q1), + k1,k2 << Dup(k), + eq_ret << eq(k1, diff_xq), + threat1(r, done, k2, q2 , x2:xs)~eq_ret; + +threat1(r, done, k, q, xxs) >< True => + r~True, done~xxs, Eraser~k, Eraser~q; + +threat1(r, done, k, q, xxs) >< False => + x1:xs1 ~ xxs, + done~x1:cnt, threat(r, cnt, S(k), q)~xs1; + + +// fun queen1 b n 0 = [] +// | queen1 b n m = +// if (member m b) orelse (threat 1 m b) then (queen1 b n (m-1)) +// else if (length b) = (n-1) then (m::b)::(queen1 b n (m-1)) +// else (queen1 (m::b) n n) @ (queen1 b n (m-1)); +// fun queen n = queen1 n [] n; + +queen(ret, n) >< () => + n1, n2 << Dup(n), + queen_(ret, [], n1)~n2; + + +queen_(r, b, n) >< Z => + r~[], Eraser~b, Eraser~n; + +queen_(r, b, n) >< S(m) => + mem_ret, done_m, done_b << member(S(m), b), + queen__chk_m_in_b(r, done_b, n, done_m)~mem_ret; + + +dec(r)><Z => r~Z; +dec(r)><S(n) => r~n; + +queen__chk_m_in_b(r, b, n, m) >< True => + m1 << dec(m), + queen_(r, b, n)~m1; + +queen__chk_m_in_b(r, b, n, m) >< False => + m1,m2 << Dup(m), + th_ret, done_b << threat(S(Z), m1, b), + queen__chk_threat(r, done_b, n, m2)~th_ret; + + + +queen__chk_threat(r, b, n, m) >< True => + m_dec << dec(m), + queen_(r, b, n)~m_dec; + +queen__chk_threat(r, b, n, m) >< False => + len_ret, done_b << len_list(b), + queen__chk_lastelem(r, done_b, n, m, len_ret)~(); + + + +queen__chk_lastelem(r, b, n, m, len_ret) >< () => + n1,nn << Dup(n), + n_dec << dec(nn), + eq_ret << eq(len_ret, n_dec), + queen__chk_lastelem2(r, b, n1, m) ~ eq_ret; + + +queen__chk_lastelem2(r,b,n, m) >< True => + b1, b2 << Dup(b), + m1, mm << Dup(m), + m_dec << dec(mm), + r~(m1:b1):cnt, queen_(cnt, b2, n)~m_dec; + +queen__chk_lastelem2(r,b,n, m) >< False => + b1, b2 << Dup(b), + r << Append(cnt1, cnt2), + n1, Dup(n2,n3) << Dup(n), + m1, mm << Dup(m), + m_dec << dec(mm), + queen_(cnt1, m1:b1, n1)~n2, queen_(cnt2, b2, n3)~m_dec; + + + +// ---------------------------------------------------------- +// main +// ---------------------------------------------------------- +n~S(S(S(S(S(S(S(S(Z)))))))), // 8 +//n~S(S(S(S(S(S(S(S(S(Z))))))))), // 9 +//n~S(S(S(S(Z)))), // 4 +//n~S(Z), // 1 + +queen(ret,n)~(), len(count)~ret; +prnat count; // count ->92 when n=8
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