From 49960d8950d001a372a0abde670a66ee60026957 Mon Sep 17 00:00:00 2001 From: Shinya Sato Date: Tue, 5 Mar 2024 18:19:27 +0900 Subject: v0.12.0 --- sample/AckSZ-3_5.in | 49 ------------------------------------------------- 1 file changed, 49 deletions(-) delete mode 100644 sample/AckSZ-3_5.in (limited to 'sample/AckSZ-3_5.in') diff --git a/sample/AckSZ-3_5.in b/sample/AckSZ-3_5.in deleted file mode 100644 index 4f41966..0000000 --- a/sample/AckSZ-3_5.in +++ /dev/null @@ -1,49 +0,0 @@ -// Ackermann function on unary natural numbers - -// Originally the function is written as follows: -// fun ack(0,y) = y+1 -// | ack(x,0) = ack(x-1,1) -// | ack(x,y) = ack(x-1,ack(x,y-1)); - -// This is written one on unary natural nunbers: -// fun ack(Z , y) = S(y) -// | ack(S(x), Z) = ack(x,S(Z)) -// | ack(S(x), S(y)) = ack(x,ack(S(x),y)); - -// For easily translation to interaction nets, -// the first argument will be moved to the last: -// fun ack(y, Z) = S(y) -// | ack(Z, S(x)) = ack(S(Z),x) -// | ack(S(y), S(x)) = ack(ack(y,S(x)),x); - -// It is traslated directly as follows: -// ack(r,y)>< Z => r~S(y); -// ack(r,y)>< S(x) => ack_Sx(r, x)~y; -// ack_Sx(r,x)>< Z => ack(r, S(Z))~x; -// ack_Sx(r,x)>< S(y) => Dup(x1,x2)~x, ack(r,cnt)~x1, ack(cnt,y)~S(x2); - -// The last connection can be optimised by applying the rule ack>< Z => r~S(y); -ack(r,y)>< S(x) => ack_Sx(r, x)~y; -ack_Sx(r,x)>< Z => ack(r, S(Z))~x; -ack_Sx(r,x)>< S(y) => Dup(x1,x2)~x, ack(r,cnt)~x1, ack_Sx(cnt,x2)~y; - - -// By the way, it is possible to write it by using abbreviation notation: -// ack(r,y)>< Z => r~S(y); -// ack(r,y)>< S(x) => r<< Z => r<< S(y) => x1,x2<< Z => a1~Z, a2~Z; -// Dup(a1,a2)>< S(x) => a1~S(w1), a2~S(w2), Dup(w1,w2)~x; - -// ack(result, y)~x -// For computation `ack 3 5', it is written as follows: -ack(result, S(S(S(S(S(Z))))))~S(S(S(Z))); - -prnat result; -exit; -- cgit v1.2.3