UNITY (programming language)
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UNITY is a programming language constructed by K. Mani Chandy and Jayadev Misra for their book Parallel Program Design: A Foundation. It is a theoretical language which focuses on what, instead of where, when or how. The language contains no method of flow control, and program statements run in a nondeterministic way until statements cease to cause changes during execution. This allows for programs to run indefinitely, such as auto-pilot or power plant safety systems, as well as programs that would normally terminate (which here converge to a fixed point).
All statements are assignments, and are separated by
#. A statement can consist of multiple assignments, of the form
a,b,c := x,y,z, or
a := x || b := y || c := z. You can also have a quantified statement list,
<# x,y : expression :: statement>, where x and y are chosen randomly among the values that satisfy expression. A quantified assignment is similar. In
<|| x,y : expression :: statement >, statement is executed simultaneously for all pairs of
y that satisfy expression.
Bubble sort the array by comparing adjacent numbers, and swapping them if they are in the wrong order. Using expected time, processors and expected work. The reason you only have expected time, is that
k is always chosen randomly from . This can be fixed by flipping
Program bubblesort declare n: integer, A: array [0..n-1] of integer initially n = 20 # <|| i : 0 <= i and i < n :: A[i] = rand() % 100 > assign <# k : 0 <= k < 2 :: <|| i : i % 2 = k and 0 <= i < n - 1 :: A[i], A[i+1] := A[i+1], A[i] if A[i] > A[i+1] > > end
You can sort in time with rank-sort. You need processors, and do work.
Program ranksort declare n: integer, A,R: array [0..n-1] of integer initially n = 15 # <|| i : 0 <= i < n :: A[i], R[i] = rand() % 100, i > assign <|| i : 0 <= i < n :: R[i] := <+ j : 0 <= j < n and (A[j] < A[i] or (A[j] = A[i] and j < i)) :: 1 > > # <|| i : 0 <= i < n :: A[R[i]] := A[i] > end
Program shortestpath declare n,k: integer, D: array [0..n-1, 0..n-1] of integer initially n = 10 # k = 0 # <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] = rand() % 100 > assign <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] := min(D[i,j], D[i,k] + D[k,j]) > || k := k + 1 if k < n - 1 end
We can do this even faster. The following programs computes all pairs shortest path in time, using processors and work.
Program shortestpath2 declare n: integer, D: array [0..n-1, 0..n-1] of integer initially n = 10 # <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] = rand() % 10 > assign <|| i,j : 0 <= i < n and 0 <= j < n :: D[i,j] := min(D[i,j], <min k : 0 <= k < n :: D[i,k] + D[k,j] >) > end
After round ,
D[i,j] contains the length of the shortest path from to of length . In the next round, of length , and so on.
- K. Mani Chandy and Jayadev Misra (1988) Parallel Program Design: A Foundation.