ersatz-0.3: A monad for expressing SAT or QSAT problems using observable sharing.

A monad for expressing SAT or QSAT problems using observable sharing.

For example, we can express a full-adder with:

full_adder :: Bit -> Bit -> Bit -> (Bit, Bit)
full_adder a b cin = (s2, c1 || c2)
  where (s1,c1) = half_adder a b
        (s2,c2) = half_adder s1 cin

half_adder :: Bit -> Bit -> (Bit, Bit)
half_adder a b = (a `xor` b, a && b)

Longer Examples

Included are a couple of examples included with the distribution. Neither are as fast as a dedicated solver for their respective domains, but they showcase how you can solve real world problems involving 10s or 100s of thousands of variables and constraints with ersatz.

ersatz-sudoku

% time ersatz-sudoku
Problem:
┌───────┬───────┬───────┐
│ 5 3   │   7   │       │
│ 6     │ 1 9 5 │       │
│   9 8 │       │   6   │
├───────┼───────┼───────┤
│ 8     │   6   │     3 │
│ 4     │ 8   3 │     1 │
│ 7     │   2   │     6 │
├───────┼───────┼───────┤
│   6   │       │ 2 8   │
│       │ 4 1 9 │     5 │
│       │   8   │   7 9 │
└───────┴───────┴───────┘
Solution:
┌───────┬───────┬───────┐
│ 5 3 4 │ 6 7 8 │ 9 1 2 │
│ 6 7 2 │ 1 9 5 │ 3 4 8 │
│ 1 9 8 │ 3 4 2 │ 5 6 7 │
├───────┼───────┼───────┤
│ 8 5 9 │ 7 6 1 │ 4 2 3 │
│ 4 2 6 │ 8 5 3 │ 7 9 1 │
│ 7 1 3 │ 9 2 4 │ 8 5 6 │
├───────┼───────┼───────┤
│ 9 6 1 │ 5 3 7 │ 2 8 4 │
│ 2 8 7 │ 4 1 9 │ 6 3 5 │
│ 3 4 5 │ 2 8 6 │ 1 7 9 │
└───────┴───────┴───────┘
ersatz-sudoku  1,13s user 0,04s system 99% cpu 1,179 total

ersatz-regexp-grid

This solves the "regular crossword puzzle" (grid.pdf) from the 2013 MIT mystery hunt.

% time ersatz-regexp-grid

SPOILER

ersatz-regexp-grid  2,45s user 0,05s system 99% cpu 2,502 total

Modules

Ersatz