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mpsh can perform various set theory operations on the output of programs, specified by special characters after pipes. Seperate lines of the text are parsed as set elements. For instance: the intersection of two commands includes only the lines that appear in the output of both commands:

```mpsh\$ ls dir1 |^ ls dir2
```

(Bear in mind that this follows set theory, not simple text filtering, so duplicates and original order are not maintained.)

You can treat the text output of any command as a set, or enter sets directly using curly braces (but with spaces instead of commas):

```mpsh\$ { red green } |U { blue orange }
```

```mpsh\$ ls |- { *.o }
```

The basic set theory operations are:

 Union: |U Intersection: |^ Difference: |\ Synonym for difference: |- Symmetric difference: |o

You can also execute commands conditionally based on set theory tests.

If A is a subset of B, execute C:

```mpsh\$ command-a |< command-b ; command-c
```

If B is a subset of A, execute C:

```mpsh\$ command-a |> command-b ; command-c
```

If A equals B, execute C:

```mpsh\$ command-a |= command-b ; command-c
```

```mpsh\$ { red } |< { red green blue } ; echo red is a subset of rgb.
red is a subset of rgb.
```

Some more examples - take the intersection of *.c with the union of the outputs of command1 and command2, then send that to the sort command:

```mpsh\$ command1 |U command2 |^ { *.c } | sort
```

Open gimp with all the jpg's in the current directory, except *t.jpg:

```mpsh\$ gimp ( { *.jpg } |- { *t.jpg } )
```

The set theory operators are a bit superficial. Sets are deduplicated but subsets aren't, etc. Does not support infinite sets.