copilot-libraries-2.2.0: Libraries for the Copilot language.

Copyright (c) 2011 National Institute of Aerospace / Galois, Inc. Safe Haskell2010

Copilot.Library.LTL

Description

Bounded Linear Temporal Logic (LTL) operators. For a bound `n`, a property `p` holds if it holds on the next `n` transitions (between periods). If `n == 0`, then the trace includes only the current period. For example,

```  eventually 3 p
```

holds if `p` holds at least once every four periods (3 transitions).

Interface: See `Examples/LTLExamples.hs` in the Copilot repository.

You can embed an LTL specification within a Copilot specification using the form:

```  operator spec
```

For some properties, stream dependencies may not allow their specification. In particular, you cannot determine the "future" value of an external variable. In general, the Copilot.Library.PTLTL library is probably more useful.

Synopsis

# Documentation

Property `s` holds at the next period. For example:

```          0 1 2 3 4 5 6 7
s      => F F F T F F T F ...
next s => F F T F F T F ...
```

Note: s must have sufficient history to `drop` a value from it.

Arguments

 :: Integral a => a `n` -> Stream Bool `s` -> Stream Bool

Property `s` holds at some period in the next `n` periods. If `n == 0`, then `s` holds in the current period. We require `n >= 0`. E.g., if ```p = eventually 2 s```, then we have the following relationship between the streams generated:

```s => F F F T F F F T ...
p => F T T T F T T T ...
```

always :: Integral a => a -> Stream Bool -> Stream Bool Source

Property `s` holds for the next `n` periods. We require `n >= 0`. If ```n == 0```, then `s` holds in the current period, e.g., if `p = always 2 s`, then we have the following relationship between the streams generated:

```     0 1 2 3 4 5 6 7
s => T T T F T T T T ...
p => T F F F T T ...
```

until :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool Source

`until n s0 s1` means that `eventually n s1`, and up until at least the period before `s1` holds, `s0` continuously holds.

release :: Integral a => a -> Stream Bool -> Stream Bool -> Stream Bool Source

`release n s0 s1` means that either `always n s1`, or `s1` holds up to and including the period at which `s0` becomes true.