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History Types | ||
============= | ||
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In order to improve the expressivity of Kind 2's specification language, | ||
the tool provides a built-in type constructor that allows users to | ||
refer to an `unbounded` number of previous values of a stream. | ||
Specifically, the unary type constructor ``history(x)``, that | ||
takes a stream ``x`` of arbitrary type ``T`` as its single argument, | ||
represents the set of all streams ``z`` of values of type ``T`` such that | ||
at any time ``t >= 0``, there exists a ``k`` in the interval ``[0, t]`` such that | ||
``z(t) = x(k)``. | ||
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For instance, given a node with an input stream ``x`` and an output | ||
stream ``y``, both with the same type, the property `the current value of stream y | ||
equals the current value or a previous value of a stream x plus one` | ||
can't be expressed in Lustre. However, using the type constructor | ||
``history``, one can easily express the property as | ||
``exists (z: history(x)) y=z+1``. | ||
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Notice that ``history(x)`` denotes a refinement type, | ||
suggesting its applicability wherever a type is expected in the model. | ||
However, at present, the implementation restricts the use of the | ||
type constructor ``history`` to the type of a quantified variable. | ||
We plan to lift this restriction in future versions of Kind 2. |
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