33 lines
2.0 KiB
TeX
33 lines
2.0 KiB
TeX
\noindent{}A goal shared between all programming languages is to provide a certain level
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of abstraction: an assembly language allows you to abstract from the binary
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instructions and memory positions; Low-level imperial languages, like FORTRAN,
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were the first to allow you to abstract from the processor architecture of the
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target machine; and nowadays writing a program requires little knowledge of the
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actual workings of the hardware on which the program is executed.
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Freuder states that the ``Holy Grail'' of programming languages would be where
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the user merely states the problem, and the computer solves it and that
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\gls{constraint-modelling} is one of the biggest steps towards this goal to
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this day \autocite*{freuder-1997-holygrail}. Different from imperative (and
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even other declarative) languages, in a \cml{} the modeller does not describe
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how to solve the problem, but rather provides the problem requirements. You
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could say that a constraint model actually describes the solution to the
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problem.
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In a constraint model, instead of specifying the manner in which we can find
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the solution, we give a concise description of the problem. We describe what we
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already know, the \parameters{}, what we wish to know, the \variables{}, and
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the relationships that should exist between them, the \constraints{}.
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This type of combinatorial problem is typically called a \gls{csp}. The goal of
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a \gls{csp} is to find values for the \variables{} that satisfy the
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\constraints{} or prove that no such assignment exists. Many \cmls\ also
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support the modelling of \gls{cop}, where a \gls{csp} is augmented with a
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\gls{objective} \(z\). In this case the goal is to find a solution that
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satisfies all \constraints{} while minimising (or maximising) \(z\).
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Although a constraint model does not contain any instructions on how to find a
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suitable solution, these models can generally be given to a dedicated solving
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program, or \solver{} for short, that can find a solution that fits the
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requirements of the model.
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