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Signed primitive integers defined on top of the existing unsigned ones
with two's complement.
The module Sint63 includes the theory of signed primitive integers that
differs from the unsigned case.
Additions to the kernel:
les (signed <=), lts (signed <), compares (signed compare),
divs (signed division), rems (signed remainder),
asr (arithmetic shift right)
(The s suffix is not used when importing the Sint63 module.)
The printing and parsing of primitive ints was updated and the
int63_syntax_plugin was removed (we use Number Notation instead).
A primitive int is parsed / printed as unsigned or signed depending on
the scope. In the default (Set Printing All) case, it is printed in
hexadecimal.
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Ack-by: SkySkimmer
Ack-by: ppedrot
Reviewed-by: vbgl
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Following a request from Pierre-Marie Pédrot in #13258
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This will enable to define numeral notation on non inductive by using
an inductive type as proxy and those translations to translate to/from
the actual type to the inductive type.
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Add headers to a few files which were missing them.
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Most of these files were introduced after #6543 but used older headers
copied from somewhere else.
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This work makes it possible to take advantage of a compact
representation for integers in the entire system, as opposed to only
in some reduction machines. It is useful for heavily computational
applications, where even constructing terms is not possible without such
a representation.
Concretely, it replaces part of the retroknowledge machinery with
a primitive construction for integers in terms, and introduces a kind of
FFI which maps constants to operators (on integers). Properties of these
operators are expressed as explicit axioms, whereas they were hidden in
the retroknowledge-based approach.
This has been presented at the Coq workshop and some Coq Working Groups,
and has been used by various groups for STM trace checking,
computational analysis, etc.
Contributions by Guillaume Bertholon and Pierre Roux <Pierre.Roux@onera.fr>
Co-authored-by: Benjamin Grégoire <Benjamin.Gregoire@inria.fr>
Co-authored-by: Vincent Laporte <Vincent.Laporte@fondation-inria.fr>
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