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Add support for evaluation of type-level natural numbers.Iavor S. Diatchki <iavor.diatchki@gmail.com>Fri, 13 Sep 2013 06:19:21 +0000https://git.haskell.org/ghc.git/commitdiff/1f77a5341cbd6649a6bc2af868002728cd79b9d7
https://git.haskell.org/ghc.git/commitdiff/1f77a5341cbd6649a6bc2af868002728cd79b9d7
Add support for evaluation of type-level natural numbers.
Add support for evaluation of type-level natural numbers.
This patch implements some simple evaluation of type-level expressions
featuring natural numbers. We can evaluate *concrete* expressions that
use the built-in type families (+), (*), (^), and (<=?), declared in
GHC.TypeLits. We can also do some type inference involving these
functions. For example, if we encounter a constraint such as `(2 + x) ~ 5`
we can infer that `x` must be 3. Note, however, this is used only to
resolve unification variables (i.e., as a form of a constraint improvement)
and not to generate new facts. This is similar to how functional
dependencies work in GHC.
The patch adds a new form of coercion, `AxiomRuleCo`, which makes use
of a new form of axiom called `CoAxiomRule`. This is the form of evidence
generate when we solve a constraint, such as `(1 + 2) ~ 3`.
The patch also adds support for built-in type-families, by adding a new
form of TyCon rhs: `BuiltInSynFamTyCon`. such built-in type-family
constructors contain a record with functions that are used by the
constraint solver to simplify and improve constraints involving the
built-in function (see `TcInteract`). The record in defined in `FamInst`.
The type constructors and rules for evaluating the type-level functions
are in a new module called `TcTypeNats`.