Rather than translating the constraints to a Dybjer-Setzer IR code
we can produce an ad-hoc definition of a `Domain` that we will be
able to make runtime irrelevant.
This means that compiled code will never need to construct a proof
that a value is in the domain of the function: it will simply run
the function!
This builds a .o from the generated C, and statically links with the
libidris2_support library. It doesn't yet dynamically link with any
additional libraries.
Written by Volkmar Frinken (@vfrinken). This is intended as a
lightweight (i.e. minimal dependencies) code generator that can be
ported to multiple platforms, especially those with memory constraints.
It shouldn't be expected to be anywhere near as fast as the Scheme back
end, for lots of reasons. The main goal is portability.
Refactor the DIY equational reasoning library to be a bit more like
the generic pre-order reasoning library:
Change the `...` notation into a constructor for a new `Step` datatype.
This seems to help idris disambiguate between the two kinds of
reasoning when they're used in the same file (e.g., frex).
Co-authored-by: Ohad Kammar <ohad.kammar@ed.ac.uk>
Division Theorem. For every natural number `x` and positive natural
number `n`, there is a unique decomposition:
`x = q*n + r`
with `q`,`r` natural and `r` < `n`.
`q` is the quotient when dividing `x` by `n`
`r` is the remainder when dividing `x` by `n`.
This commit adds a proof for this fact, in case
we want to reason about modular arithmetic (for example, when dealing
with binary representations). A future, more systematic, development could
perhaps follow: @clayrat 's (idris1) port of Coq's binary arithmetics:
https://github.com/sbp/idris-bi/blob/master/src/Data/Bin/DivMod.idrhttps://github.com/sbp/idris-bi/blob/master/src/Data/Biz/DivMod.idrhttps://github.com/sbp/idris-bi/blob/master/src/Data/BizMod2/DivMod.idr
In the process, it bulks up the stdlib with:
+ a generic PreorderReasoning module for arbitrary preorders,
analogous for the equational reasoning module
+ some missing facts about Nat operations.
+ Refactor some Nat order properties using a 'reflect' function
Co-authored-by: Ohad Kammar <ohad.kammar@ed.ac.uk>
Co-authored-by: G. Allais <guillaume.allais@ens-lyon.org>
