This has a much better behaviour with respect to proof search and
the coverage checker realising we don't need to consider the Z case
than the `Not (x = Z)` we used earlier.
We've always just used 0, which isn't correct if the function is going
to be used in a runtime pattern match. Now calculate correctly so that
we're explicit about which type level variables are used at runtime.
This might cause some programs to fail to compile, if they use functions
that calculate Pi types. The solution is to make those functions
explicitly 0 multiplicity. If that doesn't work, you may have been
accidentally trying to use compile-time only data at run time!
Fixes#1163
This is an alternative to using `fastUnpack` and `fastPack` to work
on lists of characters.
Using this to refactor the lexer and benchmarking the resulting
compiler on building idris2 shows it's 3 to 5s slower than the
current implementation that goes via `List Char`.
This may be backend-dependent so I still push this to contrib,
with the plan of running further benchmarks in the future.
It's disappointing to have to do this, but I think necessary because
various issue reports have shown it to be unsound (at least as far as
inference goes) and, at the very least, confusing. This patch brings us
back to the basic rules of QTT.
On the one hand, this makes the 1 multiplicity less useful, because it
means we can't flag arguments as being used exactly once which would be
useful for optimisation purposes as well as precision in the type. On
the other hand, it removes some complexity (and a hack) from
unification, and has the advantage of being correct! Also, I still
consider the 1 multiplicity an experiment.
We can still do interesting things like protocol state tracking, which
is my primary motivation at least.
Ideally, if the 1 multiplicity is going to be more generall useful,
we'll need some kind of way of doing multiplicity polymorphism in the
future. I don't think subtyping is the way (I've pretty much always come
to regret adding some form of subtyping).
Fixes#73 (and maybe some others).
This also changes the return type of `char` and `string`. They
previously returned `()`, they now return `Char` and `String`
repectively.
Signed-off-by: Alex Humphreys <alex.humphreys@here.com>
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!
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>
