Ideally, liftIO would always be linear, but that has lots of knock-on
effects for other monads which we might want to put in HasIO, now that
subtyping is gone. We'll have to revisit this when we have some kind of
multiplicity polymorphism.
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!
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>
* [contrib] Add misc libraries to contrib
Expose some `private` function in libs/base that I needed, and seem like
their visibility was forgotten
I'd appreciate a code review, especially to tell me I'm
re-implementing something that's already elsewhere in the library
Mostly extending existing functionality:
* `Data/Void.idr`: add some utility functions for manipulating absurdity.
* `Decidable/Decidable/Extra.idr`: add support for double negation elimination in decidable relations
* `Data/Fun/Extra.idr`:
+ add `application` (total and partil) for n-ary functions
+ add (slightly) dependent versions of these operations
* `Decidable/Order/Strict.idr`: a strict preorder is what you get when
you remove the diagonal from a pre-order. For example, `<` is the
associated preorder for `<=` over `Nat`.
Analogous to `Decidable.Order`. The proof search mechanism struggled
a bit, so I had to hack it --- sorry.
Eventually we should move `Data.Fun.Extra.Pointwise` to `Data.Vect.Quantifiers` in base
but we don't have any interesting uses for it at the moment so it's not
urgent.
Co-authored by @gallais
For lack of a better place, I've put it in `Syntax.PreorderReasoning`
These equations are natural in equational reasoning, but less so when
rewriting, so that's why it's there
