natural-arithmetic.cabal

cabal-version:   2.2
name:            natural-arithmetic
version:         0.2.1.0
synopsis:        Arithmetic of natural numbers
description:
  A search for terms like `arithmetic` and `natural` on hackage reveals
  no shortage of libraries for handling the arithmetic of natural
  numbers. How is this library any different some of the others? It has
  a particular purpose: providing a foundation on top on which other
  libraries may define types indexed by sizes. This uses GHC's
  non-inductively-defined `GHC.TypeNats.Nat`. As a rule, this does not
  use `unsafeCoerce` internally anywhere.
  .
  Perhaps the most direct competitor to `natural-arithmetic` is a
  typechecker plugin like
  <https://github.com/yav/type-nat-solver type-nat-solver>. The big
  difference is that `type-nat-solver` can really only be used in
  application code, not in library code. This is because libraries
  should not require the presence of typechecker plugins. Technically,
  they can (you could document it), but many developers will not
  use libraries that have unusual install procedures like this.
  .
  This library, in places, requires users to use the 'TypeApplications`
  language extension. This is done when a number is only need at
  the type level (without a runtime witness).
  .
  This library uses a non-minimal core, providing redundant primitives
  in `Arithmetic.Lt` and `Arithmetic.Lte`. This is done in the interest
  of making it easy for user to assemble proofs. Recall that proof
  assembly is done by hand rather than by an SMT solver, so removing
  some tediousness from this is helpful to users.
  .
  This library provides left and variants variants of several functions.
  For example, `Arithmetic.Lte` provides both `substituteL` and
  `substituteR`. This is only done when there are two variants of
  a function. For substitution, this is the case because we have
  `b = c, a ≤ b ==> a ≤ c` and `a = c, a ≤ b ==> c ≤ b`. So, we
  provide both `substituteL` and `substituteR`. However,
  for addition of inequalities, we have four possible variants:
  `a ≤ b, c ≤ d ==> a + c ≤ b + d`, `a ≤ b, c ≤ d ==> c + a ≤ b + d`,
  `a ≤ b, c ≤ d ==> a + c ≤ d + b`, `a ≤ b, c ≤ d ==> c + a ≤ d + b`.
  Consequently, we only provide a single `plus` function, and users
  must use `Arithmetic.Plus.commutative` to further manipulate the
  inequality.
  .
  Here are the proof-manipulation vocabulary used by this library.
  Many of these terms are not standard, but we try to be consistent
  in this library:
  .
  * Weaken: Increase an upper bound without changing the bounded value
  .
  * Increment: Increase an upper bound along with the bounded value
  .
  * Decrement: Decrease an upper bound along with the bounded value
  .
  * Substitute: Replace a number with an equal number

homepage:        https://github.com/byteverse/natural-arithmetic
bug-reports:     https://github.com/byteverse/natural-arithmetic/issues
license:         BSD-3-Clause
license-file:    LICENSE
author:          Andrew Martin
maintainer:      amartin@layer3com.com
copyright:       2019 Andrew Martin
category:        Math
extra-doc-files: CHANGELOG.md
tested-with:     GHC ==9.4.8 || ==9.6.3 || ==9.8.1

common build-settings
  default-language: Haskell2010
  ghc-options:      -Wall -Wunused-packages

library
  import:          build-settings
  exposed-modules:
    Arithmetic.Equal
    Arithmetic.Fin
    Arithmetic.Lt
    Arithmetic.Lte
    Arithmetic.Nat
    Arithmetic.Plus
    Arithmetic.Types
    Arithmetic.Unsafe

  build-depends:
    , base      >=4.14  && <5
    , unlifted  >=0.2.1

  hs-source-dirs:  src
  ghc-options:     -O2

source-repository head
  type:     git
  location: git://github.com/byteverse/natural-arithmetic.git