mixed-types-num: Alternative Prelude with numeric and logic expressions typed bottom-up
This package provides a version of Prelude where
unary and binary operations such as
have their result type derived from the parameter type(s),
dividing an integer by an integer, giving a rational:
let n = 1 :: Integer in n/(n+1) :: Rational
1/2 :: Rational
(The type Rational would be derived automatically because
integer literals are always of type
Num t => t.)
adding an integer and a rational, giving a rational:
(length [x])+1/3 :: Rational
taking natural, integer and fractional power using the same operator:
2^2 :: Integer
2.0^(-2) :: Rational
(double 2)^(1/2) :: Double
The following examples require package aern2-real:
2^(1/2) :: CauchyReal
pi :: CauchyReal
sqrt 2 :: CauchyReal
comparing an integer with an (exact) real number, giving a
... x :: CauchyReal ... if (isCertainlyTrue (x > 1)) then ...
Arithmetic operations are provided via multi-parameter type classes and the result type is given by associated type families. For example:
(+) :: (CanAddAsymmetric t1 t2) => t1 -> t2 -> AddType t1 t2
The type constraint
CanAdd t1 t2 implies both
CanAddAsymmetric t1 t2 and
CanAddAsymmetric t2 t1.
For convenience there are other aggregate type constraints such as
CanAddThis t1 t2, which implies that the result is of type
CanAddSameType t, which is a shortcut for
CanAddThis t t.
The arithmetic type classes are accompanied by generic hspec test suites, which are specialised to concrete instance types for their testing. These test suites include the expected algebraic properties of operations, such as commutativity and associativity of addition.
Not all numerical operations are supported yet. Eg
atanare missing at the moment.
Inferred types can be very large. Eg for
f a b c = sqrt (a + b * c + 1)the inferred type is:
f: (CanMulAsymmetric t1 t2, CanAddAsymmetric t4 (MulType t1 t2), CanAddAsymmetric (AddType t4 (MulType t1 t2)) Integer, CanSqrt (AddType (AddType t4 (MulType t1 t2)) Integer)) => t4 -> t1 -> t2 -> SqrtType (AddType (AddType t4 (MulType t1 t2)) Integer)
Due to limitations of some versions of ghc, type inferrence sometimes fails. Eg
add1 = (+ 1)fails (eg with ghc 8.0.2) unless we explicitly declare the type
add1 :: (CanAdd Integer t) => t -> AddType t Integeror use an explicit parameter, eg
add1 x = x + 1.
To find out more, please read the documentation for the modules in the order specified in Numeric.MixedTypes.
The idea of having numeric expressions in Haskell with types derived bottom-up was initially suggested and implemented by Pieter Collins. This version is a fresh rewrite by Michal Konečný.
|Versions [faq]||0.1.0.0, 0.1.0.1, 0.2, 0.2.0.1, 0.3, 0.3.0.1, 0.3.1, 0.3.1.1, 0.3.1.2, 0.3.1.3, 0.3.1.4, 0.3.1.5, 0.3.2, 0.4.0, 0.4.0.1 (info)|
|Dependencies||base (==4.*), convertible (>=220.127.116.11 && <1.2), hspec (>=2.1 && <2.5), hspec-smallcheck (>=0.3 && <0.5), QuickCheck (>=2.7 && <2.10), smallcheck (==1.1.*) [details]|
|Copyright||(c) 2015-2017 Michal Konecny|
|Maintainer||Michal Konecny <firstname.lastname@example.org>|
|Source repo||head: git clone https://github.com/mikkonecny/mixed-types-num|
|Uploaded||by MichalKonecny at Wed Mar 8 23:10:17 UTC 2017|
|Distributions||LTSHaskell:0.3.1.5, NixOS:0.4.0.1, Stackage:0.4.0.1|
|Downloads||3049 total (257 in the last 30 days)|
|Rating||(no votes yet) [estimated by rule of succession]|
Docs available [build log]
Last success reported on 2017-03-08 [all 1 reports]
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