IgorWolkov/typed-formula

Write type safe formulas like in a textbook on mathematics

Overview

type-formula allows you to write lazy formulas in a type safe mode and calculate a value when it needed.

Using typed-formula

Stable version, dependencies and repository are coming soon...

Useful reach examples

• Loan accounting calculations in one day with typed-formula

Generic Formulas

typed-formula provides functionality to build formulas for numeric calculations on top of Integers, Longs and Double wrapped into Numbers.

Let's define simple formulas to calculate area and a volume of a figure. Firstly define measurements.

import karazinscalausersgroup.typed.formula.Value
import karazinscalausersgroup.typed.formula.numbers.{Number, Value}
import karazinscalausersgroup.typed.formula.numbers.operations._


scala> val length = Value[Number](1)
length: Value[Number] = Expression(IntNumber(1))

scala> val width = Value[Number](3)
width: Value[numbers.Number] = Expression(IntNumber(3))

scala> val height = Value[Number](2.0)
height: Value[numbers.Number] = Expression(DoubleNumber(2.0))

Now we can easily define formulas

scala> val area = length * width
area: Value[Number] * Value[Number] = (Expression(IntNumber(1)) * Expression(IntNumber(3)))

scala> val volume = area * height
volume: Value[Number] * Value[Number] * Value[Number] = ((Expression(IntNumber(1)) * Expression(IntNumber(3))) * Expression(DoubleNumber(2.0)))

and calculate values

scala> area.v
res0: Number = IntNumber(3)

scala> volume.v
res1: Number = DoubleNumber(6.0)

Custom formulas

Let's rewrite the example with custom classes for formula terms

import karazinscalausersgroup.typed.formula.Value
import karazinscalausersgroup.typed.formula.numbers.{Number, Value}
import karazinscalausersgroup.typed.formula.numbers.operations._


case class Length(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Width(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Height(value: Double) extends Value[Number] {
  def v = Number(value)
}

scala>  val length = Length(1)
length: Length = Expression(IntNumber(1))

scala> val width = Width(3)
width: Width = Expression(IntNumber(3))

scala> val height = Height(2.0)
height: Height = Expression(DoubleNumber(2.0))

Now we can define formulas with custom terms

scala> val area = length * width
area: Length * Width = (Expression(IntNumber(1)) * Expression(IntNumber(3)))

scala> val volume = area * height
volume: Length * Width * Height = ((Expression(IntNumber(1)) * Expression(IntNumber(3))) * Expression(DoubleNumber(2.0)))

and calculate values

scala> area.v
res0: Number = IntNumber(3)

scala> volume.v
res1: Number = DoubleNumber(6.0)

Supported operations

In current version only operations for Numbers are supported.

Linear operations

Let's define two variables

import karazinscalausersgroup.typed.formula.Value
import karazinscalausersgroup.typed.formula.numbers.{Number, Value}
import karazinscalausersgroup.typed.formula.numbers.operations._


scala> val a = Value[Number](3)
a: Value[Number] = Expression(IntNumber(3))

scala> val b = Value[Number](5)
b: Value[Number] = Expression(IntNumber(5))

typed-formula supports following linear operation:

addition

scala> a + b
res1: Value[Number] + Value[Number] = (Expression(IntNumber(3)) + Expression(IntNumber(5)))

subtraction

scala> a - b
res2: Value[Number] - Value[Number] = (Expression(IntNumber(3)) - Expression(IntNumber(5)))

unary minus

Unlike unary_ definitions for methods, it is impossible to overload types. That's why ~ (tilde) represents unary minus on type level. However it's possible to use - as unary minus with values.

scala> -a
res3: ~[Value[Number]] = -Expression(IntNumber(3)))

multiplication

scala> a * b
res4: Value[Number] * Value[Number] = (Expression(IntNumber(3)) * Expression(IntNumber(5)))

division

scala> a / b
res9: Value[numbers.Number] / Value[numbers.Number] = (Expression(IntNumber(3)) / Expression(IntNumber(5)))

"Series" operations and formula builder

Formula builder

Let's get to the example with measurements

import karazinscalausersgroup.typed.formula.numbers.Number.Zero
import karazinscalausersgroup.typed.formula.numbers.builder._
import karazinscalausersgroup.typed.formula.numbers.operations._
import karazinscalausersgroup.typed.formula.numbers.{Number, Val


case class Length(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Width(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Height(value: Double) extends Value[Number] {
  def v = Number(value)
}

scala>  val length = Length(1)
length: Length = Expression(IntNumber(1))

scala> val width = Width(3)
width: Width = Expression(IntNumber(3))

scala> val height = Height(2.0)
height: Height = Expression(DoubleNumber(2.0))

Let's pack all measurements into a list.

scala> val measurements = length :: width :: height :: Nil
measurements: List[Value[numbers.Number] with Product with Serializable{def v: Product with Serializable with Number{def v: AnyVal; type N >: Double with Int <: AnyVal}}] = List(Expression(IntNumber(1)), Expression(IntNumber(3)), Expression(DoubleNumber(2.0)))

Now we can build formulas on the fly. Take into account that build works only for lists of Values.

scala> val areaOpt = build[Length * Width](measurements)
areaOpt: Option[Length * Width] = Some((Expression(IntNumber(1)) * Expression(IntNumber(3))))


scala> val volumeOpt = build[Length * Width * Height](measurements)
volumeOpt: Option[Length * Width * Height] = Some(((Expression(IntNumber(1)) * Expression(IntNumber(3))) * Expression(DoubleNumber(2.0))))

If it's possible to build formula build returns Some formula otherwise it returns None. For some reasons it may be preferable to fail on compile time if it is impossible to build a formula, but this soft check is necessary for Σ operation.

Σ

Suppose there is a series of measurements. We can calculate additive characteristics for this series.

import karazinscalausersgroup.typed.formula.Value
import karazinscalausersgroup.typed.formula.numbers.{Number, Value}
import karazinscalausersgroup.typed.formula.numbers.operations._


case class Length(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Width(value: Int) extends Value[Number] {
  def v = Number(value)
}

case class Height(value: Double) extends Value[Number] {
  def v = Number(value)
}

Define a foldable entity for collection of measurements

case class Measurements(expressions: List[Value[Number]]) extends Foldable[Number, Value[Number]] {
  lazy val op: (Expression[Number], Value[Number]) => Expression[Number] = (acc, value) => acc + value
  lazy val initial = Value(Zero)
}

scala> val measurements1 = Measurements(Length(1) :: Width(3) :: Height(2.0) :: Nil)
measurements1: Measurements = Expression(DoubleNumber(6.0))

scala> val measurements2 = Measurements(Length(4) :: Width(6) :: Height(5.0) :: Nil)
measurements2: Measurements = Expression(DoubleNumber(15.0))

scala> val measurements3 = Measurements(Length(7) :: Width(9) :: Height(8.0) :: Nil)
measurements3: Measurements = Expression(DoubleNumber(24.0))

And define an implicit foldable entity for series of measurements

case class Series(expressions: List[Measurements]) extends Foldable[Number, Measurements] {
  lazy val op: (Expression[Number], Measurements) => Expression[Number] = (acc, value) => acc + value
  lazy val initial = Value(Zero)
}

scala> implicit val series: Series = Series(measurements1 :: measurements2 :: measurements3 :: Nil)
series: Series = Expression(DoubleNumber(45.0))

It is also needed to add implicit default entities. This option will be described later.

scala> implicit val defaults: List[Value[Number]] = Nil
defaults: List[Value[Number]] = List()

Now we can calculate some additive characteristics. The sum of all lengths:

scala> Σ[Length].v
res0: IntNumber = IntNumber(12)

The sum of all volumes:

scala> Σ[Length * Width * Height].v
res1: DoubleNumber = DoubleNumber(630.0)

Let's define 4th dimension for time:

  case class Time(value: Long) extends Value[Number] {
    def v = Number(value)
  }

If we try to build formula for a volume of hypercube we get 0 because there is no Time in the measurements and we can't build the formula

scala> Σ[Length * Width * Height * Time].v
res3: IntNumber = IntNumber(0)

To resolve this issue we can add some Time to defaults. Keep in mind that the value of Time will be added to each measurements. You can't provide several values for Time, only the first value of Time from defaults will be used.

scala> implicit val defaults: List[Value[Number]] = Time(10) :: Nil
res4: List[Value[Number]] = List(Time(10))

scala> Σ[Length * Width * Height * Time].v
res5: DoubleNumber = DoubleNumber(6300.0)

License

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this software except in compliance with the License.

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.