Types vs Tests

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background-image: url(img/fp-tower/website-background.svg)

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# Julien Truffaut

.thirty-seven-left[
<img src="img/fp-tower/julien-truffaut.jpg" alt="Julien Truffaut" style="width:300px;"/>
]

## Author of a Scala FP course: Foundations

## Maintainer of Monocle 🧐
]

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background-image: url(img/types-vs-tests/cardinality-1.svg)

# Types are set

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background-image: url(img/types-vs-tests/cardinality-2.svg)

# Types are set

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background-image: url(img/types-vs-tests/cardinality-nothing-unit.svg)

# Types are set

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background-image: url(img/types-vs-tests/cardinality-list-unit.svg)

# Types are set

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background-image: url(img/types-vs-tests/cardinality-io-unit.svg)

# Types are set

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# Types are constraints

```scala
val x: Int = 5
```

```scala
val y: Int = false
// error: type mismatch;
//  found   : Boolean(false)
//  required: Int
```

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# Types are constraints

```tut
increment(2)
```

```scala
increment("hello")
// error: type mismatch;
//  found   : String("hello")
//  required: Int
```
]

.fifty-two-right[
```scala
def increment(x: Int): Int =
  x.toString
// error: type mismatch;
//  found   : String
//  required: Int
```
]

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# But there are limited

```scala
def increment(x: Int): Int = x + 2
```

```scala
def increment(x: Int): Int = 0
```
]

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class: center, middle

# Tests

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class: center, middle

# Unit Tests

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# Unit tests are constraints

"increment at 0" in {
    assert(increment(0) == 1)
}

"increment at 1" in {
    assert(increment(1) == 2)
}
```
]

.fifty-two-right[.center[
<img src="img/types-vs-tests/increment-unit-test-1.svg" alt="Unit test increment" style="width:480px;"/>
]]

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# Unit tests are constraints

"increment at 0" in {
    assert(increment(0) == 1)
}

"increment at 1" in {
    assert(increment(1) == 2)
}
```
]

.fifty-two-right[.center[
<img src="img/types-vs-tests/increment-unit-test-2.svg" alt="Unit test increment" style="width:480px;"/>
]]

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# But they are limited

"increment at 0" in {
    assert(increment(0) == 1)
}

"increment at 1" in {
    assert(increment(1) == 2)
}
```
]

.fifty-two-right[.center[
<img src="img/types-vs-tests/increment-unit-test-3.svg" alt="Unit test increment" style="width:480px;"/>
]]

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class: center, middle

# Both types and tests constrain the implementation of a function

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class: center, middle

# How much?

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# A => B is a type

val increment: Int => Int =
  x => x + 1
```
]

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class: center, middle

# Type is a set

# &&

# A => B is a type

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background-image: url(img/types-vs-tests/function-set-1.svg)

# A function is a set

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background-image: url(img/types-vs-tests/function-set-2.svg)

# A function is a set

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background-image: url(img/types-vs-tests/function-set-3.svg)

# Unit tests

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class: center, middle

# Valid Implementation Count (VIC)

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class: middle

.fifty-seven-left[.center[
# number of possible implementations - implementations made invalid because of tests
]]

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background-image: url(img/types-vs-tests/vic.svg)

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class: center, middle

# The smaller VIC is, the more constrained is f

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background-image: url(img/types-vs-tests/vic-of-1.svg)

# VIC(f) = 1

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background-image: url(img/types-vs-tests/vic-1.svg)

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background-image: url(img/types-vs-tests/vic-2.svg)

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background-image: url(img/types-vs-tests/function-cardinality-1.svg)

# Function is a mapping

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# |A => B|

.sixty-two-right[.center[
<img src="img/types-vs-tests/function-cardinality-2.svg" alt="Function cardinality" style="width:600px;"/>
]]

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# |A => B|

.sixty-two-right[.center[
<img src="img/types-vs-tests/function-cardinality-2.svg" alt="Function cardinality" style="width:600px;"/>
]]

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# |A => B|

.sixty-two-right[.center[
<img src="img/types-vs-tests/function-cardinality-3.svg" alt="Function cardinality" style="width:600px;"/>
]]

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# |A => B|

.thirty-seven-left[
 
```scala
|{x, y} => B| =
 |{x} => B| + // y -> a
 |{x} => B| + // y -> b
 |{x} => B| + // y -> c
 |{x} => B| + // y -> d
 |{x} => B| + // y -> e
```
]