```
id : ? {A : Set} ? A ? A
id x = x
```

Ask the right questions to secure the right Agda talent among an increasingly shrinking pool of talent.

Agda is a dependently typed functional programming language, originally developed by Ulf Norell at Chalmers University of Technology, Sweden. It is designed to be a platform for research in type theory, dependent types, and interactive theorem proving. Agda is named after Agda Åman, the first woman to receive a Ph.D. in computer science in Sweden. The language is influenced by other functional programming languages such as Haskell and ML. It is open-source and its development is hosted on GitHub.

The next 20 minutes of the interview should attempt to focus more specifically on the development questions used, and the level of depth and skill the engineer possesses.

Inductive types in Agda are types that are defined by a finite set of constructors. Coinductive types, on the other hand, are types that are defined by a potentially infinite set of observations.

A dependent type in Agda is a type that depends on a value. This allows for more expressive types and more powerful type checking.

The main difference is that Agda is a dependently typed language, which means that types can depend on values. This allows for more expressive types and more powerful type checking. Agda also supports interactive theorem proving, which is not common in other functional programming languages.

Agda is a dependently typed language, which means that types can depend on values. It also supports interactive theorem proving, inductive and coinductive types, and has a module system.

Agda is a dependently typed functional programming language that has been designed to be a language for mathematics, software verification, and general-purpose programming.

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The field of programming is constantly evolving, so it's important for the candidate to be willing to learn and adapt to new technologies and methodologies.

Teamwork is important in a programming role as projects often require collaboration with others.

Experience with other functional programming languages can be beneficial as it can provide a broader perspective and understanding of programming concepts.

Good communication skills are important in any job, but especially in programming where the candidate will need to explain complex concepts and solutions.

This is crucial because programming involves a lot of problem-solving and the candidate should be able to demonstrate this skill.

This is important because Agda is a dependently typed functional programming language and it is crucial for the candidate to have a deep understanding of it.

The next 20 minutes of the interview should attempt to focus more specifically on the development questions used, and the level of depth and skill the engineer possesses.

Coinductive types in Agda are used to represent potentially infinite data structures. They are defined by a potentially infinite set of observations, and can be used to model things like streams and infinite lists.

The main benefit of using Agda for software verification is that it allows for formal verification of the correctness of the software. This is done by writing a program that represents the proof of the correctness of the software, which is then verified by the Agda type checker.

A module in Agda is a way to group related definitions. It can contain types, functions, and other modules.

The main difference is that dependent types can depend on values, while regular types cannot. This allows for more expressive types and more powerful type checking in Agda.

Interactive theorem proving in Agda is done by writing a program that represents the proof of the theorem. The Agda type checker then verifies the correctness of the proof.

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A skilled Agda engineer should demonstrate proficiency in functional programming, a deep understanding of type theory, and problem-solving skills. Red flags include lack of experience with formal verification tools, inability to explain complex concepts, and poor problem-solving abilities.

```
id : ? {A : Set} ? A ? A
id x = x
```

```
_+_ : N ? N ? N
zero + n = n
(suc m) + n = suc (m + n)
```

```
filter : ? {A : Set} ? (A ? Bool) ? List A ? List A
filter p [] = []
filter p (x ? xs) with p x
... | true = x ? filter p xs
... | false = filter p xs
```

```
mutual
data _|_ (m n : N) : Set where
zero|n : zero | n
suc|n : ? {m'} ? suc m' | n ? m | suc n
_/_ : N ? N ? N
m / n with m |? n
... | yes p = zero
... | no ¬p with suc (m / n)
... | q = suc q
```

```
record Point (A : Set) : Set where
constructor mkPoint
field
x : A
y : A
```

```
record _˜_ {A : Set} (x : A) : A ? Set where
constructor refl
field
proof : x = x
```

The final few interview questions for a Agda candidate should typically focus on a combination of technical skills, personal goals, growth potential, team dynamics, and company culture.

The main difference is that when using Agda for software verification, the focus is on proving properties about the software, while when using it for general-purpose programming, the focus is on writing programs that perform computations. However, in both cases, the Agda type checker is used to ensure the correctness of the software or proofs.

Agda can be used for mathematics by encoding mathematical concepts and proofs in the language. The Agda type checker then verifies the correctness of the proofs.

One of the main challenges of using Agda for general-purpose programming is that it requires a different mindset compared to traditional programming languages. In particular, programming in Agda often involves proving properties about the program, which can be more time-consuming and difficult than traditional programming.

Dependent types can be used for software verification in Agda by encoding the properties of the software in the types. The Agda type checker then verifies that the software satisfies these properties.

The main difference is that inductive types are defined by a finite set of constructors, while coinductive types are defined by a potentially infinite set of observations. This makes inductive types suitable for representing finite data structures, and coinductive types suitable for representing potentially infinite data structures.

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