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ISABELLE is a generic proof assistant, allowing mathematical formulas to be expressed in a formal language and providing tools for proving those formulas in a logical manner. It was developed in the late 1980s by Lawrence Paulson at the University of Cambridge and Tobias Nipkow at the Technical University of Munich. The software represents proofs as data structures, allowing users to manipulate them with high-level commands. ISABELLE supports several logical formalisms, including first-order logic, higher-order logic, Zermelo-Fraenkel set theory and the modal logics S4 and S5. Its extensive use in theorem proving research makes it an invaluable tool for computer scientists worldwide.

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

First 20 minutes

General ISABELLE app knowledge and experience

The first 20 minutes of the interview should seek to understand the candidate's general background in ISABELLE application development, including their experience with various programming languages, databases, and their approach to designing scalable and maintainable systems.

Can you briefly explain what ISABELLE is used for?

ISABELLE is used for formal verification. It's a proof assistant tool that helps in the development of formal proofs by providing a framework for creating and managing such proofs.

How would you install ISABELLE on a Linux machine?

You would first download the ISABELLE distribution, then extract the archive and set the 'ISABELLE_HOME' environment variable to the location of the extracted archive. After that, you would add 'ISABELLE_HOME/bin' to your PATH.

What are some of the main features of ISABELLE?

ISABELLE has a number of features including support for higher-order logic, a customizable proof engine, and an integrated development environment.

How would you specify a simple theorem in ISABELLE?

You would use the 'theorem' keyword followed by the name of the theorem and its specification. For example, 'theorem add_comm: "a + b = b + a"'.

What is a proof in the context of ISABELLE?

A proof in ISABELLE is a formal demonstration that given certain assumptions, a particular statement is true. It is constructed using a sequence of inference rules.

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What you’re looking for early on

Does the candidate have a strong understanding of ISABELLE?

Has the candidate demonstrated problem-solving skills?

Is the candidate able to communicate effectively?

Has the candidate shown experience with similar projects?

Next 20 minutes

Specific ISABELLE development questions

The next 20 minutes of the interview should focus on the candidate's expertise with specific backend frameworks, their understanding of RESTful APIs, and their experience in handling data storage and retrieval efficiently.

Describe the difference between ISABELLE/HOL and ISABELLE/ZF.

ISABELLE/HOL is based on higher-order logic, which allows for reasoning about functions and sets in a simple and intuitive way. ISABELLE/ZF, on the other hand, is based on Zermelo-Fraenkel set theory, which is more expressive but also more complex.

What is the role of the Isar language in ISABELLE?

Isar is a language for structured proofs in ISABELLE. It provides a high-level language for writing proofs that are easy to read and write.

Can you explain how tactics work in ISABELLE?

Tactics in ISABELLE are functions that take a goal and return a sequence of subgoals. They are used to guide the proof process by breaking down complex goals into simpler ones.

How would you prove a theorem in ISABELLE using the 'apply' method?

You would first state the theorem using the 'theorem' keyword, then use the 'apply' method to apply tactics to the goal. For example, 'apply (rule add_comm)' would apply the commutativity rule to the current goal.

What are some of the advantages of using a proof assistant like ISABELLE?

Proof assistants like ISABELLE provide a rigorous framework for developing formal proofs, which can increase confidence in the correctness of the results. They also provide tools for managing complex proofs and automating routine tasks.

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At this point, a skilled ISABELLE engineer should demonstrate strong problem-solving abilities, proficiency in ISABELLE programming language, and knowledge of software development methodologies. Red flags include lack of hands-on experience, inability to articulate complex concepts, or unfamiliarity with standard coding practices.

Digging deeper

Code questions

These will help you see the candidate's real-world development capabilities with ISABELLE.

What does this simple Isabelle code do?
lemma "(A ? B) ? (B ? A)"
apply (rule impI)
apply (erule conjE)
apply (rule conjI)
apply assumption+
done
This Isabelle code is proving the lemma that if A and B are true, then B and A are true. It's essentially proving the commutativity of logical 'and' operator.
What does this Isabelle code snippet do?
datatype 'a list = Nil | Cons 'a  'a list
fun append :: "'a list ? 'a list ? 'a list" where
"append Nil ys = ys" |
"append (Cons x xs) ys = Cons x (append xs ys)"
This code defines a list datatype and an append function for the list. The append function takes two lists and appends the second list to the first one. The function uses pattern matching for two cases: when the first list is Nil, and when the first list is a Cons.
What will this Isabelle code do?
fun rev :: "'a list ? 'a list" where
"rev Nil = Nil" |
"rev (Cons x xs) = append (rev xs) (Cons x Nil)"
This Isabelle code defines a function rev that reverses a list. It uses pattern matching for two cases: when the list is Nil, and when the list is a Cons. In the latter case, it recursively calls rev on the tail of the list, and appends the head to the result.
What does this Isabelle code snippet do?
datatype 'a tree = Leaf | Node "'a tree" 'a "'a tree"
fun mirror :: "'a tree ? 'a tree" where
"mirror Leaf = Leaf" |
"mirror (Node l x r) = Node (mirror r) x (mirror l)"
This code defines a binary tree datatype and a mirror function for the tree. The mirror function takes a tree and returns a new tree that is the mirror image of the original one. It uses pattern matching for two cases: when the tree is a Leaf, and when the tree is a Node.

Wrap-up questions

Final candidate for ISABELLE Developer role questions

The final few questions should evaluate the candidate's teamwork, communication, and problem-solving skills. Additionally, assess their knowledge of microservices architecture, serverless computing, and how they handle ISABELLE application deployments. Inquire about their experience in handling system failures and their approach to debugging and troubleshooting.

How would you use ISABELLE to verify a complex software system?

You would first formalize the specifications of the system in ISABELLE, then construct a proof that the system meets these specifications. This might involve proving properties about the system's behavior, or showing that certain error conditions cannot occur.

Describe the difference between a 'proof' and a 'lemma' in ISABELLE.

In ISABELLE, a 'proof' is a formal demonstration that a particular statement is true, while a 'lemma' is a subsidiary or intermediate theorem in a proof. Lemmas are used to break down complex proofs into smaller, more manageable parts.

How would you debug a proof in ISABELLE that isn't going as expected?

ISABELLE provides several tools for debugging proofs, including the 'proof' command, which shows the current goal and the assumptions, and the 'oops' command, which discards the current proof attempt. You can also use the 'apply' command with different tactics to see how they affect the goal.

ISABELLE application related

Product Perfect's ISABELLE development capabilities

Beyond hiring for your ISABELLE engineering team, you may be in the market for additional help. Product Perfect provides seasoned expertise in ISABELLE projects, and can engage in multiple capacities.

ISABELLE Consultive assessments

ISABELLE Application Conversion Assessment ISABELLE Application Integration Assessment ISABELLE Data & Database Integration Assessment

Custom ISABELLE development projects

Custom ISABELLE App Conversion ISABELLE Custom App Development Process App UI Design for ISABELLE Facelifts

Hiring guide for ISABELLE Engineers

ISABELLE Developer Hiring Guide

What you’re looking for early on

The ideal back-end app developer

What you’re looking to see on the ISABELLE engineer at this point.

ISABELLE Consultive assessments

Custom ISABELLE development projects