science

MiniKanren

MiniKanren is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand MiniKanren rather than just read about it. In short: miniKanren is a family of programming languages for relational programming, first developed by Will Byrd. As relations are bidirectional, if miniKanren is given an expression and a desired output, miniKanren can run the expression "backward", finding all possible inputs to the expression that produce the desired output.

Key takeaways

MiniKanren belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MiniKanren to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MiniKanren from memory before moving on to harder problems.

Reference excerpt

miniKanren is a family of programming languages for relational programming, first developed by Will Byrd. As relations are bidirectional, if miniKanren is given an expression and a desired output, miniKanren can run the expression "backward", finding all possible inputs to the expression that produce the desired output. This bidirectional behavior allows the user to constrain both the input to the program and the result of the program simultaneously. miniKanren performs an interleaved search which will eventually find any solution that exists, even if any one branch of the search tree is infinitely long and contains no solutions. If no solution exists, miniKanren may search forever if the search tree is infinite. An example of miniKanren code is evalo, a relational goal that relates expressions to the values that they evaluate to. When evalo is called in miniKanren like so: (evalo q q), it will generate quines, that is, expressions q that when run will evaluate to themselves. The book The Reasoned Schemer uses miniKanren to demonstrate relational programming, and provides a complete implementation in Scheme. The core of the language fits on two printed pages. The Scheme implementation of miniKanren is designed to be easily understood, modified, and extended. microKanren is another language in the miniKanren family, notable for its minimalist implementation in fewer than 40 lines of Scheme. αleanTAP is a program written in αKanren, an extension of miniKanren for nominal logic. Given a theorem, it can find a proof, making it a theorem-prover. Given a proof, it can find the theorem, making it a theorem-checker. Given part of a proof and part of a theorem, it will fill in the missing parts of the proof and the theorem, making it a theorem-explorer. There are implementations of miniKanren in Clojure, Dart, Haskell, JavaScript, Python, Racket, Ruby, Scala, and Swift. The canonical implementation is an embedded language in Scheme. The Clojure core.logic library was inspired by miniKanren. The name kanren comes from a Japanese word (関連) meaning "relation".

See also Logic programming Tree traversal

References

External links Official website

Worked examples

Example 1 — a first encounter with MiniKanren

Start with the simplest possible case. Write down what MiniKanren claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MiniKanren before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MiniKanren ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MiniKanren

In research: MiniKanren appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MiniKanren in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MiniKanren is common in secondary-school and first-year university syllabi. It links to neighbouring topics Logic programming, Programming languages, so understanding it makes those chapters shorter.
In everyday life: Look for MiniKanren outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study MiniKanren in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MiniKanren means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MiniKanren out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MiniKanren in simple terms?

Why does MiniKanren matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MiniKanren?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MiniKanren.