computer science

Term graph

Term graph is a computer 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 Term graph rather than just read about it. In short: A term graph is a representation of an expression in a formal language as a generalized graph whose vertices are terms. Term graphs are a more powerful form of representation than expression trees because they can represent not only common subexpressions (i.e. they can take the structure of a directed acyclic graph) but also cyclic/recursive subexpressions (cyclic digraphs).

Key takeaways

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

Reference excerpt

A term graph is a representation of an expression in a formal language as a generalized graph whose vertices are terms. Term graphs are a more powerful form of representation than expression trees because they can represent not only common subexpressions (i.e. they can take the structure of a directed acyclic graph) but also cyclic/recursive subexpressions (cyclic digraphs). Abstract syntax trees cannot represent shared subexpressions since each tree node can only have one parent; this simplicity comes at the cost of efficiency due to redundant duplicate computations of identical terms. For this reason term graphs are often used as an intermediate language at a subsequent compilation stage to abstract syntax tree construction via parsing. The phrase "term graph rewriting" is often used when discussing graph rewriting methods for transforming expressions in formal languages. Considered from the point of view of graph grammars, term graphs are not regular graphs, but hypergraphs where an n-ary word will have a particular subgraph in first place, another in second place, and so on, a distinction that does not exist in the usual undirected graphs studied in graph theory. Term graphs are a prominent topic in programming language research since term graph rewriting rules can formally expressing a compiler's operational semantics. Term graphs are also used as abstract machines capable of modelling chemical and biological computations as well as graphical calculi such as concurrency models. Term graphs can perform automated verification and logical programming since they are well-suited to representing quantified statements in first order logic. Symbolic programming software is another application for term graphs, which are capable of representing and performing computation with abstract algebraic structures such as groups, fields and rings. The TERMGRAPH conference focuses entirely on research into term graph rewriting and its applications. Term graphs are also used in type inference, where the graph structure aids in implementing type unification.

Worked examples

Example 1 — a first encounter with Term graph

Start with the simplest possible case. Write down what Term graph claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer 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 Term graph 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 Term graph 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 Term graph

In research: Term graph appears in computer 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 Term graph 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: Term graph is common in secondary-school and first-year university syllabi. It links to neighbouring topics Formal methods stubs, Formal systems, Graph data structures, so understanding it makes those chapters shorter.
In everyday life: Look for Term graph 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 Term graph in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Term graph 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 Term graph out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Term graph in simple terms?

Why does Term graph matter?

Because it connects several computer 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 Term graph?

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 Term graph.