Programming Language Semantics

operational · denotational · axiomatic · effects

1:00

Four rigorous frameworks for defining what programs mean — operational, denotational, axiomatic, and type-and-effect systems.

By the end, you can

Distinguish syntax from semantics and explain why a formal semantics is valuable.
Contrast small-step and big-step operational semantics, and identify the unique advantage of small-step.
Describe what a denotational semantics assigns to an assignment, a sequence, and a while loop.
Explain why a while loop requires a least fixed point and sketch the Kleene chain construction.
Read a Hoare triple and apply the assignment axiom backward to derive a precondition.
Identify a valid loop invariant and use it to prove a postcondition once the loop exits.
State the progress and preservation theorems and explain how they together prove type soundness.
Interpret an effect annotation on a function type and explain what it guarantees statically.

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