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Contents

November 8: Denotational Semantics -- Basics and Relationship to Operational Semantics

Introduction (PostScript Slides)

Methods for semantics specifications; preview on basic structure of denotational definitions.

Syntax (PostScript Slides)

Concrete and abstract syntax definitions; corresponding proof techniques.

Semantic Domains (PostScript Slides)

Semantic algebras; examples of primitive domains; compound domains; recursive function and domain definitions.

Domain Theory I (PostScript Slides)

] Sets; functions; semantic domains.

Basic Structure of Denotational Definitions (PostScript Slides)

A calculator language.

Imperative Languages I (PostScript Slides)

A language with assignment.

Introduction to Operational Semantics

Operational semantics of IMP; a proof of the equivalence of language constructs.

Operational vs Denotational Semantics

Denotational semantics of IMP; equivalence of the semantics.

November 15: Denotational Semantics -- Deepening and Relationship to Axiomatic Semantics

Imperative Languages II

An interactive file editor; input and output; altering the properties of stores; delayed evaluation; multiple stores; noncommunicating commands.

Domain Theory II

Recursively defined functions; partial orderings; continuous functions; least fixed points; domains are cpos; examples.

Axiomatic Semantics

The idea; an assertion language; semantics of assertions; proof rules for partial corrrectness; soundness; an example.

Completeness of the Hoare Rules

Gödel's Incompletenness Theorem; weakest preconditions and expressiveness; proof of Gödel's Theorem; verification conditions; predicate transformers.

December 13: Languages with Contexts

Languages with Contexts I

A block-structured language; stack-managed storage; the meaning of identifiers.

Languages with Contexts II

An applicative language; scoping rules; self-application; recursive definitions.

Languages with Contexts III

Compound data structures.

January 11: Language Design Principles

Language Design Principles I

Abstraction; recursive bindings.

Language Design Principles II

Parameterization; polymorphism and typing.

Language Design Principles III

Correspondence; qualification; orthagonality.