Denotational

Denotational semantics of state State (such as a heap) and simple imperative features can be straightforwardly modeled in the denotational semantics described above.

A basic denotational semantics in domain theory is compositional because it is given as follows.

Also the mathematical structure of operational semantics and denotational semantics can become very close.

As originally developed by Strachey and Scott, denotational semantics provided the denotation (meaning) of a computer program as a function that mapped input into output.

At the denotational level, the term refers to situations where a single entity can be seen to mean more than one mathematical object.

Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do.

Defining a computer language is usually done in relation to an abstract machine (so-called operational semantics ) or as a mathematical function ( denotational semantics ).

Denotational semantics as source-to-source translation It is often useful to translate one programming language into another.

Denotations of recursive programs Denotational semantics are given to a program phrase as a function from an environment (that has the values of its free variables) to its denotation.

Double brackets Double brackets (or white square brackets), ⟦ ⟧, are used to indicate the semantic evaluation function in formal semantics for natural language and denotational semantics for programming languages.

For semantics in the traditional style, full abstraction may be understood roughly as the requirement that "operational equivalence coincides with denotational equality".

It is for this reason that the approach using domains, as introduced above, yields a denotational semantics that is not fully abstract.

The technical difference is in the denotational semantics of expressions containing failing or divergent computations.

This is especially important when the denotational semantics is rather mathematical and abstract, and the operational semantics is more concrete or closer to the computational intuitions.

This work also formed the basis for the denotational semantics of programming languages.

We now give a denotational semantics to program fragments, using the following scheme.