Standard semantics
The standard interpretation of a term in some language yields the term’s standard denotational semantics, i.e. its “meaning”. This is usually given by a semantic function which maps a term in the abstract syntax to a point in some domain. The domain is the interpretation of the term’s type. The semantic function also takes an environment – a function which maps the free variables of the term to their meaning. We say that a domain point “denotes”, or “is the denotation of”, a term. A non-standard semantics results from some other interpretation, e.g. an abstract interpretation.
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