axiomatic semantics

theory A set of assertions about properties of a system and

how they are effected by program execution. The axiomatic

semantics of a program could include pre- and post-conditions

for operations. In particular if you view the program as a

state transformer (or collection of state transformers), the

axiomatic semantics is a set of invariants on the state which

the state transformer satisfies.

E.g. for a function with the type:

sort_list :: [T] -@# [T]

we might give the precondition that the argument of the

function is a list, and a postcondition that the return value

is a list that is sorted.

One interesting use of axiomatic semantics is to have a

language that has a finitely computable sublanguage that is

used for specifying pre and post conditions, and then have the

compiler prove that the program will satisfy those conditions.

See also operational semantics, denotational semantics.

(1995-11-09)