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# Axiomatic semantics

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.
(1995-11-09)

Tagged:

• Axiomatically

pertaining to or of the nature of an axiom; self-evident; obvious. aphoristic. Contemporary Examples Which is to say, the existence of a bad thing does not imply, axiomatically, that there is a legislative solution to it. Even Good Laws Sometimes Don’t Work Megan McArdle October 30, 2012 To people on the right, it’s axiomatically the […]

• Axiomatization

noun the process of defining mathematical systems by a set of axioms Examples The Boolean logic of propositions has many different axiomatizations which are formally equivalent.

• Axion

a hypothetical particle having no charge, zero spin, and small mass: postulated in some forms of quantum chromodynamics. noun (physics) a hypothetical neutral elementary particle postulated to account for certain conservation laws in the strong interaction n. 1978, from axial + scientific suffix -on.

• Axioplasm

axioplasm axioplasm ax·i·o·plasm (āk’sē-ə-plāz’əm) n. Variant of axoplasm.

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