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For example, ESC/Java and the Java Modeling Language add annotations for specifying preconditions and postconditions to Java. Likewise, Spec# and Frama-C add similar constructs to the C# and C programming languages. However, these languages are known to contain numerous features which pose difficult or insurmountable problems for verification. [8]
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
Involutive negation (unary) can be added as an additional negation to t-norm logics whose residual negation is not itself involutive, that is, if it does not obey the law of double negation . A t-norm logic L {\displaystyle L} expanded with involutive negation is usually denoted by L ∼ {\displaystyle L_{\sim }} and called L {\displaystyle L ...
In C (and some other languages descended from C), double negation (!!x) is used as an idiom to convert x to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not special in this regard, it is sometimes important to ensure that a canonical value is ...
In a dagger category , a morphism is called . unitary if † =,; self-adjoint if † =.; The latter is only possible for an endomorphism:.The terms unitary and self-adjoint in the previous definition are taken from the category of Hilbert spaces, where the morphisms satisfying those properties are then unitary and self-adjoint in the usual sense.
It is frequently the case that antiautomorphisms are involutions, i.e. the square of the antiautomorphism is the identity map; these are also called involutive antiautomorphism s. For example, in any group the map that sends x to its inverse x −1 is an involutive antiautomorphism. A ring with an involutive antiautomorphism is called a *-ring ...
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Here is an example, in C-like pseudocode, of an integer variant computed from some upper bound on the number of iterations remaining in a while loop. However, C allows side effects in the evaluation of expressions, which is unacceptable from the point of view of formally verifying a computer program.