unification Let an operation amgu(x = t, ASub) of abstract unification for equation x = t, x ∈ V , t ∈ Term, and ASub an abstract substitution (the domain of which contains variables t̂ ∪ {x}). Abstract unification for equation t1 = t2, t1 ∈ Term, t2 ∈ Term, in the context of abstract substitution ASub (the domain of which contains variables t̂1 ∪ t̂2) is given by Amgu(solve(t1 = t2), ASub), where...

In 6, 5] a technique for the automatic derivation of an Abstract Interpretation Domain for (the Abstract Data Types part) of LOTOS speciications has been proposed. In this paper we present an abstract model of process semantics, Abstract Trace Semantics, which is built on top of the above mentioned Abstract Interpretation Domain and which we use as a model for an abstract interpretation of a li...

Domain: Interval Abstract Semantics: the ExampleSemantics: the Example I Abstract values: +, -, 0 I Abstract operations: I Sound: the signedness properties preserve in the abstract domain See the extension of the Prof. Alex Aiken’s example

Semantics Similar to concrete semantics:  A complete lattice (L#, ≤) as the domain for abstract elements  A monotone function F# corresponding to the concrete function F  Then the abstract semantics is the least fixed point of F#, lfp F# If F# “correctly approximates” F, then lfp F# “correctly approximates” lfp F. Fixpoint Transfer Theorem Local Correctness Global Correctness An Example Abst...

Semantics Similar to concrete semantics:  A complete lattice (L#, ≤) as the domain for abstract elements  A monotone function F# corresponding to the concrete function F  Then the abstract semantics is the least fixed point of F#, lfp F# If F# “correctly approximates” F, then lfp F# “correctly approximates” lfp F. An Example Abstract Domain for Values of Variables How to relate the two?  Co...

We propose a hierarchical shape abstract domain, so as to infer structural invariants of dynamic structures such as lists living inside static structures, such as arrays. This programming pattern is often used in safety critical embedded software as an alternative to dynamic memory allocation. Our abstract domain precisely describes such hierarchies of structures. It combines several instances ...