Incremental Equational Constraint Analyses

Interpretation −→ Constraint Analyzer Abstract Conditional Narrowing e ∈ g ∧ u ∈ Ō(e) ∧ (λ → ρ ⇐ ẽ) << RA ∧ σ = mguA({(e|u)κ = λ}) 〈⇐ g, κ〉 ;A 〈⇐ (g ∼ {e}) ∪ {e[u ← ρ]} ∪ ẽ, κσ〉Conditional Narrowing e ∈ g ∧ u ∈ Ō(e) ∧ (λ → ρ ⇐ ẽ) << RA ∧ σ = mguA({(e|u)κ = λ}) 〈⇐ g, κ〉 ;A 〈⇐ (g ∼ {e}) ∪ {e[u ← ρ]} ∪ ẽ, κσ〉 where mguA is the abstract mgu RA is a simplified abstract program which always terminates Abstract success set semantics ∆(⇐ g) = {κ ∈ SubA | 〈⇐ g, ǫ〉 ;A 〈⇐ true, κ〉} unsatisfiability ∆(⇐ g) = Ø → g unsatisfiable Abstract Narrowing as Constraint AnalyzerNarrowing as Constraint Analyzer ∆(⇐ c ∪ c̃) 6= Ø c c̃ −→ c ∪ c̃ '