A precise type analysis of logic programs

Backward Type Inference Generalises Type Checking

“…The domain for the backward type analysis is the same as that for a forward type analysis [18]. A type system is first introduced on which the domain is based.…”

“…In forward type analysis [18], abstract unification takes as inputs an equation E and a type constraint φ (an upper approximation) and produces as output a type constraint ψ (another upper approximation) which describes mgu(θ(E)) • θ whenever φ describes θ. In backward type analysis, abstract unification takes as inputs an equation E and a type constraint ψ (a lower approximation) and produces as output a type constraint φ (another lower approximation) which describes θ whenever ψ describes mgu(θ(E))•θ.…”

“…This is achieved by depth-k abstraction -a technique that is frequently applied in type analysis [1,3,18]. Sub-terms at depth k in a type R are replaced with 0 (rather than 1), resulting a type R such that R R. Thus, application of depth-k abstraction to types in the post-condition φ in a demand p(x), φ obtains a post-condition φ which is at least as strong as φ.…”

“…The backward type analysis proposed in this paper is based on a novel abstract semantics (that will be presented in a companion paper) that relaxes this requirement. The backward type analysis is obtained by specialising the new abstract semantics with domain operators for type inference and in particular type inference using an abstract domain [18] which is particularly precise since it is disjunctive and supports nondeterministic regular types. The resulting analysis is the first analysis that infers type signatures for a logic program.…”

Path dependent analysis of logic programs

“…Much research has been done in abstract interpretation of logic programs [11]. A number of (generic) abstract semantics, also called frameworks or schemes [4,6,17,23,26,38,39,43] have been proposed for analysis of logic programs; and they have been specialised for the detection of determinacy [13], data dependency analyses [14,21], mode inference [14,53], program transformation [49], type inference [22,33,34], termination proof [55,5], etc.…”