We present algorithms for unification and antiunification in the Calculus of Constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higher-order patterns, a notion investigated for the simply-typed λ-calculus by Miller. Most general unifiers and least common antiinstances are shown to exist and are unique up to a simple equivalence. The uni...

The Curry-Howard isomorphism 1 is the basis of typed functional programming. By means of this isomorphism, the intuitionistic proof of a formula can be seen as a functional program, whose type is the formula itself. In this way, the computation process has its logic realization in the proof normalization procedure. Both the implicative fragment of the intuitionistic propositional logic together...

in recent years, soft computing methods have generated a large research interest. the synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. a particular evolutionary algorithm (ea) is differential evolution (de). as for any ea, de algorithm also requires parameters tuning to achieve desirable performance. in this paper tuning the perturbation factor vector of de ...

Auditing is an increasingly important operation for computer programming, for example in security (e.g. to enable history-based access control) and to enable reproducibility and accountability (e.g. provenance in scientific programming). Most proposed auditing techniques are ad hoc or treat auditing as a second-class, extralinguistic operation; logical or semantic foundations for auditing are n...

Injectivity with respect to morphisms having λ-presentable domains and codomains is characterized: such injectivity classes are precisely those closed under products, λ-directed colimits, and λ-pure subobjects. This sharpens the result of the first two authors (Trans. Amer. Math. Soc. 336 (1993), 785-804). In contrast, for geometric logic an example is found of a class closed under directed col...

In recent years, soft computing methods have generated a large research interest. The synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. A particular evolutionary algorithm (EA) is differential evolution (DE). As for any EA, DE algorithm also requires parameters tuning to achieve desirable performance. In this paper tuning the perturbation factor vector of DE ...

In recent years, soft computing methods have generated a large research interest. The synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. A particular evolutionary algorithm (EA) is differential evolution (DE). As for any EA, DE algorithm also requires parameters tuning to achieve desirable performance. In this paper tuning the perturbation factor vector of DE ...

We develop the semantic foundations of the specification language HasCasl, which combines algebraic specification and functional programming on the basis of Moggi’s partial λ-calculus. Generalizing Lambek’s classical equivalence between the simply typed λ-calculus and cartesian closed categories, we establish an equivalence between partial cartesian closed categories (pccc’s) and partial λ-theo...

We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry–Howard correspondence to obtain typed concurrent λ-calculi; each of them features a specific communication mechanism, including broadcasting and cyclic messageexchange, and enhanced expressive power w.r.t. the λ-calculus. Moreover they all implement forms of code mobility. Our results provide a fi...

Generic rst-order logic (GFOL) is a rst-order logic parameterized with terms de ned axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. GFOL has a complete Gentzen system generalizing that of FOL. An important fragment of GFOL, called HORN, possesses a much simpler Gentzen system, simil...