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- Vincenzo Manca, Antonino Salibra, Giuseppe Scollo
- Theor. Comput. Sci.
- 1990

- Antonino Salibra
- Theor. Comput. Sci.
- 2000

The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory logic in this regard since it is a rst-order algebraic… (More)

- Antonino Salibra, Giuseppe Scollo
- Mathematical Structures in Computer Science
- 1996

- Stefania Lusin, Antonino Salibra
- J. Log. Comput.
- 2004

Lambda theories are equational extensions of the untyped lambda calculus that are closed under derivation. The set of lambda theories is naturally equipped with a structure of complete lattice, where the meet of a family of lambda theories is their intersection, and the join is the least lambda theory containing their union. In this paper we study the… (More)

- Antonino Salibra, Giuseppe Scollo
- COMPASS/ADT
- 1991

Abs t rac t . The notion of institution is dissected into somewhat weaker notions. We introduce a novel notion of institution morphism, and characterize preservation of institution properties by corresponding properties of such morphisms. Target of this work is the stepwise construction of a general framework for translating logics, and algebraic… (More)

- Don Pigozzi, Antonino Salibra
- Fundam. Inform.
- 1997

- Antonino Salibra
- Fundam. Inform.
- 2001

The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the first-order predicate logic. In this paper we prove that the lattice of lambda theories is not modular and that the variety generated by the term algebra of a semi-sensible… (More)

- Giulio Manzonetto, Antonino Salibra
- 21st Annual IEEE Symposium on Logic in Computer…
- 2006

In this paper we show that the Stone representation theorem for Boolean algebras can be generalized to combinatory algebras. In every combinatory algebra there is a Boolean algebra of central elements (playing the role of idempotent elements in rings), whose operations are defined by suitable combinators. Central elements are used to represent any… (More)

- Antonio Bucciarelli, Antonino Salibra
- MFCS
- 2003

A longstanding open problem in lambda-calculus, raised by G.Plotkin, is whether there exists a continuous model of the untyped lambda-calculus whose theory is exactly the beta-theory or the beta-eta-theory. A related question, raised recently by C.Berline, is whether, given a class of lambda-models, there is a minimal theory represented by it. In this… (More)

- Antonino Salibra, Robert Goldblatt
- Inf. Comput.
- 1999

A lambda theory satisfies an equation between contexts, where a context is a *-term with some ``holes'' in it, if all the instances of the equation fall within the lambda theory. In the main result of this paper it is shown that the equations (between contexts) valid in every lambda theory have an explicit finite equational axiomatization. The variety of… (More)