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Papers by Yiorgos Stavrinos

By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a t... more By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a term in the simply typed lambda calculus à la Curry. A development becomes a usual β-reduction in the simply typed lambda calculus and the corresponding properties of developments come out from the corresponding properties (strong normalization and Church-Rosser) holding in this system. In this way we obtain a complete simulation of the notion of development into the system of simply typed lambda calculus.

By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a t... more By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a term in the simply typed lambda calculu a la Curry. A development becomes a usual β-reduction in the simply typed lambda calculus and the corresponding properties of developments come out from the corresponding properties (strong normalization and Church-Rosser) holding in this system. In this way we obtain a complete simulation of the notion of development into the system of simply typed lambda calculus. URL: http://www.mat.ufmg.br/lsfa2008/accepted-papers.html

We examine how the reducibility method is applied to prove various properties of lambda-calculus ... more We examine how the reducibility method is applied to prove various properties of lambda-calculus and we distinguish the conditions that the properties must fulfill for the method to run.

The Australasian Journal of Logic

We give a proof via reducibility of the Church-Rosser property for the system D of λ-calculus wit... more We give a proof via reducibility of the Church-Rosser property for the system D of λ-calculus with intersection types. As a consequence we can get the confluence property for developments directly, without making use of the strong normalization property for developments, by using only the typability in D and a suitable embedding of developments in this system. As an application we get a proof of the Church-Rosser theorem for the untyped λ-calculus.

Linear logic deals with two kinds of conjunction, multiplicative ⊗ and additive &. For these conn... more Linear logic deals with two kinds of conjunction, multiplicative ⊗ and additive &. For these connectives both sequents A⊗B ⇒ A &B and A&B ⇒ A⊗B are not derivable. Another system with two kinds of conjunction (and disjunction) is Intersection and Union Logic IUL [3,6,5] which aims to give a logical foundation for intersection and union types [1]. In IUL, conjunction ∧ is an asynchronous connective and has a multiplicative definition whereas intersection ∩ being synchronous is necessarily additive [3]. For these connectives, A ∧B ⇒ A ∩B is not derivable whereas A ∩B ⇒ A ∧B is and thus intersection ∩ behaves as a special synchronous conjunction. To investigate further the nature of these connectives we define a translation ( ) ◦ of IUL in linear logic and prove a full embedding. In the translation of ∩ we take into account the additive aspect of ∩ and therefore (A ∩B) ◦ = A ◦ & B ◦, whereas for ∧ and ⊗ we consider general elimination rules [4,2] and thus we translate (A ∧ B) ◦ =!A ◦ ⊗!...

The intersection type assignment system IT (shown in Figure 1) is a deductive system that assigns... more The intersection type assignment system IT (shown in Figure 1) is a deductive system that assigns formu-lae (built from the intuitionistic implication → and the intersection ∩) as types to the untyped λ-calculus. It has been defined by Coppo and Dezani [6], in order to increase the typability power of the simple type assignment system. In fact, IT has a strong typability power, since it gives types to all the strongly

e-mail: g.stavrinosmath.ntua.gr Abstra t We give a new proof of the Chur h-Rosser theorem using a... more e-mail: g.stavrinosmath.ntua.gr Abstra t We give a new proof of the Chur h-Rosser theorem using a system of - al ulus with onjun-tive (interse tion) types. We prove rst the Chur h-Rosser theorem for the typed terms with a redu ibility like method. Then the full Chur h-Rosser theorem is proved by working with a system in whi h ontrol is taken over -redu tions and where all terms are typable.

By using an infinity of extra constants every λ-term with indexed redexes is interpreted into a t... more By using an infinity of extra constants every λ-term with indexed redexes is interpreted into a term in the simply typed λ-calculus à la Curry. A development becomes a usual β-reduction in the simply typed lambda calculus and the corresponding properties of developments come out from the corresponding properties (strong normalization and Church-Rosser) holding in this system. In this way we obtain a complete simulation of the notion of development into the system of simply typed lambda calculus. Keywords: developments, strong normalization, Church-Rosser property, simple types 1.

A logical foundation for the intersection and union types assignment system (IUT) is proposed. We... more A logical foundation for the intersection and union types assignment system (IUT) is proposed. We present Intersection-Union Logic (IUL) as an extension of Intersection Logic (IL) by adding rules for union and we examine some properties of this system and its relation with intuitionistic minimal logic.

Abstract. We examine a logical foundation for the intersection and union types assignment system ... more Abstract. We examine a logical foundation for the intersection and union types assignment system (IUT). The proposed system is Intersection and Union Logic (IUL), an extension of Intersection Logic (IL) with the canonical rules for union. We investigate two different formalisms for IUL, as well as its properties and its relation with minimal intuitionistic logic.

Submitted by ΑΝΝΑ ΠΟΡΤΙΝΟΥ (annaportinou@ekt.gr) on 2016-06-10T07:31:40Z No. of bitstreams: 1 1.4... more Submitted by ΑΝΝΑ ΠΟΡΤΙΝΟΥ (annaportinou@ekt.gr) on 2016-06-10T07:31:40Z No. of bitstreams: 1 1.49_ΑΝ_18_6_12.pdf: 8812689 bytes, checksum: 6269186d9bdf8b1be223b035b58b8898 (MD5)

Fundamenta Informaticae

We examine a logical foundation for the intersection and union types assignment system (IUT). The... more We examine a logical foundation for the intersection and union types assignment system (IUT). The proposed system is Intersection and Union Logic (IUL), an extension of Intersection Logic (IL) with the canonical rules for union. We investigate two different formalisms for IUL, as well as its properties and its relation with minimal intuitionistic logic.

Fundamenta Informaticae

Yiorgos Stavrinos: Generalized Developments in λ-calculus 1/17 Outline Generalized developments λ... more Yiorgos Stavrinos: Generalized Developments in λ-calculus 1/17 Outline Generalized developments λ-calculi with types Embedding Finiteness of gen. developments Conclusion Outline Generalized developments λ-calculi with types Embedding Finiteness of gen. developments Conclusion Yiorgos Stavrinos: Generalized Developments in λ-calculus 2/17 Outline Generalized developments λ-calculi with types Embedding Finiteness of gen. developments Conclusion • V =

http://www.mathcomp.leeds.ac.uk/turing2012/WScie12/Images/abstracts-booklet.pdf, p.129

URL: http://www.math.ucla.edu/\~asl/bsl/1202/1202-007.ps (see pp. 322-323)

By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a t... more By using an infinity of extra variables every λ-term with indexed redexes is interpreted into a term in the simply typed lambda calculu a la Curry. A development becomes a usual β-reduction in the simply typed lambda calculus and the corresponding properties of developments come out from the corresponding properties (strong normalization and Church-Rosser) holding in this system. In this way we obtain a complete simulation of the notion of development into the system of simply typed lambda calculus. URL: http://www.mat.ufmg.br/lsfa2008/accepted-papers.html

The Australasian Journal of Logic

Fundamenta Informaticae

http://www.mathcomp.leeds.ac.uk/turing2012/WScie12/Images/abstracts-booklet.pdf, p.129

URL: http://www.math.ucla.edu/\~asl/bsl/1202/1202-007.ps (see pp. 322-323)