Remarks on isomorphisms in typed lambda calculi with empty and sum types

Fiore, Marcelo; Cosmo, Roberto Di; Balat, Vincent

doi:10.1109/lics.2002.1029824

Cited by 23 publications

(35 citation statements)

References 27 publications

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“…Fiore, Di Cosmo and Balat [10] have answered Problem 7 in the negative within the context of cartesian closed categories with finite coproducts. 5 Problem 8.…”

Section: Problemmentioning

confidence: 99%

The saga of the High School Identities

Burris

Yeats

2005

Algebra univers.

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“…Fiore, Di Cosmo and Balat [10] have answered Problem 7 in the negative within the context of cartesian closed categories with finite coproducts. 5 Problem 8.…”

Section: Problemmentioning

confidence: 99%

The saga of the High School Identities

Burris

Yeats

2005

Algebra univers.

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“…What is known about the isomorphism of types of E, in general, are the following facts, both proved in [8].…”

Section: Introductionmentioning

confidence: 98%

“…Theorem 2 (Martin-Wilkie-Gurevič-Fiore-DiCosmo-Balat [8,11,19,28]). Isomorphism is not finitely axiomatizable, that is, for no finite set of axioms T can we show that f ∼ = g always implies T f .…”

Section: Introductionmentioning

confidence: 99%

Axioms and decidability for type isomorphism in the presence of sums

Ilik

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High-School Identities (HSI) is complete for a significant subclass of types; that it is decidable for that subclass when two types are isomorphic; that, for the whole of the set of types, a recursive extension of the axioms of HSI exists that is complete; and that, for the whole of the set of types, the question as to whether two types are isomorphic is decidable when base types are to be interpreted as finite sets. We also point out certain related open problems.

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“…As far as we know, the latest advances concerning the problem of characterizing formulae isomorphic in the whole of intuitionistic propositional logic (which is related to Tarski's high-school algebra problem; cf. [3]) were made in [2] and [16]. 1 There is a related result characterizing isomorphic formulae in the analogous multiplicative fragment of linear logic, which corresponds to symmetric monoidal closed categories, and is common to classical and intuitionistic linear logic (see [9] and [22]).…”

Section: Introductionmentioning

confidence: 99%

Isomorphic formulae in classical propositional logic

Došen

Petric

2011

Mathematical Logic Qtrly

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Key words isomorphic formulae, classical propositional logic, classical linear propositional logic, categories, equality of deductions, identity of proofs, categorial coherence. MSC (2010) 03F03, 03F07, 03F52, 03G30Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

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Remarks on isomorphisms in typed lambda calculi with empty and sum types

Abstract: Abstract

Cited by 23 publications

References 27 publications

The saga of the High School Identities

The saga of the High School Identities

Axioms and decidability for type isomorphism in the presence of sums

Isomorphic formulae in classical propositional logic

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