9781848905153 - computational paths. the calculus of equality de freitas ramos, arthur; de queiroz, ruy j g b; grisi de oliveira, anjolina (16 resultados)
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Computational Paths. The Calculus of Equality
Freitas Ramos, Arthur; De Queiroz, Ruy J G B; Grisi De Oliveira, Anjolina
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Computational Paths. The Calculus of Equality
Freitas Ramos, Arthur; De Queiroz, Ruy J G B; Grisi De Oliveira, Anjolina
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Paperback. Condición: new. Paperback. When are two proofs of the same proposition equal? This book answers through computational paths - explicit syntactic witnesses that record how one proof-term rewrites into another. Continuing the programme begun in The Functional Interpretation of Logical Deduction (2011), it extends the Cu…rry-Howard correspondence and the tradition of labelled deductive systems into a rewrite calculus of proof equalities. Part I develops a 77-rule rewrite system on paths, proves it confluent and terminating, and derives decidable path equivalence from unique normal forms. Part II uncovers the higher-dimensional structure latent in this calculus: paths assemble into a weak w-groupoid, with 2-cells as derivations between paths, 3-cells as coherences between derivations, and the Eckmann-Hilton argument recovered directly from rewrite combinatorics. Part III turns outward - to path induction and the J-eliminator, the failure of UIP and the resulting proof-relevance, fundamental groupoids of combinatorial spaces, and the framework's relationship to Homotopy Type Theory, category theory, and higher algebra. The approach shares conceptual ground with HoTT but diverges in its commitments: where HoTT posits univalence and higher inductive types, computational paths offer explicit rewrite witnesses and effective normalisation, with path equivalence rendered decidable rather than postulated. A companion Lean 4 formalization machine-checks the core constructions and major theorems. Aimed at logicians, type theorists, and mathematicians concerned with the computational content of equality, the volume is self-contained - appendices cover term rewriting and higher groupoids - while charting a research programme that reaches toward dependent types, directed rewriting, and homotopical semantics. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Computational Paths. The Calculus of Equality
Freitas Ramos, Arthur; De Queiroz, Ruy J G B; Grisi De Oliveira, Anjolina
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Computational Paths. The Calculus of Equality
Freitas Ramos, Arthur; De Queiroz, Ruy J G B; Grisi De Oliveira, Anjolina
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Paperback. Condición: new. Paperback. When are two proofs of the same proposition equal? This book answers through computational paths - explicit syntactic witnesses that record how one proof-term rewrites into another. Continuing the programme begun in The Functional Interpretation of Logical Deduction (2011), it extends the Cu…rry-Howard correspondence and the tradition of labelled deductive systems into a rewrite calculus of proof equalities. Part I develops a 77-rule rewrite system on paths, proves it confluent and terminating, and derives decidable path equivalence from unique normal forms. Part II uncovers the higher-dimensional structure latent in this calculus: paths assemble into a weak w-groupoid, with 2-cells as derivations between paths, 3-cells as coherences between derivations, and the Eckmann-Hilton argument recovered directly from rewrite combinatorics. Part III turns outward - to path induction and the J-eliminator, the failure of UIP and the resulting proof-relevance, fundamental groupoids of combinatorial spaces, and the framework's relationship to Homotopy Type Theory, category theory, and higher algebra. The approach shares conceptual ground with HoTT but diverges in its commitments: where HoTT posits univalence and higher inductive types, computational paths offer explicit rewrite witnesses and effective normalisation, with path equivalence rendered decidable rather than postulated. A companion Lean 4 formalization machine-checks the core constructions and major theorems. Aimed at logicians, type theorists, and mathematicians concerned with the computational content of equality, the volume is self-contained - appendices cover term rewriting and higher groupoids - while charting a research programme that reaches toward dependent types, directed rewriting, and homotopical semantics. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
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Paperback. Condición: new. Paperback. When are two proofs of the same proposition equal? This book answers through computational paths - explicit syntactic witnesses that record how one proof-term rewrites into another. Continuing the programme begun in The Functional Interpretation of Logical Deduction (2011), it extends the Cu…rry-Howard correspondence and the tradition of labelled deductive systems into a rewrite calculus of proof equalities. Part I develops a 77-rule rewrite system on paths, proves it confluent and terminating, and derives decidable path equivalence from unique normal forms. Part II uncovers the higher-dimensional structure latent in this calculus: paths assemble into a weak w-groupoid, with 2-cells as derivations between paths, 3-cells as coherences between derivations, and the Eckmann-Hilton argument recovered directly from rewrite combinatorics. Part III turns outward - to path induction and the J-eliminator, the failure of UIP and the resulting proof-relevance, fundamental groupoids of combinatorial spaces, and the framework's relationship to Homotopy Type Theory, category theory, and higher algebra. The approach shares conceptual ground with HoTT but diverges in its commitments: where HoTT posits univalence and higher inductive types, computational paths offer explicit rewrite witnesses and effective normalisation, with path equivalence rendered decidable rather than postulated. A companion Lean 4 formalization machine-checks the core constructions and major theorems. Aimed at logicians, type theorists, and mathematicians concerned with the computational content of equality, the volume is self-contained - appendices cover term rewriting and higher groupoids - while charting a research programme that reaches toward dependent types, directed rewriting, and homotopical semantics. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
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Taschenbuch. Condición: Neu. Computational Paths. The Calculus of Equality | Arthur Freitas Ramos (u. a.) | Taschenbuch | Englisch | 2026 | College Publications | EAN 9781848905153 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.
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Taschenbuch. Condición: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - When are two proofs of the same proposition equal This book answers through computational paths - explicit syntactic witnesses that record how one proof-term rewrites into another. Continuing the programme begun in The Functional Interpr…etation of Logical Deduction (2011), it extends the Curry-Howard correspondence and the tradition of labelled deductive systems into a rewrite calculus of proof equalities. Part I develops a 77-rule rewrite system on paths, proves it confluent and terminating, and derives decidable path equivalence from unique normal forms. Part II uncovers the higher-dimensional structure latent in this calculus: paths assemble into a weak ¿-groupoid, with 2-cells as derivations between paths, 3-cells as coherences between derivations, and the Eckmann-Hilton argument recovered directly from rewrite combinatorics. Part III turns outward - to path induction and the J-eliminator, the failure of UIP and the resulting proof-relevance, fundamental groupoids of combinatorial spaces, and the framework's relationship to Homotopy Type Theory, category theory, and higher algebra. The approach shares conceptual ground with HoTT but diverges in its commitments: where HoTT posits univalence and higher inductive types, computational paths offer explicit rewrite witnesses and effective normalisation, with path equivalence rendered decidable rather than postulated. A companion Lean 4 formalization machine-checks the core constructions and major theorems. Aimed at logicians, type theorists, and mathematicians concerned with the computational content of equality, the volume is self-contained - appendices cover term rewriting and higher groupoids - while charting a research programme that reaches toward dependent types, directed rewriting, and homotopical semantics.
