Computational Paths. The Calculus of Equality (Paperback)
Language: English
Published by College Publications, 2026
- Softcover
- New
Seller: Grand Eagle Retail, Bensenville, IL, U.S.A.Grand Eagle Retail
AbeBooks seller since October 12, 2005
Condition: New
£ 31.78
Quantity: 1 available
Add to basketItem description from seller
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 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 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.…
Seller Inventory # 9781848905153
- Title
- Computational Paths. The Calculus of Equality (Paperback)
- Author
- Arthur Freitas Ramos
- Publisher
- College Publications
- Publication year
- 2026
- Condition
- new
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1848905157
- ISBN 13
- 9781848905153
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 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 ω-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.
"Synopsis" may belong to another edition of this title.
Grand Eagle Retail
Bensenville, IL, U.S.A.
AbeBooks seller since October 12, 2005
Shipping rates within U.S.A.
| Item | 6 to 14 business days | 6 to 16 business days |
|---|---|---|
| First item | £ 0.00 | £ 0.00 |
Payment methods
Seller's business information
APOLLO ONLINE CORP.
605 Geddes Street
Wilmington, DE U.S.A. 19805
Terms of sale
We guarantee the condition of every book as it¿s described on the Abebooks web sites. If you¿ve changed
your mind about a book that you¿ve ordered, please use the Ask bookseller a question link to contact us
and we¿ll respond within 2 business days.
Books ship from California and Michigan.
Right of withdrawal
If you are a consumer you can withdraw from the contract in accordance with the following. Consumer means any natural person who is acting for purposes which are outside his trade, business, craft or profession.
Information regarding the right of withdrawal
Statutory right to withdraw
You have the right to withdraw from this contract within 14 days without giving any reason.
The withdrawal period will expire after 14 days from the day on which you acquire, or a third party other than the carrier and indicated by you acquires, physical possession of the last good or the last lot or piece.
To exercise the right of withdrawal, electronically fill in and submit a clear statement on our website, under "My Purchases" in "My Account". We will communicate to you an acknowledgement of receipt of such a withdrawal on a durable medium (e.g. by e-mail) without delay.
To meet the withdrawal deadline, it is sufficient for you to send your communication concerning your exercise of the right of withdrawal before the withdrawal period has expired.
Effects of withdrawal
If you withdraw from this contract, we will reimburse to you all payments received from you, including the costs of delivery (except for the supplementary costs arising if you chose a type of delivery other than the least expensive type of standard delivery offered by us).
We may make a deduction from the reimbursement for loss in value of any goods supplied, if the loss is the result of unnecessary handling by you.
We will make the reimbursement without undue delay, and not later than 14 days after the day on which we are informed about your decision to withdraw from this contract.
We will make the reimbursement using the same means of payment as you used for the initial transaction, unless you have expressly agreed otherwise; in any event, you will not incur any fees as a result of such reimbursement.
We may withhold reimbursement until we have received the goods back, or you have supplied evidence of having sent back the goods, whichever is the earliest.
You shall send back the goods or hand them over to Grand Eagle Retail, Bensenville, Illinois, U.S.A., without undue delay and in any event not later than 14 days from the day on which you communicate your withdrawal from this contract to us. The deadline is met if you send back the goods before the period of 14 days has expired. You will have to bear the direct cost of returning the goods. You are only liable for any diminished value of the goods resulting from the handling other than what is necessary to establish the nature, characteristics and functioning of the goods.
Exceptions to the right of withdrawal
The right of withdrawal does not apply to:
- The delivery of newspapers, journals or magazines with the exception of subscription contracts; and
- The supply of digital content which is not supplied on a tangible medium (e.g. on a CD or DVD) if you accepted when you placed your order that we could start to deliver it, and that you could not withdraw once delivery had started.
Shipping terms
Orders usually ship within 2 business days. All books within the US ship free of charge. Delivery is 4-14 business days anywhere in the United States.
Books ship from California and Michigan.
If your book order is heavy or oversized, we may contact you to let you know extra shipping is required.