{"product_id":"the-clausal-theory-of-types-paperback-9780521117906","title":"The Clausal Theory of Types (Paperback) 9780521117906","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Clausal Theory of Types\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eIn this book is presented the theoretical foundation of a higher-order logic programming language with equality, based on the clausal theory of types.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eD. A. Wolfram (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521117906, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 30 July 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e136 pages\u003cbr\u003e24.4 x 17 x 0.7 cm, 0.23 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eLogic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic with equality, known as the Clausal Theory of Types. By restricting this logic to Horn clauses, a concise form of logic programming that incorporates functional programming is achieved. The book begins by reviewing the fundamental Skolem-Herbrand-Gödel Theorem and resolution, which are then extrapolated to a higher-order setting; this requires introducing higher-order equational unification which builds in higher-order equational theories and uses higher-order rewriting. The logic programming language derived has the unique property of being sound and complete with respect to Henkin-Andrews general models, and consequently of treating equivalent terms as identical. First published in 1993, the book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Logic programming: a case study\u003cbr\u003e 3. Simply typed l-calculus\u003cbr\u003e 4. Higher-order logic\u003cbr\u003e 5. Higher-order equational unification\u003cbr\u003e 6. Higher-order equational logic programming.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006526640408,"sku":"9780521117906","price":26.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521117906i_ae4335b0-af68-42b7-a57d-7d9461a1e030.jpg?v=1691371583","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-clausal-theory-of-types-paperback-9780521117906","provider":"Freshly Printed Books","version":"1.0","type":"link"}