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Type Theory and Functional Programming (International Computer Science Series)

Type Theory And Functional Programming

Penned By Simon Thompson
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4.85
70,169 Global Ratings
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Type Theory and Functional Programming (International Computer Science Series)

Type Theory And Functional Programming

Penned By Simon Thompson
4.85 70,169 Ratings
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Editor's Note:
Constructive Type theory has been a topic of research interest to computer scientists, mathematicians, logicians and philosophers for a number of years. For computer scientists it provides a framework which brings together logic and programming languages in a most elegant and fertile program development and verification can proceed within a single system. Viewed in a different way, type theory is a functional programming language with some novel features, such as the totality of all its functions, its expressive type system allowing functions whose result type depends upon the value of its input, and sophisticated modules and abstract types whose interfaces can contain logical assertions as well as signature information. A third point of view emphasizes that programs (or functions) can be extracted from proofs in the logic.The book can be thought of as giving both a first and a second course in type theory. It begins with introductory material on logic and functional programming, and follow this by presenting the system of type theory itself, together with many examples. As well as this, this book goes further, looking at the system from a mathematical perspective, thus elucidating a number of its important properties. This book then takes a critical look at the profusion of suggestions in the literature about why and how type theory could be augmented. In doing this, this book is aiming at a moving target; it must be the case that further developments will have been made before the book reaches the press. Nonetheless, such an survey can give the reader a much more developed sense of the potential of type theory, as well as giving the background of what is to come.Book The first three chapters survey the three fields upon which type theory logic, the lambda-calculus and functional programming and constructive mathematics. The surveys are short, establishing terminology, notation and a general context for the discussion; pointers to the relevant literature and in particular to more detailed introductions are provided. In the second chapter this book discusses some issues in the lambda-calculus and functional programming which suggest analogous questions in type theory.The fourth chapter forms the focus of the book. This book gives the formal system for type theory, developing examples of both programs and proofs as we go along. These tend to be short, illustrating the construct just introduced - Chapter 6 contains many more examples.The system is expressive, as witnessed by the previous chapter, but are programs given in their most natural or efficient form? Chapter 7 provides a host of proposals of how to augment the system.Chapter eight examines the foundations of the how it compares with other systems for constructive mathematics, how models of it are formed and used and how certain of the rules, the closure rules, may be seen as being generated from the introduction rules, which state what are the canonical members of each type. The book ends with a survey of related systems, implemented or not, and some concluding remarks.

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Length N/A Pages
Language Eng
Released August 1, 1991
Identifier (ISBN) 11364683
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Simon Thompson
The Mind Behind the Work
Simon Thompson

After spending years working in the corporate world, Simon Thompson finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Mary Martin
Mary Martin January 08, 2024
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Joshua Wright May 11, 2025
"A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
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Sharon Rodriguez
Sharon Rodriguez January 26, 2025
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
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Joseph Roberts April 25, 2024
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"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
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Thomas Rivera August 02, 2024
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
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Richard Hill October 12, 2025
"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
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Melissa Evans June 17, 2025
"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
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"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
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"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Ryan Rivera
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"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
Margaret Carter
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"Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
John Thompson
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend."
Carol Wilson
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"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Kevin Phillips
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
David Hall
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
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Ashley Reyes December 15, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
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"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
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Kimberly Flores May 21, 2024
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Deborah Rodriguez
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"I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars."
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"Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Nicholas Lopez
Nicholas Lopez September 09, 2024
"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Donna King
Donna King March 21, 2025
"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Cynthia Wilson
Cynthia Wilson December 27, 2024
"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
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"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Jacob Lee
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"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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Ashley Reyes July 24, 2025
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
John Thompson
John Thompson April 07, 2024
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
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"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
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"Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Jennifer Brown
Jennifer Brown January 24, 2025
"Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
Joseph Roberts
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"Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Kimberly King
Kimberly King June 06, 2025
"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Daniel Lewis
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"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me."
Andrew Lee
Andrew Lee October 09, 2025
"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Kevin Robinson
Kevin Robinson June 03, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
Ashley Reyes
Ashley Reyes December 08, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Ashley Evans
Ashley Evans April 15, 2024
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Laura Torres
Laura Torres February 20, 2024
"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Paul Allen
Paul Allen July 03, 2024
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Robert Thomas
Robert Thomas June 05, 2024
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Paul Sanchez
Paul Sanchez May 21, 2024
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
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Dorothy Miller September 14, 2024
"I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average."
Robert Lewis
Robert Lewis June 21, 2025
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
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"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Linda Flores
Linda Flores December 09, 2025
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Margaret Flores
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
William Adams
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"A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me."
Sandra Gonzalez
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"A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
Edward  Parker
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"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
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"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars."
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"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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Lisa Collins
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Thomas Collins
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"Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
David Allen
David Allen February 13, 2025
"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
Emily Hill
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Donna Thomas
Donna Thomas June 07, 2024
"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
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Donna Harris May 28, 2025
"Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average."
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"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
Andrew White
Andrew White August 25, 2025
"A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Andrew Jackson
Andrew Jackson August 12, 2024
"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
David Edwards
David Edwards February 26, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Amanda White
Amanda White August 23, 2025
"A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average."
Sandra Gonzalez
Sandra Gonzalez May 23, 2024
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
Mark Walker
Mark Walker October 30, 2024
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
James Hill
James Hill July 15, 2024
"A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Ryan Walker
Ryan Walker October 20, 2025
"A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel."
James Garcia
James Garcia November 08, 2025
"Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Jessica Harris
Jessica Harris October 25, 2024
"Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
Carol Mitchell
Carol Mitchell July 17, 2025
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
Kevin Williams
Kevin Williams September 04, 2024
"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
William Martin
William Martin September 14, 2024
"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Joshua Walker
Joshua Walker December 12, 2025
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Barbara Martinez
Barbara Martinez December 06, 2024
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Edward Garcia
Edward Garcia January 19, 2024
"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
Richard Cruz
Richard Cruz June 04, 2024
"Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time."
Richard Cruz
Richard Cruz September 14, 2024
"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Paul Sanchez
Paul Sanchez March 27, 2024
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Sharon Rodriguez
Sharon Rodriguez August 15, 2025
"I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars."
Brian Clark
Brian Clark July 02, 2024
"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
Barbara Green
Barbara Green February 16, 2024
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Ashley Lopez
Ashley Lopez March 03, 2025
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Linda Phillips
Linda Phillips May 23, 2025
"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
George Williams
George Williams January 24, 2024
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
Mary Carter
Mary Carter January 23, 2024
"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
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