Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline. In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself. The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.

Per Martin-Löf''s work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf''s earliest papers.

Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.

Aimed at researchers in mathematics, philosophy and logic, this book provides the first organic exposition of dynamic constructivism and the mathematics ensuing in practice, including discussion of the technical development of the field and outlining the philosophical and methodological motivations underlying the evolution of the discipline. In dynamic constructivism, mathematics is seen as the result of a dynamic process of interaction between the construction of mathematical entities, by abstraction and by idealization, and their selection according to their efficiency in applications to reality and in the organisation of mathematics itself. The crucial benefit of this vision is its independence from dogmas and external authorities. A practical consequence is full respect for the diverse areas of mathematics - mainly computation, spatial intuition, deduction, and abstract axiomatic method - without reducing one to another. As a second consequence, a dynamic interaction between different 'epistemological levels' is always active and present, in the development of mathematics in practice, the study of its foundations and its formalisation in a computer language.

Per Martin-Löf''s work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf''s earliest papers.

Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.