Introduction to higher order categorical logic
Introduction to higher order categorical logic
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
An on-line arithmetic unit for bit-pipelined rational arithmetic
Journal of Parallel and Distributed Computing - Parallelism in Computer Arithmetic
On the productivity of recursive list definitions
ACM Transactions on Programming Languages and Systems (TOPLAS)
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Constructing the real numbers in HOL
Formal Methods in System Design - Special issue on higher order logic theorem proving and its applications, II
Handbook of logic in computer science (vol. 3)
Maple V: programming guide
Constructive domain theory as a branch of intuitionistic pointfree topology
Theoretical Computer Science
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Vicious circles: on the mathematics of non-wellfounded phenomena
Vicious circles: on the mathematics of non-wellfounded phenomena
Representing inductively defined sets by wellorderings in Martin-Löf's type theory
Theoretical Computer Science
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Lazy computation with exact real numbers
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Induction and recursion on the partial real line with applications to Real PCF
Theoretical Computer Science - Special issue on real numbers and computers
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Computable analysis: an introduction
Computable analysis: an introduction
Types and programming languages
Types and programming languages
The Mathematica Book
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
On the syntax of infinite objects: an extension of Martin-Löf's theory of expressions
COLOG '88 Proceedings of the International Conference on Computer Logic
COLOG '88 Proceedings of the International Conference on Computer Logic
Comparing Functional Paradigms for Exact Real-Number Computation
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
A Foundation for Computable Analysis
SOFSEM '97 Proceedings of the 24th Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
A Survey of Exact Arithmetic Implementations
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
The iRRAM: Exact Arithmetic in C++
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Comparing the Theory of Representations and Constructive Mathematics
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Lazy Functional Algorithms for Exact Real Functionals
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
COLOG '88 Proceedings of the International Conference on Computer Logic
Handbook of automated reasoning
Proof-assistants using dependent type systems
Handbook of automated reasoning
A Priori Worst-Case Error Bounds for Floating-Point Computations
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Real PCF extended with integration
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
A golden ratio notation for the real numbers
A golden ratio notation for the real numbers
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
A categorical programming language
A categorical programming language
Rational arithmetic units in computer systems
Rational arithmetic units in computer systems
The realizability approach to computable analysis and topology
The realizability approach to computable analysis and topology
Realizability: a historical essay
Mathematical Structures in Computer Science
Domain theory and differential calculus (functions of one variable)
Mathematical Structures in Computer Science
On the non-sequential nature of the interval-domain model of real-number computation
Mathematical Structures in Computer Science
Modelling general recursion in type theory
Mathematical Structures in Computer Science
Theoretical Computer Science - Real numbers and computers
A Large-Scale Experiment in Executing Extracted Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
A unifying approach to recursive and co-recursive definitions
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Filters on coinductive streams, an application to eratosthenes' sieve
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Formalising exact arithmetic in type theory
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
A Functional Algorithm for Exact Real Integration with Invariant Measures
Electronic Notes in Theoretical Computer Science (ENTCS)
Proofs of randomized algorithms in Coq
Science of Computer Programming
From coinductive proofs to exact real arithmetic
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Minlog: a tool for program extraction supporting algebras and coalgebras
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
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In this paper we will discuss various aspects of computable/constructive analysis, namely semantics, proofs and computations. We will present some of the problems and solutions of exact real arithmetic varying from concrete implementations, representation and algorithms to various models for real computation. We then put these models in a uniform framework using realisability, which opens the door to the use of type theoretic and coalgebraic constructions both in computing and reasoning about these computations. We will indicate that it is often natural to use constructive logic to reason about these computations.