Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Programming with Proofs: A Second Order Type Theory
ESOP '88 Proceedings of the 2nd European Symposium on Programming
Constructions: A Higher Order Proof System for Mechanizing Mathematics
EUROCAL '85 Invited Lectures from the European Conference on Computer Algebra-Volume I - Volume I
Extended projection—new method to extract efficient programs from constructive proofs
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Extraction of redundancy-free programs from constructive natural deduction proofs
Journal of Symbolic Computation
Explicit polymorphism and CPS conversion
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Synthesis of ML programs in the system Coq
Journal of Symbolic Computation - Special issue on automatic programming
QPC2: A constructive calculus with parameterized specifications
Journal of Symbolic Computation - Special issue on automatic programming
A type system for certified binaries
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Least and greatest fixed points in intuitionistic natural deduction
Theoretical Computer Science - Special issue on theories of types and proofs
Least and greatest fixed points in intuitionistic natural deduction
Theoretical Computer Science - Special issue on theories of types and proofs
Automatic Synthesis of Recursive Programs: The Proof-Planning Paradigm
Automated Software Engineering
Studies of a Theory of Specifications with Built-in Program Extraction
Journal of Automated Reasoning
Type-Based Useless-Code Elimination for Functional Programs
SAIG '00 Proceedings of the International Workshop on Semantics, Applications, and Implementation of Program Generation
Useless-Code Detection and Elimination for PCF with Algebraic Data types
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Proof of Imperative Programs in Type Theory
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
A Static Calculus of Dependencies for the -Cube
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A conjunctive type system for useless-code elimination
Mathematical Structures in Computer Science
Automatic useless-code elimination for HOT functional programs
Journal of Functional Programming
Verification of non-functional programs using interpretations in type theory
Journal of Functional Programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
A type system for certified binaries
ACM Transactions on Programming Languages and Systems (TOPLAS)
Formal proof of a program: Find
Science of Computer Programming
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
Formal correctness of conflict detection for firewalls
Proceedings of the 2007 ACM workshop on Formal methods in security engineering
Lightweight semiformal time complexity analysis for purely functional data structures
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Algebra of Programming Using Dependent Types
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Algebra of programming in agda: Dependent types for relational program derivation
Journal of Functional Programming
An operational approach to program extraction in the calculus of constructions
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Program extraction in simply-typed higher order logic
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
A certified distributed security logic for authorizing code
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
On the rôle of minimal typing derivations in type-driven program transformation
Proceedings of the Tenth Workshop on Language Descriptions, Tools and Applications
Realizability and parametricity in pure type systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Modularising inductive families
Proceedings of the seventh ACM SIGPLAN workshop on Generic programming
A Computational Interpretation of Parametricity
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Classical program extraction in the calculus of constructions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Hasochism: the pleasure and pain of dependently typed haskell programming
Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
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We define in this paper a notion of realizability for the Calculus of Constructions. The extracted programs are terms of the Calculus that do not contain dependent types. We introduce a distinction between informative and non-informative propositions. This distinction allows the removal of the “logical” part in the development of a program. We show also how to use our notion of realizability in order to interpret various axioms like the axiom of choice or the induction on integers. A practical example of development of program is given in the appendix.