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Program Extraction from Normalization Proofs

2006
*
Studia Logica: An International Journal for Symbolic Logic
*

*From*the formal

*proofs*

*programs*are machine-

*extracted*that implement variants of the well-known

*normalization*-by-evaluation algorithm. ... The case study is used to test and compare the

*program*

*extraction*machineries of the three

*proof*assistants in a non-trivial setting. ... As to be expected, the change

*from*strong to weak

*normalization*does not affect the

*extracted*

*programs*. ...

##
###
Program Extraction from Proofs of Weak Head Normalization

2005
*
BRICS Report Series
*

Subsequently we use Kreisel's modified realizability to

doi:10.7146/brics.v12i12.21878
fatcat:atitabzthzgwxmzqmyura5feu4
*extract*evaluation algorithms*from*the*proofs*, following Berger; the*proofs*are based on Tait-style reducibility predicates, and hence the*extracted*... We formalize two*proofs*of weak head*normalization*for the simply typed lambda-calculus in first-order minimal logic: one for*normal*-order reduction, and one for applicative-order reduction in the object ... They also outlined a process of "*program**extraction*" with which their*normalization*algorithms can be obtained*from*simple instances of a*normalization**proof*due to Martin-Löf, and noticed the connection ...##
###
Program Extraction From Proofs of Weak Head Normalization

2006
*
Electronical Notes in Theoretical Computer Science
*

Subsequently we use Kreisel's modified realizability to

doi:10.1016/j.entcs.2005.11.056
fatcat:eum43xmwb5erhmh7pm5ilobcwe
*extract*evaluation algorithms*from*the*proofs*, following Berger; the*proofs*are based on Tait-style reducibility predicates, and hence the*extracted*... We formalize two*proofs*of weak head*normalization*for the simply typed lambda-calculus in firstorder minimal logic: one for*normal*-order reduction, and one for applicative-order reduction in the object ... They also outlined a process of "*program**extraction*" with which their*normalization*algorithms can be obtained*from*simple instances of a*normalization**proof*due to Martin-Löf, and noticed the connection ...##
###
Program extraction from normalization proofs
[chapter]

*
Lecture Notes in Computer Science
*

*From*the formal

*proofs*

*programs*are machine-

*extracted*that implement variants of the well-known

*normalization*-by-evaluation algorithm. ... The case study is used to test and compare the

*program*

*extraction*machineries of the three

*proof*assistants in a non-trivial setting. ... As to be expected, the change

*from*strong to weak

*normalization*does not affect the

*extracted*

*programs*. ...

##
###
Synthesis of ML programs in the system Coq

1993
*
Journal of symbolic computation
*

*From*a constructive

*proof*formalized in Coq, one

*extracts*a functional

*program*which can be compiled and executed in ML. This paper describes how to obtain ML

*programs*

*from*

*proofs*in Coq. ... We study the specification of the problem, the development of the

*proof*and the

*extraction*of the executable ML

*program*. ... ACKNOWLEDGMENTS We thank Xavier Leroy and Chet Murthy for their help in analysing the behavior of the optimized

*normalization*function. ...

##
###
Extracting a Normalization Algorithm in Isabelle/HOL
[chapter]

2006
*
Lecture Notes in Computer Science
*

We present a formalization of a constructive

doi:10.1007/11617990_4
fatcat:pe2szgcl2vbqzemfy2ukhtjlne
*proof*of weak*normalization*for the simply-typed λ-calculus in the theorem prover Isabelle/HOL, and show how a*program*can be*extracted**from*it. ... Thus, the*program*obtained*from*this*proof*is typable in simply-typed higher-order logic as implemented in Isabelle/HOL, and a*proof*of its correctness can automatically be derived within the system. ... We show how a provably correct*program*can automatically be*extracted**from*this*proof*using Isabelle's framework for*program**extraction*[9, 10] . ...##
###
The Specialization and Transformation of Constructive Existence Proofs

1989
*
International Joint Conference on Artificial Intelligence
*

The transformation of constructive

dblp:conf/ijcai/Madden89
fatcat:qwqnsbe4ujhfxn5l2ticrtsl6e
*program*synthesis*proofs*is discussed and compared with the more traditional approaches to*program*transformation. ... An example system for adapting*programs*to special situations by transforming constructive synthesis*proofs*has been reconstructed and is compared with the original implementation [Goad, 1980b, Goad, 1980a ... then, once completed,*extract*an algorithm*from*the transformed*proof*. ...##
###
Towards the theory of programming in constructive logic
[chapter]

1990
*
Lecture Notes in Computer Science
*

We develop an approach to the theory of

doi:10.1007/3-540-52592-0_78
fatcat:wy7miwvy5jgmxdpzkw5mmhlcly
*extracting**programs**from**proofs*based on constructive semantics of the first order formulas called consTrucTive TruLb. The underlying ideas are discussed. ... There are essentially two groups of methods of*extracting**programs**from**proofs*. ... Thus the algorithm for*extracting**programs**from**proofs*should be based on this notion. ...##
###
APPLICATIONS OF INDUCTIVE DEFINITIONS AND CHOICE PRINCIPLES TO PROGRAM SYNTHESIS
[chapter]

2005
*
From Sets and Types to Topology and Analysis
*

We describe two methods of

doi:10.1093/acprof:oso/9780198566519.003.0008
fatcat:n4z453pujrenfgte7abt4tkjhi
*extracting*constructive content*from*classical*proofs*, focusing on theorems involving infinite sequences and nonconstructive choice principles. ... in term rewriting theory for termination*proofs*[CTB94,Tou02]. ... a*program**from*the latter*proof*. ...##
###
Protocols between Programs and Proofs
[chapter]

2001
*
Lecture Notes in Computer Science
*

The methodology we use for automatically

doi:10.1007/3-540-45142-0_2
fatcat:y62xq3w6infltbvlws55qlc4ea
*extracting*"correct"*programs**from**proofs*is a development of the well-known Curry-Howard process. ... In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the*programs**extracted**from*it. ... Theorem 1 above shows that we can*extract*a new*program*that satisfies the Skolemized version of the formula*from*whose*proof*we*extracted*the*program*. ...##
###
Synthesis of Moduli of Uniform Continuity by the Monotone Dialectica Interpretation in the Proof-system MinLog

2007
*
Electronical Notes in Theoretical Computer Science
*

The automated synthesis of such moduli proceeds

doi:10.1016/j.entcs.2007.01.023
fatcat:mbhog62lvzdplpemv3mwh4lwgu
*from*a*proof*of the hereditarily extensional equality (≈) of t to itself, hence a*proof*in a weakly extensional variant of Berger-Buchholz-Schwichtenberg's ... We*extract*on the computer a number of moduli of uniform continuity for the first few elements of a sequence of closed terms t of Gödel's T of type (N → N) → (N → N). ... Schwichtenberg for having suggested to us that the already available formulations of the Monotone (or Bounded) Dialectica may not be satisfying enough*from*the computer-applied viewpoint. ...##
###
Eliminating Proofs from Programs

2002
*
Electronical Notes in Theoretical Computer Science
*

This paper presents a step in the development of an operational approach to

doi:10.1016/s1571-0661(04)80505-x
fatcat:n7i3v2v2prh5dmtvgsled2e2l4
*program**extraction*in type theory. In order to get a*program**from*a lambda term, the logical parts need to be removed. ... In the general setting the properties confluence, subject reduction, and strong*normalization*are studied. ... Conclusions Evaluating a*program*-i.e. applying β-reduction -to a*program*that contains logical parts is rather inefficient. ...##
###
Light Dialectica Program Extraction from a Classical Fibonacci Proof

2007
*
Electronical Notes in Theoretical Computer Science
*

We demonstrate

doi:10.1016/j.entcs.2006.10.050
fatcat:ozqg6y3sbne4xc3xpycrd32iea
*program**extraction*by the Light Dialectica Interpretation (LDI) on a minimal logic*proof*of the classical existence of Fibonacci numbers. ... Although syntactically different, it also has the same computational complexity as the original*program*yielded by the refined A-translation*from*the undistorted input classical Fibonacci*proof*. ... Introduction There has been quite some work in the last years in the field of*program**extraction**from*classical*proofs*. ...##
###
A Context-based Approach to Proving Termination of Evaluation

2009
*
Electronical Notes in Theoretical Computer Science
*

For each of the

doi:10.1016/j.entcs.2009.07.090
fatcat:firz4v2zebfmxpvqkiyatry5fe
*proofs*we present its computational content that takes the form of an evaluator in continuation-passing style and is an instance of*normalization*by evaluation. ... Acknowledgement We are grateful to Olivier Danvy for his willingness to*proof*-read the article at a short notice, and for his helpful, comprehensive comments. ... Some of the*proofs*have been formalized in*proof*assistants and*normalizers*have been*extracted**from*them in the form of functional*programs*[4, 6] . ...##
###
Uniform Heyting arithmetic

2005
*
Annals of Pure and Applied Logic
*

*programs*

*from*a rather large class of classical first-order

*proofs*while keeping explicit control over the levels of recursion and the decision procedures for predicates used in the

*extracted*

*program*. ... We present an extension of Heyting arithmetic in finite types called Uniform Heyting Arithmetic (HA u ) that allows for the

*extraction*of optimized

*programs*

*from*constructive and classical

*proofs*. ...

*From*[4] we have taken the uniform quantifier {∀x} introduced there to

*extract*the well-known

*normalization*-by-evaluation

*program*

*from*the Tait/Troelstra

*proof*of strong

*normalization*of the simply typed ...

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