Program Extraction from Normalization Proofs

Program Extraction from Normalization Proofs

This paper describes formalizations of Tait’s normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. 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...

Program Extraction From Proofs of Weak Head Normalization

We formalize two proofs of weak head normalization for the simply typed lambdacalculus in first-order minimal logic: one for normal-order reduction, and one for applicative-order reduction in the object language. Subsequently we use Kreisel’s modified realizability to extract evaluation algorithms from the proofs, following Berger; the proofs are based on Tait-style reducibility predicates, and...

Implementing program extraction from CL1-proofs

Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of computability and formulas to represent computational problems. Logic CL1 is a deductive system for a fragment of CoL. The logical vocabulary contains all of the operat...

Re ned Program Extraction from Classical Proofs

It is well known that it is undecidable in general whether a given programmeets its speci cation In contrast it can be checked easily by a machine whether a formal proof is correct and from a constructive proof one can automatically extract a corresponding program which by its very construction is correct as well This at least in principle opens a way to produce correct software e g for safety ...

Reened Program Extraction from Classical Proofs: Some Case Studies