Extracting ω's programs from proofs in the calculus of constructions

Moving proofs-as-programs into practice

“…The problem of extracting clear programs from proofs in the Calculus of Constructions has been addressed by PaulinMohring [9,11]. The approach separates "computationally informative" and "non-informative" propositions by syntactic means.…”

“…Researchers have addressed this problem in various constructive systems in an attempt to improve the * This work was performed by the author while a member of the formal methods group at NASA Langley Research Center. The author is currently visiting Cornell University, and can be contacted at 4116 Upson Hall, Cornell University, Ithaca, NY, 14850. efficiency, readability, and understanding of extracted programs [11,5,12]. This paper presents a methodology for specification and proof in the Nuprl system that yields clean recursive programs as extracts.…”

A Formalization of Static Analyses in System F

“…The work of C. Paulin (see [Pau89,PM89]) might be seen as a forerunner of type based systems for this kind of dead code analysis. In this work a system to extract F ω programs from Calculus of Constructions (CC for short) proofs is developed.…”

“…One may like to prove that the first occurrence of x is dead, hence typed on P rop (if we adopt [PM89] conventions). The problem comes from the second occurrence of x which is alive and hence should be typed on Spec.…”

Algebra of Programming Using Dependent Types

“…In their terminology sort-der would be a deliverable -an element of a dependent Σ-type pairing up a function and a proof of correctness. In the Coq tradition Program Extraction has been used already from Paulin-Mohring's early paper [18] to the impressive four-colour theorem development (including the development of a verified compiler). Our contribution is more modest -we aim at formally checked but still readable Algebra-of-Programming style derivations.…”