Realizability interpretation of proofs in constructive analysis

From Constructive Mathematics to Computable Analysis via the Realizability Interpretation

Constructive mathematics is mathematics without the use of the principle of the excluded middle. There exists a wide array of models of constructive logic. One particular interpretation of constructive mathematics is the realizability interpretation. It is utilized as a metamathematical tool in order to derive admissible rules of deduction for systems of constructive logic or to demonstrate the...

Constructive Kripke Semantics and Realizability

What is the truth-value structure of realizability? How can realizability style models be integrated with forcing techniques from Kripke and Beth semantics, and conversely? These questions have received answers in Hyland’s [33], Läuchli’s [43] and in other, related or more syntactic developments cited below. Here we re-open the investigation with the aim of providing more constructive answers t...

A realizability interpretation for classical analysis

We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀x∃yA(x, y), this provides a recursive type 1 function which computes the function given by f(x) = y iff y is the least number such that A(x, y).

Constructive Proofs or Constructive Statements?

In this work the following question is considered: is Sergeraert’s “Constructive Algebraic Topology” (CAT, in short) really constructive (in the strict logical sense of the word “constructive”)? We have not an answer to that question, but we are interested in the following: could have a positive (or negative) answer to the previous question an influence in the problem of proving the correctness...

Constructive Methods in Automatic Analysis of Correctness Proofs ?