Argument
Rocq
Overview
The Rocq Prover (formerly named Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical checking of proofs of these assertions, assists in finding formal proofs using proof automation routines and extraction of a certified program from the constructive proof of its formal specification.
Rocq works within the theory of the calculus of inductive constructions, a derivative of the calculus of constructions. Rocq is not an automated theorem prover but includes automatic theorem proving tactics (procedures) and various decision procedures.
The Association for Computing Machinery awarded Thierry Coquand, Gérard Huet, Christine Paulin-Mohring, Bruno Barras, Jean-Christophe Filliâtre, Hugo Herbelin, Chetan Murthy, Yves Bertot, and Pierre Castéran with the 2013 ACM Software System Award for Rocq (when it was named Coq).
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Perhaps strictly we could repeat the reasoning of number III. But as we have said, this reasoning is complete induction, and it is precisely the principle of complete induction whose justification would be the point in question.
Henri Poincaré, The Foundations of Science
Close in meaning to Rocq; the term itself is not named.
One of the most successfully cultivated branches of philosophy in our time is what is called inductive logic, the study of the conditions under which our sciences have evolved. Writers on this subject have begun to show a singular unanimity as to what the laws of nature and elements of fact mean, when formulated by mathematicians, physicists and chemists. When the first mathematical, logical and natural…
William James, Pragmatism
States what Rocq is.
In geometry, instead of the tedious apparatus of fallacious proofs for obvious truisms which constitutes the beginning of Euclid, the learner should be allowed at first to assume the truth of everything obvious, and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing, such as those in which it is shown that three or more lines meet in a point.
Bertrand Russell, Mysticism and Logic and Other Essays
Close in meaning to Rocq; the term itself is not named.
Philosophers who discussed Rocq
Related ideas
- French language
- Four color theorem
- Proof assistant
- Integer
- Geometry
- Commutative property
- Cambridge
- Type theory
- Higher-order logic
- MIT Press
- Decidability (logic)
- England
- Formal specification
- Constructive proof
- Associative property
Place in the tradition
Part of Intuitionistic logic.