Formal Proof—Theory and Practice

syntax trees almost copying the abstract grammar: type term = Var of string | Fn of string * term list;; and express in a direct recursive way the function returning the set of variables in a term: let rec vars tm =

[1]  M. Lecat.  Erreurs de mathématiciens des origines à nos jours , 1935 .

[2]  Martin Davis,et al.  The Universal Computer: The Road from Leibniz to Turing , 2002 .

[3]  M. Eckert,et al.  Water-art problems at Sanssouci—Euler’s involvement in practical hydrodynamics on the eve of ideal flow theory , 2008 .

[4]  Freek Wiedijk,et al.  The Seventeen Provers of the World , 2006 .

[5]  C. W. H. Lam.  Opinion: How Reliable Is a Computer-Based Proof? , 1990 .

[6]  W. Marciszewski,et al.  Mechanization Of Reasoning In A Historical Perspective. , 1995 .

[7]  John McCarthy,et al.  Computer programs for checking mathematical proofs , 1962 .

[8]  Michael J. C. Gordon,et al.  Edinburgh LCF: A mechanised logic of computation , 1979 .

[9]  George Polya,et al.  Induction and Analogy in Mathematics , 1954 .

[10]  Imre Lakatos,et al.  On the Uses of Rigorous Proof. (Book Reviews: Proofs and Refutations. The Logic of Mathematical Discovery) , 1977 .

[11]  M. Davis.  A Computer Program for Presburger’s Algorithm , 1983 .

[12]  K. Appel,et al.  Every Planar Map Is Four Colorable , 2019, Mathematical Solitaires & Games.

[13]  S. Lane.  Mathematics, Form and Function , 1985 .

[14]  Donald MacKenzie,et al.  Mechanizing Proof: Computing, Risk, and Trust , 2001 .

[15]  Cora Diamond,et al.  Wittgenstein's Lectures on the Foundations of Mathematics. , 1977 .

[16]  A. Whitehead.  An Introduction to Mathematics , 1949, Nature.

[17]  John Harrison,et al.  A Skeptic's Approach to Combining HOL and Maple , 1998, Journal of Automated Reasoning.

[18]  John Harrison,et al.  Floating-Point Verification Using Theorem Proving , 2006, SFM.

[19]  Béla Bollobás,et al.  Littlewood's Miscellany , 1986 .

[20]  J. Davenport.  Editor , 1960 .

[21]  William McCune,et al.  Solution of the Robbins Problem , 1997, Journal of Automated Reasoning.

[22]  Nicolas Bourbaki,et al.  Eléments de Mathématique , 1964 .

[23]  John Harrison,et al.  Proof Style , 1996, TYPES.

[24]  Fred P. Brooks,et al.  The Mythical Man-Month , 1975, Reliable Software.

[25]  Thomas Tymoczko.  New directions in the philosophy of mathematics : an anthology , 1998 .

[26]  Vaughan R. Pratt.  Anatomy of the Pentium Bug , 1995, TAPSOFT.

[27]  Nicolas Bourbaki,et al.  Theory of sets , 1968 .