Theorem Proving with the Real Numbers

[1]  Gérard P. Huet,et al.  Constructive category theory , 2000, Proof, Language, and Interaction.

[2]  Sara Negri,et al.  The continuum as a formal space , 1999, Arch. Math. Log..

[3]  Matt Kaufmann,et al.  A Mechanically Checked Proof of the , 1998 .

[4]  Laurent Théry,et al.  Proving and Computing: a Certified Version of the Buchberger's Algorithm , 1997 .

[5]  Michael Norrish.  An abstract dynamic semantics for C , 1997 .

[6]  Kurt Mehlhorn,et al.  Checking geometric programs or verification of geometric structures , 1996, SCG '96.

[7]  A. Wilkie.  Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function , 1996 .

[8]  S Miner Paul,et al.  Defining the IEEE-854 Floating-Point Standard in PVS , 1995 .

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

[10]  Randal E. Bryant,et al.  Formal verification by symbolic evaluation of partially-ordered trajectories , 1995, Formal Methods Syst. Des..

[11]  Michael Kantrowitz,et al.  Functional Verification of a Multiple-issue, Pipelined, Superscalar Alpha Processor - the Alpha 21164 CPU Chip , 1995, Digit. Tech. J..

[12]  Don Libes.  Exploring expect - a Tcl-based toolkit for automating interactive programs (2. ed.) , 1995 .

[13]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

[14]  van Ls Bert Benthem Jutting,et al.  Checking Landau's “Grundlagen” in the Automath System: Appendices 3 and 4 (The PN-lines; Excerpt for “Satz 27”) , 1994 .

[15]  Valerie Menissier-Morain Menissier.  Arithmetique exacte : conception, algorithmique et performances d'une implementation informatique en precision arbitraire , 1994 .

[16]  D. Verkest,et al.  A proof of the nonrestoring division algorithm and its implementation on an ALU , 1994, Formal Methods Syst. Des..

[17]  Claire Jones.  Completing the rationals and metric spaces in LEGO , 1993 .

[18]  Monica Nesi.  Value-Passing CCS in HOL , 1993, HUG.

[19]  John Harrison,et al.  Extending the HOL Theorem Prover with a Computer Algebra System to Reason about the Reals , 1993, HUG.

[20]  Thomas F. Melham.  The HOL logic extended with quantification over type variables , 1993, Formal Methods Syst. Des..

[21]  Heinz Kredel,et al.  Gröbner Bases: A Computational Approach to Commutative Algebra , 1993 .

[22]  John Van Tassel.  Femto-VHDL : the semantics of a subset of VHDL and its embedding in the HOL proof assistant , 1993 .

[23]  Joakim von Wright,et al.  Mechanizing some advanced refinement concepts , 1992, Formal Methods Syst. Des..

[24]  Norbert Kajler,et al.  CAS/PI: a portable and extensible interface for computer algebra systems , 1992, ISSAC '92.

[25]  John M. Rushby,et al.  Design Choices In Specification Languages And Verification Systems , 1991, 1991., International Workshop on the HOL Theorem Proving System and Its Applications.

[26]  Jeffrey J. Joyce,et al.  A Two-Level Formal Verification Methodology using HOL and COSMOS , 1991, CAV.

[27]  Joakim von Wright.  Mechanising the Temporal Logic of Actions in HOL , 1991, International Conference on Theorem Proving in Higher Order Logics.

[28]  Jeffrey J. Joyce.  More Reasons Why Higher-Order Logic is a Good Formalism for Specifying and Verifying Hardware , 1990 .

[29]  Brian A. Wichmann.  Towards a Formal Specification of Floating Point , 1989, Comput. J..

[30]  H. B. Thompson.  Taylor's Theorem Using the Generalized Riemann Integral , 1989 .

[31]  Ping Tak Peter Tang.  Table-driven implementation of the exponential function in IEEE floating-point arithmetic , 1989, TOMS.

[32]  John N. Hooker,et al.  A quantitative approach to logical inference , 1988, Decis. Support Syst..

[33]  Daniel Lazard,et al.  Quantifier Elimination: Optimal Solution for Two Classical Examples , 1988, J. Symb. Comput..

[34]  G. Sambin.  Intuitionistic Formal Spaces — A First Communication , 1987 .

[35]  Lesław W. Szczerba.  The Use of Mizar MSE in a Course in Foundations of Geometry , 1987 .

[36]  Lawrence C. Paulson,et al.  Logic and computation - interactive proof with Cambridge LCF , 1987, Cambridge tracts in theoretical computer science.

[37]  C. Pomerance.  Very short primality proofs , 1987 .

[38]  W. Marck.  Executing Temporal Logic Programs by Ben Moszkowski , 1986, SGAR.

[39]  Donald E. Richmond.  An Elementary Proof of a Theorem in Calculus , 1985 .

[40]  J. Michael Spivey,et al.  Understanding Z : A specification language and its formal semantics , 1985, Cambridge tracts in theoretical computer science.

[41]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[42]  R. Stansifer.  Presburger''s Article on Integer Arithmetic: Remarks and Translation , 1984 .

[43]  D. Sutherland.  Formal verification of mathematical software , 1984 .

[44]  Sloman,et al.  Automation of Reasoning , 1983, Symbolic Computation.

[45]  M. Payne,et al.  Radian reduction for trigonometric functions , 1983, SGNM.

[46]  Robin Milner,et al.  A Theory of Type Polymorphism in Programming , 1978, J. Comput. Syst. Sci..

[47]  Vaughan R. Pratt,et al.  Every Prime has a Succinct Certificate , 1975, SIAM J. Comput..

[48]  Gérard P. Huet,et al.  A Unification Algorithm for Typed lambda-Calculus , 1975, Theor. Comput. Sci..

[49]  José Sanmartín Esplugues.  Introduction to model theory and to the metamathematics of algebra , 1971 .

[50]  Ivan N. Pesin,et al.  Classical and modern integration theories , 1970 .

[51]  Norman D. Megill,et al.  Metamath A Computer Language for Pure Mathematics , 1969 .

[52]  Ralph Henstock,et al.  A Riemann-Type Integral of Lebesgue Power , 1968, Canadian Journal of Mathematics.

[53]  Jean-Louis Krivine,et al.  Éléments de logique mathématique : théorie des modèles , 1967 .

[54]  A. Robinson,et al.  Non-standard analysis , 1966 .

[55]  D. Prawitz.  Natural Deduction: A Proof-Theoretical Study , 1965 .

[56]  S. Lojasiewicz,et al.  Triangulation of semi-analytic sets , 1964 .

[57]  W. Rudin.  Principles of mathematical analysis , 1964 .

[58]  Joe B. Roberts.  The Real Number System in an Algebraic Setting , 1962 .

[59]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[60]  Jack E. Volder.  The CORDIC Trigonometric Computing Technique , 1959, IRE Trans. Electron. Comput..

[61]  J. Kurzweil.  Generalized ordinary differential equations and continuous dependence on a parameter , 1957 .

[62]  K. Mahler,et al.  On the approximation of logarithms of algebraic numbers , 1953, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[63]  Julia Robinson,et al.  Definability and decision problems in arithmetic , 1949, Journal of Symbolic Logic.

[64]  H M Macneille.  A Unified Theory of Integration. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[65]  A. Tarski,et al.  Über unerreichbare Kardinalzahlen , 1938 .

[66]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[67]  B. Russell,et al.  Introduction to Mathematical Philosophy , 1920, The Mathematical Gazette.

[68]  B. Russell,et al.  Principia Mathematica Vol. I , 1910 .