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History of Interactive Theorem Proving

John Harrison, Josef Urban, Freek Wiedijk (2014)

Interactive Theorem Proving An arrangement where the machine and a human user work together interactively to produce a formal proof.

Possibilities:

Computer as a checker of a formal proof produced by a human Prover may be highly automated and powerful

Most of the earliest work on computer-assisted proof in the 1950s

A computer program for Presburger’s algorithm Davis 1957

A proof method for quantification theory: Its justification and realization Gilmore 1960

A computer procedure for quantification theory Davis and Putnam 1960

Toward Mechanical Mathematics Wang 1960

A mechanical proof procedure and its realization in an electronic computer Dag Prawitz, Håken Prawitz, Neri Voghera 1960

and 1960s

A machine-oriented logic based on the resolution principle Robinson 1965

An inverse method of establishing deducibility in classical predicate calculus Maslov 1964

Mechanical theorem-proving by model elimination Loveland 1968

was dedicated to automated theorem proving.

AI-style approaches:

The logic theory machine Newell and Simon 1956

Realization of a geometry-theorem proving machine Gelerntner 1959

Some automatic proofs in analysis Bledsoe 1984

The work of proof in the age of human-machine collaboration Dick 2011

Proofchecker Paul Abrahams Machine Verification of Mathematical Proof (1963)

Paul Abrahams introduced in embryonic form many ideas that became significant later:

  • a kind of macro facility for derived inference rules
  • the integration of calculational derivations as well as natural deduction rules

Automatic theorem proof-checking in set theory: A preliminary report — Bledsoe and Gilbert 1967 was inspired by Bledsoe’s interest in formalizing the already unusually formal proofs in his PhD adviser A. P. Morse’s ‘Set Theory’.