Lecture 03a: Introduction to Higher-Order Logic and Interactive Theorem Proving

Lambda Calculus

Untyped Lambda Calculus

Simply Typed Lambda Calculus

Further reading:

Classical Higher-Order Logic (HOL)

Syntax and Shorthands of HOL

Standard-Model Semantics of HOL

Axioms of HOL

Results Proved in HOL

Further reading:

LCF Theorem Proving Approach

Some Interactive Provers

HOL - use directly ML

HOL Light - compact version, written in OCaml

Isabelle - popular, ML part largely hidden

PVS - automation through decision procedures

Coq - also very popular, more automation introduced recently; more complex logic

NuPRL - more complex type theory, constructive mathematics

ACL2 - emphasis on executable functions, quantifier-free statements, automated induction, pioneering industrial-scale case studies