Abstract
The development of interactive tactic based theorem provers started with the LCF system [10], a system to support automated reasoning in Dana Scotts “Logic for Computable Functions”. The main idea was to base the prover on a small trusted kernel, while also allowing for ordinary user extensions without compromising soundness. For that purpose Milner designed the functional programming language ML and embedded LCF into ML. ML allowed to represent subgoaling strategies by functions, called tactics, and to combine them by higher order functions, called tacticals. By declaring an abstract type theorem with only simple inference rules type checking guaranteed that tactics decompose to primitive inference rules. While allowing for efficient execution of recorded proofs by
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