Abstract
This paper documents some preliminary steps made to achieve a safe theorem prover for reasoning about functions that occur in denotational semantics. A theorem prover is safe when: (1) its underlying logic is consistent and (2) it enforces extensions of the logic to preserve consistency.The main idea is to extend a general purpose theorem prover with a theory of the Graph (or Pω) model of Dana Scott's LAMBDA language. This theory is extended to a theory of a typed version of LAMBDA with general recursive types.A short summary of the Graph model is given along with details of how it has been formalised in a theorem prover.The model has been constructed using the HOL theorem prover which supports a polymorphic, strongly typed higher order logic based on Church's simple type theory.KeywordsPartial OrderGraph ModelChoice FunctionTheorem ProverDenotational SemanticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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