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.
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© 1994 Springer-Verlag Berlin Heidelberg
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Petersen, K.D. (1994). Graph model of LAMBDA in higher order logic. In: Joyce, J.J., Seger, CJ.H. (eds) Higher Order Logic Theorem Proving and Its Applications. HUG 1993. Lecture Notes in Computer Science, vol 780. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57826-9_122
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DOI: https://doi.org/10.1007/3-540-57826-9_122
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