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A proofproducing software compiler for a subset of higher order logic
, 2006
"... We discuss a proofproducing compiler which translates first order recursion equations, defined in higher order logic, to assembly language. The front end of the compiler is based on a series of sourcetosource translations, starting with a semantic CPS translation and culminating in graphcolouri ..."
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Cited by 7 (1 self)
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We discuss a proofproducing compiler which translates first order recursion equations, defined in higher order logic, to assembly language. The front end of the compiler is based on a series of sourcetosource translations, starting with a semantic CPS translation and culminating in graphcolouring register allocation. Equality of the original program and the result of register allocation is proved automatically. A translation validation assertion is then generated, relating values of the original function to the result of running the compiled code on a subset of the ARM machine. Approaches to the automatic proof of this formula are also discussed.
Weyl’s predicative classical mathematics as a logicenriched type theory
, 2006
"... Abstract. In Das Kontinuum, Weyl showed how a large body of classical mathematics could be developed on a purely predicative foundation. We present a logicenriched type theory that corresponds to Weyl’s foundational system. A large part of the mathematics in Weyl’s book — including Weyl’s definitio ..."
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Cited by 5 (5 self)
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Abstract. In Das Kontinuum, Weyl showed how a large body of classical mathematics could be developed on a purely predicative foundation. We present a logicenriched type theory that corresponds to Weyl’s foundational system. A large part of the mathematics in Weyl’s book — including Weyl’s definition of the cardinality of a set and several results from real analysis — has been formalised, using the proof assistant Plastic that implements a logical framework. This case study shows how type theory can be used to represent a nonconstructive foundation for mathematics. Key words: logicenriched type theory, predicativism, formalisation 1
A typetheoretic framework for formal reasoning with different logical foundations
 Proc of the 11th Annual Asian Computing Science Conference
, 2006
"... different logical foundations ..."
Deductive Translation Validation for a Subset of Higher Order Logic
"... Abstract. We discuss a proofproducing compiler for a subset of higher order logic. The translation validation is automatic, and is based on Hoare rules derived from a compositional semantics for sequences of instructions for an ARMlike machine. Partial and total correctness are dealt with. The mai ..."
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Abstract. We discuss a proofproducing compiler for a subset of higher order logic. The translation validation is automatic, and is based on Hoare rules derived from a compositional semantics for sequences of instructions for an ARMlike machine. Partial and total correctness are dealt with. The main focus is on issues in the intermediate level and backend of the compiler. 1