Semantic subtyping with an SMT solver

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Semantic subtyping with an SMT solver (2010)

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by Gavin M. Bierman , Andrew D. Gordon , Catalin Hritcu , David Langworthy

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BibTeX

@TECHREPORT{Bierman10semanticsubtyping,
    author = {Gavin M. Bierman and Andrew D. Gordon and Catalin Hritcu and David Langworthy},
    title = {Semantic subtyping with an SMT solver},
    institution = {},
    year = {2010}
}

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Abstract

We study a first-order functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and type-test (a Boolean expression testing whether a value belongs to a type). Our core calculus can express a rich variety of typing idioms; for example, intersection, union, negation, singleton, nullable, variant, and algebraic types are all derivable. We formulate a semantics in which expressions denote terms, and types are interpreted as first-order logic formulas. Subtyping is defined as valid implication between the semantics of types. The formulas are interpreted in a specific model that we axiomatize using standard first-order theories. On this basis, we present a novel type-checking algorithm able to eliminate many dynamic tests and to detect many errors statically. The key idea is to rely on an SMT solver to compute subtyping efficiently. Moreover, interpreting types as formulas allows us to call the SMT solver at run-time to compute instances of types.

Keyphrases

smt solver boolean expression many error rich variety standard first-order theory specific model novel combination key idea many dynamic test first-order functional language valid implication first-order logic formula core calculus refinement type novel type-checking algorithm algebraic type

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