Specification Refinement with System F

Constructive Data Refinement in Typed Lambda Calculus

“…A case in point is offered by PER models of System F, where the extra latitude and flexibility given by defining the exponential PER pre-logically allows for a number of possibly novel natural model constructions. Finally, a notion of pre-logical relation for System F would raise the intriguing question of the relationship between this framework and the one in [Han99], where data refinements in the style of [ST88] are translated into System F using existential types.…”

A Higher-Order Simulation Relation for System F

“…In [12] an account of algebraic specification refinement [38,37] is mapped to the first-order type-theoretic refinement notion, and the two accounts of refinement are shown to coincide. Important issues in algebraic specification refinement, such as the choice of input sorts [36] and the stability of constructors [39,37,10], are automatically resolved in the type-theoretic setting.…”

“…In [12] a proof method from algebraic specification for proving observational refinements [5,4,6] is imported into the type-theory logic by adding axioms postulating the existence of quotients and sub-objects. Work related to this is [33,42].…”