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This work proposes a type system for checking Abstract Non-Interference in the setting of simply-typed lambda calculus with basic types and recursion. A lambda-expression satisfies Abstract Non-Interference relatively to a given semantic property if an attacker which can only see program data up to that property cannot infer, by observing a computation, private data from public ones. Attackers are abstract interpretations of program semantics. The type analysis infers, for an expression, a security type which approximates the secret kernel for the expression, i.e. the most powerful harmless attacker for which the expression is secure. The type system is proven to be correct, that is, private information is not revealed to an attacker which is unable to distinguish different values belonging to the inferred type.