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In Types as Abstract Interpretations, Cousot seems to propose a method to derive various type systems by succesive abstract interpretation of the denotational semantics of an untyped lambda-calculus. There is a key step missing from the paper. It is claimed that:

For clarity of the presentation, the design of the Church/-Curry monotype semantics $T^C ⟦\cdot⟧$ by abstract interpretation of the collecting semantics $C ⟦\cdot⟧$ is postponed to Section 7. Anyway the result is well-known:

However, in section 7 he rather addresses the polytype to monotype abstraction. In summary, what I'm looking for is an explanation on how one derives the type system of Church/Curry monotype semantics (which to me looks like the STLC + recursion + some integer constructs) by abstract interpretation of the semantics.

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    $\begingroup$ Maybe of interests is this CST question. $\endgroup$ – Martin Berger Mar 20 at 10:45
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    $\begingroup$ Your question elicits just a "yes/no" answer. You may want to rephrase it to clarify what it is you really want to know. $\endgroup$ – Stefan Mar 21 at 15:29
  • $\begingroup$ @Stefan I have rephrased my question. Thanks for the advice $\endgroup$ – Rodrigo Mar 26 at 23:09

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