Outline of a Proof Theory of Parametricity

  title={Outline of a Proof Theory of Parametricity},
  author={Harry G. Mairson},
ion: Application: $.. \frac{\Gamma,x.A\vdash M.B\Gamma\vdash\Pi x.A.B.s}{\Gamma\vdash\lambda x.A.M.\Pi x\cdot A.B}...\cdot$ . $\Gamma\vdash M$ : $\Pi_{X}$ : A. $B$ $\Gamma\vdash N$ : $A$ $\Gamma\vdash MN$ : $B[N/x]$ Beta-Conversion: $\Gamma\vdash A:B$ $\Gamma\vdash B:s$ $\Gamma\vdash B’$ : $s$ $\Gamma\vdash A:B’$ ($s\in\{*$ , $\square \}$ , $B$ is $\beta$-equident to $B’$ by one-step $\beta$-conversion.) Only the rule of quantification depends on S. All the other rules are common. Lemma 2.1.6… CONTINUE READING
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