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authorKazuhiko Sakaguchi2019-12-08 19:24:43 +0900
committerKazuhiko Sakaguchi2019-12-20 01:40:29 +0900
commit025dc51c2eef7e7ea302465ff05d04d6fd4e7173 (patch)
treea46e0839f515a4ff0482a6bf279f56ef5027e4a3 /dev/base_include
parent6621e7cf79d7d824461de14007b2a06cabe59aef (diff)
Coherence checking for coercions
This change improves the relaxed ambiguous path condition of coercions (#9743) to check that any circular inheritance path of `C >-> C` is definitionally equal to the identity function of the class `C`. Moreover, for a new inheritance path `p : C >-> D` and existing (valid) one `q : C >-> D`, the new mechanism does not report the ambiguity of `p` and `q` if they have a common element, that is to say: `p = p1 @ [c] @ p2` and `q = q1 @ [c] @ q2` for some coercion `c` and inheritance paths `p1`, `p2`, `q1`, and `q2`. In that case, convertibility of `p1` and `q1`, also, `p2` and `q2` should be checked; thus, checking the ambiguity of `p` and `q` is redundant with them. If the new mechanism does not report any ambiguous path, the inheritance graph must be coherent [Barthe 1995, Sect. 3.2] [Saïbi 1997, Sect. 7]: 1. for any circular path `p : C >-> C`, `p` is definitionally equal to the identity function, and 2. for any two paths `p, q : C >-> D`, `p` and `q` are convertible. [Barthe 1995] Gilles Barthe, Implicit coercions in type systems, In: TYPES '95, LNCS, vol 1158, Springer, 1996, pp 1-15. [Saïbi 1997] Amokrane Saïbi, Typing algorithm in type theory with inheritance, In: POPL '97, ACM, 1997, pp 292-301.
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