Sound and Complete Bidirectional Typechecking for Higher-Rank Polymorphism and Indexed Types: Lemmas and Proofs
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چکیده
B Properties of the Declarative System 23 1 Lemma (Declarative Weakening) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 Lemma (Declarative Term Substitution) . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Lemma (Reflexivity of Declarative Subtyping) . . . . . . . . . . . . . . . . . . . . . 23 4 Lemma (Subtyping Inversion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5 Lemma (Subtyping Polarity Flip) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6 Lemma (Transitivity of Declarative Subtyping) . . . . . . . . . . . . . . . . . . . . . 23
منابع مشابه
Sound and Complete Bidirectional Typechecking for Higher-Rank Polymorphism and Indexed Types
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatyp...
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Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatyp...
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ANONYMOUS AUTHOR(S) Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generaliz...
متن کاملLemmas and Proofs for “Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism”
A Declarative Subtyping 6 A.1 Properties of Well-Formedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 Proposition (Weakening) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Proposition (Substitution) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 A.2 Reflexivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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Bidirectional typechecking has become popular in advanced type systems because it works in many situations where inference is undecidable. In this paper, I show how to cleanly handle parametric polymorphism in a bidirectional setting, even in the presence of subtyping. The first contribution is a bidirectional type system that supports first-class (higher-rank and impredicative) polymorphism bu...
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