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This paper investigates language constructs for high-level and type-safe manipulation of JSON objects in a typed functional language. A major obstacle in representing JSON in a static type system is their heterogeneous nature: in most practical JSON APIs, a JSON array is a heterogeneous list consisting of, for example, objects having common fields and possibly some optional fields. This paper presents a typed calculus that reconciles static typing constraints and heterogeneous JSON arrays based on the idea of partially dynamic records originally proposed and sketched by Buneman and Ohori for complex database object manipulation. Partially dynamic records are dynamically typed records, but some parts of their structures are statically known. This feature enables us to represent JSON objects as typed data structures. The proposed calculus smoothly extends with ML-style pattern matching and record polymorphism. These results yield a typed functional language where the programmer can directly import JSON data as terms having static types, and can manipulate them with the full benefits of static polymorphic type-checking. The proposed calculus has been embodied in SML#, an extension of Standard ML with record polymorphism and other practically useful features. This paper also reports on the details of the implementation and demonstrates its feasibility through examples using actual Web APIs. The SML# version 3.1.0 compiler includes JSON support presented in this paper, and is available from Tohoku University as open-source software under a BSD-style license.