The type inference and coercion facilities in the scratchpad II interpreter

Abstract

Abstrac tThe Scratchpad II system is an abstract datatype programming language, a compiler for the language, a library of packages of polymorphic functions an d parametrized abstract datatypes, and an interpreter tha t provides sophisticated type inference and coercion facilities . Although originally designed for the implementatio n of symbolic mathematical algorithms, Scratchpad 11 is a general purpose programming language . This paper discusses aspects of the implementation of the interpreter and how it attempts to provide a user friendly and relatively weakly typed front end for the strongly typed programming language .

Overview of the Mathemagix Type System

“…Indeed, in Axiom, the mechanism of implicit conversions [36] partially depends on heuristics, which makes its behaviour quite unpredictable in non trivial situations. We have done a lot of experimentation with the introduction of implicit conversions in the Mathemagix type system, and decided to ban them from the core language.…”

“…In practice the above idea works very well. Apart from more pathological theoretical problems that will be discussed below, the only practically important problem that we do not treat currently, is finding a "smallest common supertype" with respect to type conversions (see also [36]). …”

“…The Scratchpad system [21,15] was at the origin of yet another interesting family of computer algebra systems, especially after the introduction of domains and categories as function values and dependent types in Modlisp and Scratchpad II [23,36,22]. These developments were at the forefront of language design and type theory [12,29,28].…”

Interfacing mathemagix with C++

“…The Modlisp [17] and Scratchpad II [12] systems were at the origin of yet another interesting family of computer algebra systems, especially after the introduction of domains as function return values and dependent types [18,20,30]. These developments were at the forefront of language design Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”

Signatures: A language extension for improving type abstraction and subtype polymorphism in C++

“…The key language construct added to support type abstraction in C++ and to allow separating subtyping from inheritance is called a signature. Signatures, in this language extension, are related to types in RUSSELL [16] [29], categories in AXIOM [22] and its predecessor SCRATCHPAO TI [35,36], and types in POOL-l [4].…”