| J.G.Hook: Understanding Russell, a first attempt, in Semantics of Data Types, Lecture Notes in Computer Science 173, pp. 51-67, Springer-Verlag, 1984. |
.... been widely studied; they include intuitionistic logic and type theory [Scott 70] Martin Lf 80] second order lambda calculus [Girard 72] Reynolds 74] Fortune 83] Bruce 84] Automath [de Bruijn 80] Barendregt 83] the theory of constructions [Coquand 85a, 85b] the foundations of Russell [Hook 84] Donahue 85] and a calculus with Type:Type [Meyer 86] Somehow, a clear connection between these ideas, from the programming language point of view, was missing. For example, Girard discovered that a dependent type system where Type:Type holds is inconsistent Page 3 as a logic system (but it ....
J.G.Hook: Understanding Russell, a first attempt, in Semantics of Data Types, Lecture Notes in Computer Science 173, pp. 51-67, Springer-Verlag, 1984.
....and a length function which maps a list of arbitrary element type into its integer length. It is also possible to write a generic sorting package that works on any type with an ordering relation. Other languages that used or helped develop these ideas include CLU [Liskov 81] Russell [Demers 79, Hook 84] Hope [Burstall 80] Ponder [Fairbairn 82] and Poly [Matthews 85] Finally, we should mention generic procedures of the kind found in Ada, which are parametrized templates that must be instantiated with actual parameter values before they can be used. The 7 polymorphism of Ada s generic ....
J.G.Hook: Understanding Russell, a first attempt, in Sematics of Data Types, G.Kahn, D.B.MacQueen and G.Plotkin Ed. Lecture Notes in Computer Science 173, pp. 51-67, SpringerVerlag, 1984.
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