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Implicit Polymorphic Type System for the Blue Calculus
, 1997
"... The Blue Calculus is a direct extension of both the lambda and the pi calculi. In a preliminary work from Gérard Boudol, a simple type system was given that incorporates Curry's type inference for the lambdacalculus. In the present paper we study an implicit polymorphic type system, adapted fr ..."
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The Blue Calculus is a direct extension of both the lambda and the pi calculi. In a preliminary work from Gérard Boudol, a simple type system was given that incorporates Curry's type inference for the lambdacalculus. In the present paper we study an implicit polymorphic type system, adapted from the ML typing discipline. Our typing system enjoys subject reduction and principal type properties and we give results on the complexity for the type inference problem. These are interesting results for the blue calculus as a programming notation for higherorder concurrency.
Polymorphic Typing of Heterogeneous Lists
"... ion and concretization operator from pattern list type to uniform ML list type The abstraction AbsML that maps every pattern list type scheme to a set of standard ML type scheme results from the definition of the concretization and the ordering vP on pattern list types. Property 2. The abstraction ..."
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ion and concretization operator from pattern list type to uniform ML list type The abstraction AbsML that maps every pattern list type scheme to a set of standard ML type scheme results from the definition of the concretization and the ordering vP on pattern list types. Property 2. The abstraction and concretization functions (AbsML ; ConcML ) define a lower approximation. ae ` E ) øML list ae ` null(E1) ) bool ae ` E1 ) øML ae ` E2 ) øML list ae ` E1 :: E2 ) øML list ae ` E ) øML list ae ` head(E) ) øML ae ` E1 ) øML list ae ` tail(E1) ) øML list Figure 8: Standard ML list operator behavior For example the abstraction of the pattern list type (ff ! ff)(ff ! num)(!) list of the list x:x :: x:0 :: [] is: (ff ! num) list. With respect to the abstraction and concretization functions (AbsML ; ConcML ), we derive the set of rules describing the behavior of list operators on MLtypes listed on figure 8from the set of rules describing the behavior of list operators on patter...
7a NAME OF MONITORING ORGANIZATION
, 1987
"... Approved for public release; distribution is unlimited. ..."
UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE REPORT DOCUMENTATION PAGE la. REPORT SECURITY CLASSIFICATION lb. RESTRICTIVE MARKINGS
, 1941
"... I ~ II 19. ABSTRACT (Continue on reverse if necessary and identify by block number) Type inference in interactive programming environments falls short in two respects. The ability to type check definitions one at a time, and to type check some definitions but not all after one definition is modified ..."
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I ~ II 19. ABSTRACT (Continue on reverse if necessary and identify by block number) Type inference in interactive programming environments falls short in two respects. The ability to type check definitions one at a time, and to type check some definitions but not all after one definition is modified is called incremental online type inference. Current interactive programming environments perform batch type inference and require extensive type recomputation for small changes.