By Flemming Nielson

ISBN-10: 0511526571

ISBN-13: 9780511526572

ISBN-10: 0521018471

ISBN-13: 9780521018470

ISBN-10: 0521403847

ISBN-13: 9780521403849

The authors describe right here a framework during which the sort notation of sensible languages is prolonged to incorporate a notation for binding instances (that is run-time and compile-time) that distinguishes among them. therefore, the power to specify code and be certain application correctness could be more desirable. advancements are wanted, the 1st of which introduces the binding time contrast into the lambda calculus in a way analogous with the advent of sorts into the untyped lambda calculus. tools are additionally provided for introducing combinators for run-time. the second one issues the translation of the ensuing language, that is often called the combined lambda-calculus and combinatory good judgment. The concept of "parametrized semantics" is used to explain code new release and summary interpretation. The code iteration is for an easy summary computer designed for the aim, it truly is with regards to the explicit summary computing device. The summary interpretation specializes in a strictness research that generalizes Wadler's research for lists. it's also proven how the result of summary interpretation can be used to enhance the code new release.

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**Extra info for Two-Level Functional Languages**

**Sample text**

1 first presents the syntax of the 2-level A-calculus and the accompanying explanations indicate how it may carry over to more than two levels or a base language different from the typed A-calculus. -level Aexpressions and again we sketch the more general setting. Of the many wellformedness definitions that are possible we choose one that interacts well with the approach to combinator introduction to be presented in Chapter 4. 2 then studies how to transform binding time information (in the form of £-level types) into an already typed A-expression.

Ay[Az±A]. x(y) A)->(A->A)]. Ay[A->A]. x(y) of intended type <*-i = ((A=±A)z±(Az±A)) ((A->AWA->A)) First we show that ^r~1 is a well-formed expression of type ty-i. To be precise we show that 0 h ^"1 : ^-i : c By using [A] twice we see that it is sufficient to show that tenv h x(y)_ : A—>A : c for tenv = 0[((A—>A)—>(A—>A):c)/x][(A—>A:c)/y]. 1 The 2-Level A-Calculus 41 [1] tenv KliW : f : r if h f : r [*] tenv H f|[i] : £ : c if h t : c w tenv h e2 : t 2 : r tenv r e\ '. <2 : r tenv h e\ : t L : c ^env h e2 : t 2 tenv h (e a ,e 2 ) : ^ x ^ 2 : c tenv h c : ii X t2 ' T tenv h fst e : ti : r tenv h e : *!

Let DEF xi = wei • • • DEF xn=uen VAL ue HAS t2 = up let t = rBTA{t2) let DEF xi = ei • • • DEF x n =e n VAL e HAS t = 7>£A[DEF xi = ttex • • • DEF x n =ue n VAL ue HAS t] in DEF X! = ei • • • DEF x n =e n VAL e HAS t2 and this algorithm fails if and only if the explicit invocation of V^A fails. When the algorithm succeeds we know that the resulting program, or rather the result of applying TTBTA^O it, will be well-formed when regarded as a program in P(E,T). -level types) into a typed A-expression.

### Two-Level Functional Languages by Flemming Nielson

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