By Robert Harper
Varieties are the primary organizing precept of the speculation of programming languages. Language fea-
tures are manifestations of sort constitution. The syntax of a language is ruled by way of the constructs
that outline its forms, and its semantics depends upon the interactions between these constructs.
The soundness of a language design—the absence of ill-defined programs—follows obviously.
the aim of this booklet is to provide an explanation for this comment. quite a few programming language positive aspects
are analyzed within the unifying framework of style conception. A language characteristic is outlined by way of its statics,
the principles governing using the function in a software, and its dynamics, the foundations defining how
programs utilizing this selection are to be done. the concept that of safeguard emerges because the coherence of
the statics and the dynamics of a language.
during this manner we determine a starting place for the research of programming languages. yet why those
particular equipment? the most justification is supplied via the booklet itself. The equipment we use are
both exact and intuitive, delivering a uniform framework for explaining programming language
concepts. Importantly, those tools scale to quite a lot of programming language recommendations,
supporting rigorous research in their houses. even though it will require one other ebook in itself
to justify this statement, those equipment also are functional in that they're at once acceptable to imple-
mentation and uniquely potent as a foundation for mechanized reasoning. No different framework deals
as a lot.
Being a consolidation and distillation of a long time of analysis, this publication doesn't supply an
exhaustive account of the heritage of the guidelines that tell it. Suffice it to claim that a lot of the de-
velopment isn't really unique, yet really is essentially a reformulation of what has long past prior to. The notes
at the tip of every bankruptcy signpost the foremost advancements, yet should not meant as an entire
guide to the literature. For additional details and replacement views, the reader is referred
to such very good assets as Constable (1986), Constable (1998), Girard (1989), Martin-Lof ¨ (1984),
Mitchell (1996), Pierce (2002, 2004), and Reynolds (1998).
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Additional resources for Practical foundations of programming languages [draft 2nd ed.]
2 Type System The role of a type system is to impose constraints on the formations of phrases that are sensitive to the context in which they occur. For example, whether or not the expression plus( x; num[n]) is sensible depends on whether or not the variable x is restricted to have type num in the surrounding context of the expression. This example is, in fact, illustrative of the general case, in that the only information required about the context of an expression is the type of the variables within whose scope the expression lies.
The principle of hypothetical rule induction is just the principle of rule induction applied to the formal hypothetical judgment. So to show that P (Γ J ) whenever Γ R J, it is enough to show that P is closed under both the rules of R and under the structural rules. 9), whether structural or in R, we must show that if P (Γ Γ1 J1 ) and . . and P (Γ Γn Jn ), then P (Γ J ). This is just a restatement of the principle of rule induction given in Chapter 2, specialized to the formal derivability judgment Γ J.
For particular judgment forms, we freely use prefix, infix, or mixfix notation, as illustrated by the above examples, in order to enhance readability. 2 Inference Rules Inference Rules An inductive definition of a judgment form consists of a collection of rules of the form J1 ... 1) in which J and J1 , . . , Jk are all judgments of the form being defined. The judgments above the horizontal line are called the premises of the rule, and the judgment below the line is called its conclusion. If a rule has no premises (that is, when k is zero), the rule is called an axiom; otherwise it is called a proper rule.