Automatically assigned DDC number: 005131

Manually assigned DDC number: 005131

Number of references: 4

Title: There's No Substitute for Linear Logic

Author:

Subject: Philip Wadler There's No Substitute for Linear Logic

Description: Surprisingly, there is not a good fit between a syntax for linear logic in the style of Abramsky, and a semantics in the style of Seely. Notably, the Substitution Lemma is valid if and only if !A and !!A are isomorphic in a canonical way. An alternative syntax is proposed, that has striking parallels to Moggi's language for monads. In the old syntax, some terms look like the identity that should not, and vice versa; the new syntax eliminates this awkwardness. 1 Introduction This paper has two purposes: to show that linear logic has no substitute, and to propose one. The first part presents a standard syntax and semantics for linear logic, and notes some resulting difficulties. The linear logic is that of Girard [Gir87]. The syntax is based on lambda terms, following in the footsteps of Abramsky [Abr90]: the four rules associated with the `of course' type, Weakening, Contraction, Dereliction, and Promotion, are each represented by a separate term form. The semantics is based on categor...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1993-05-20

Pubyear: 1991

Format: ps

Identifier: http://citeseer.ist.psu.edu/142326.html

Source: ftp://ftp.dcs.gla.ac.uk/pub/glasgow-fp/papers/no-subst-for-linear-logic.ps.Z

Language: en

Relation:

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Rights: unrestricted

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