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Date: Wed, 20 Jul 2005 23:55:41 +0000

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Date: Wed, 20 Jul 2005 23:55:41 +0000

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http://www.w3.org/Bugs/Public/show_bug.cgi?id=1605 ------- Additional Comments From fred.zemke@oracle.com 2005-07-20 23:55 ------- What you wrote is probably useful, but I had in mind something like the following. There are still gaps in this description because I am not sure this permits the following: 1) static type error if no inference of the form statEnv |- Expr : Type can be deduced. 2) short circuit evaluation of some expressions I wrote this without seeing your second reply, which goes into some of this. But I must quit now. The group can kick this around. Execution model of the inference engine This specification does not specify a particular order of execution. Instead, it uses a theoretical device called an inference engine. There are two inference engines, one for the static analysis phase, and the other for the dynamic evaluation phase. An inference engine consists of the following components: 1. The rule base (a collection of concrete inferences); 2. The deductions (a collection of concrete judgments); 3. The rule processor (an algorithm for utilizing the rule base to populate the deductions). 4. The objectives. The inference engine stops when either: a) a deduction that is an objective is placed in the collection of deductions, or b) no further deductions can be drawn. A rule base consists of a theoretically infinite number of inferences. Since there are infinitely many possible inferences, it is impossible for this specification to enumerate all of them. Instead, this specification provides a finite number of inference patterns. Each inference pattern has some finite number of premise patterns (possibly zero) and one conclusion pattern. Premise patterns and conclusion patterns can be viewed as templates from which concrete judgments can be derived by substituting concrete syntax or values for the italicized variables in the premise or conclusion pattern. For example, here is a possible premise or conclusion pattern: dynEnv |- Expr => Value This pattern is a shorthand for the infinite number of judgments that can be obtained by substituing concrete objects for the two variables, Expr and Value. For example, "a/b" is a concrete instance of Expr, and "2" is a concrete instance of Value. Substituting these two objects in the pattern produces the concrete judgment dynEnv |- a/b => 2 Note that this judgment is not necessarily true. It is the role of the inference engine to find true judgments, out of the space of all possible judgments. The inference engine seeks to discover true judgments. Any true judgment that the inference engine discovers is placed in the collection of deductions. Also note that this judgment might be true in some contexts and might be false in other contexts. This fact is handled by initializing the inference engine with the information about the initial state of the static and dynamic environment groups. So far we have seen an example of a pattern for a single judgment. Such patterns are grouped into an iference pattern. An example of an inference pattern is dynEnv |- Expr1 => Value1 dynEnv |- Expr2 => Value2 ------------------------- dynEnv |- (Expr1, Expr2) => (Value1, Value2) This inference pattern is a template from which concrete inferences such as the following may be constructed: dynEnv |- a/b => 2 dynEnv |- x/y => 3 ------------------- dynEnv |- (a/b, x/y) => (2, 3) This specification contains many inference patterns. Each inference pattern denotes a collection of concrete inferences, consisting of all inferences that can be obtained by substituting appropriate objects for the variables in the inference pattern. Every possible combination of objects that substitute for the variables constitutes a separate concrete inference. It must also be recognized that there are infinitely many possible static and dynamic environment groups. Each concrete static environment group or concrete dynamic environment group is a possible value for the statEnv or dynEnv in judgments. Thus a judgment pattern such as dynEnv |- Expr => Value denotes the infinite collection of judgments that a particular dynamic environment group evaluates a particular expression to a value (and that concrete judgment may be true or false). The inference engine for the static analysis phase uses only those inference patterns whose conclusion begins with either "|-" or "statEnv |-". The inference engine for the dynamic phase uses all inferences in this specification. The rule processor may be visualized as a collection of "daemons". Each daemon corresponds to a particular concrete inference. If D is the daemon for a concrete inference I, then the behavior of D is as follows: if D detects that all the premises of I are in the pool of deductions, then D places the conclusion of I in the pool of deductions. The initial state of the inference engine is that the pool of deductions is empty. From this state, any concrete inference with no premises may be placed into the pool of deductions by its daemon. This will provide a collection of judgments which will enable other daemons to "fire" and place more judgments in the pool of deductions. This provides the seed to start the recursive activity of an inference engine. Once started, the inference engine could continue forever, expanding its collection of deductions. However, the user is only interested in learning certain deductions, so the inference engine can stop when the objective set by the user has been deduced. The [query/expression] supplied by the user determines the objectives. In the static analysis phase, the objectives are to find a deduction matching either of these patterns: statEnv |- Expr : Type or statEnv |- Expr raises a type error where statEnv is the initial static environment group and Expr is the user's [query/expression]. In the dynamic evaluation phase, the objective are to find a deduction matching any of these patterns; dynEnv |- Expr => Value or dynEnv |- Expr raises a type error or dynEnv |- Expr raises a dynamic error where dynEnv is the initial dynamic environment group.Received on Wednesday, 20 July 2005 23:55:46 UTC

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