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internal design of cl-match


The MATCH macro defines a block around the matching code, and the clause whose pattern matches the value returns from the block after evaluating its code. IFMATCH is defined in terms of MATCH.

pattern logic

For most patterns, the function that determines whether or not a value matches that pattern is a conjunction of boolean tests, which is represented by an AND form. OR patterns and WHEN guards are (so far) the only exceptions. An OR pattern introduces alternative patterns or subpatterns, and a WHEN guard specifies other condititions that have to be satisified for the whole pattern or a branch in an OR pattern to match. OR patterns can be embedded anywhere in the overall pattern, and guards can be placed immediately inside any OR pattern. The expanded code will be optimized to consolidate code and minimize test duplication as much as possible.

An OR pattern generates multiple branches, and multiple ORs generate a whole tree of OR forms by converting terms of the form (a or b) and (c or d) to (a and (c or d)) or (b and (c or d)).[1]

To consolidate the expanded code as much as possible, all tests not inside an OR pattern are grouped at the beginning of the conjunction, so the only term in an AND form that's allowed to be an OR form (corresponding to an OR pattern) is the last one. This makes the code both smaller and faster.

test construction

Test construction is implemented with two structure types, which are currently called TEST and CONJ. TEST is a complete test with variables and gensyms to be bound during the matching process.

CONJ stands for "conjunction". The fields in the stucture are vars, tests, gensyms, ors, and guards. Each field is a list, and the tests, ors, and guards are implicitly combined in an AND form. Tests are pushed onto the tests field in cronological (runtime) order, and the final test is just an AND form with the reversed list of tests spliced into it, along with a possible OR form or guard at the end. Likewise, gensyms, OR forms, guards, and unique variable names are pushed onto the corresponding fields as they're encountered in the pattern.

For performance reasons, it's sometimes convenient to bind one or more gensyms to sections of the value being tested. Since a nonmatching value might not even contain those substructures, all gensyms and user-defined variables are bound to NIL before the test, and are SETF'd as the test proceeds. This is done with the SETFT macro, which wraps a SETF form in a PROGN and returns true. SETFT forms are then mixed together with the pattern tests so that each gensym or variable is set after its assigned location has been found (if it exists), but before the variable or gensym is used in any tests. So the expanded code is procedural, but it should be both fast and compact.

OR patterns

Once all the regular tests have been found, the OR tests are constucted. The final form of the test is a tree where each branch node is either an OR form, or an AND form whose last term is an OR form. The leaf nodes of the test are either guards or whatever pattern tests happen to occur last. Most of the tests are expanded directly into the code, but guards are wrapped in lambda forms so guards that apply to many branches can be called from many leaf nodes without generating too much code bloat.

There's also an interaction between NOT forms and OR forms. The expansion code tries to combine them as efficiently as possible. NOT patterns can be nice if they don't mess with variable bindings, but they're tricky to implement, so we'll save them for later.

[1] It's not enough to embed OR forms in an AND form separately, continuing from an OR form as soon as a matching branch has been found. Even if one branch of an OR form passes, a second OR test might fail with the variables bound in the successful branch of the first OR, even though it would have passed with a different branch of the first OR. So all possible branch combinations have to to be tested, with branch-specific guards evaluated as appropriate after successful matching of each corresponding branch.

© 2008 Daniel S. Bensen