Rules

The Rules software is an engine for

defining patterns like (+ 0 (? x)), which means "Match any list of length 3 that begins with the symbol + and the number 0, and call its third element x";
using them to define rules like (rule (+ 0 (? x)) x), which means "If you get such a list, return its third element (otherwise return your input)"; and
composing such rules into pattern-dispatch operators and term rewriting systems.

In addition, Rules

is extensible to more kinds of patterns;
includes example term-rewriting simplifiers for logic and algebra; and
is itself meant as a pedagogical illustration of a way to write such engines.

Introduction

Rules are a pervasive human device for describing processes. It is therefore a source of great programming power to concisely instruct the computer "If you see a situation like X, do Y."

Consider the usual definition of the factorial function n!

0! = 1
n! = n * (n-1)! for positive n

We are used to programming this with an if statement, but we can also think of factorial as the union of two separate rules, which might be rendered in prefix notation as

(define factorial
  (pattern-dispatch
    (rule '(0)                          ; If the whole argument list is a single 0
          1)                            ; the answer is 1
    (rule `((? n ,positive?))           ; If a single positive n
          (* n (factorial (- n 1))))))  ; use the formula

In the case of factorial, this representation doesn't buy us much, but for a more complex function, this kind of pattern-dispatched operator can be much clearer than a nest of ifs. Being able to distribute clauses to the places in the program where they are relevant is also a source of power: object-oriented method dispatch can be seen as a form of pattern dispatch, where the patterns are retricted to be "are you an instance of this class?"

To take a more elaborate example of the use of rules, a symbolic simplifier for algebraic expressions needs to know many things like

Replace instances of "(+ 0 x)" with "x" (for any expression x)
Replace instances of "(* n1 n2)" with their product (for literal numbers n1, n2)
If you see sin^2(x) and cos^2(x) in the same sum, turn them into 1
...

Writing them out as an explicit list of concise rules like this:

(rule '(+ 0 (? x))
      x)

(rule `(* (? n1 ,number?) (? n2 ,number?))
      (* n1 n2))              ; multiply

(rule '(+ (?? t1) (expt (sin (? theta)) 2) (?? t2) (expt (cos (? theta)) 2) (?? t3))
      `(+ 1 ,@t1 ,@t2 ,@t3))  ; build a list with a + in front

makes it easier to see what the simplifier is actually doing, and therefore easier to get it right. Much the same thing happens with local optimization passes in compilers.

Installation

Just git clone this repository,

(load "rules/load")

and hack away.

If you want to develop Rules, you will want to also get the unit test framework that Rules uses. Type git submodule init and git submodule update.

Patterns

Examples

Here is a pattern that might be used for constant folding:

`(* (? x ,number?) (? y ,number?))

This means, in detail:

Match a list of exactly three elements
Whose first element is the symbol *
Whose second element produces true when given to the procedure number?
- Which bind to the name x
Whose third element also produces true when given to the procedure number?
- Which bind to the name y

Here is a pattern that might be used for simplification:

'(+ (?? stuff) (? x) (? x) (?? more))

In brief, it means "find a pair of consecutive identical terms anywhere in a sum". In detail:

Match a list
Whose first element is the symbol +
That has some elements after the first
- Which bind to the name stuff
Such that there is an element after stuff
- Which bind to the name x
Such that there is an element after x
- Such that this element is equal? to x
And bind any subsequent elements of the list to the name more.

Note that the matcher will search over all possible lengths for the stuff list to find a match (but the length of the more list can be deduced, because it must take whatever is left in the sum).

Concepts

A pattern gives a shape for a piece of data, with some "holes" -- variables -- for components of the data that may vary. A successful match entails a binding of data components to variables such that, if the variables are replaced with their bindings, the pattern and the data become equal?. If no such binding is possible, the match fails.

Patterns are recursive, meaning that a pattern for a compound structure like a list is built out of patterns for its pieces. This allows patterns to recognize very specific, complex shapes in their data, and extract deeply nested data components.

Sublists of unknown length may be matched with segment variables, which entail search within the matcher to find a matching assignment.

Unlike other pattern matching systems, variables may appear more than once in a pattern. This just means that each occurrence of the same variable must correspond to equal? data for a successful match.

Pattern Language

Patterns are Scheme list structure, interpreted according to the following rules:

(? <symbol> <procedure> ...): Pattern variable

The symbol serves as the variable's name. The optional procedures are used as predicates that restrict the possible data this variable may be bound to. This pattern matches any datum that passes all of the predicates, and binds the given name to that datum. If any predicate returns #f on the datum, this pattern fails to match. In the common case of no predicates, this pattern always matches.
(?? <symbol>): Segment variable

This pattern must occur as a subpattern of a list pattern. The symbol serves as the variable's name. This pattern matches a sublist of the enclosing list of any length (including zero) and binds that sublist to the given name.
(<pattern> ...): List

A list whose first symbol is neither ? nor ?? is a pattern that matches a list if and only if the elements of the data list match the subpatterns of the list pattern (in order). In this case, the list pattern binds all the variables bound by its subpatterns. If more than one subpattern binds the same name, those data must agree (up to equal?). Variable-length lists can be matched using segment variables.
<procedure>: Explicit combinator

A Scheme procedure that appears as a pattern is taken to be a matcher combinator (see Extension). In particular, to match the literal list (? x) (which, if used as a pattern, would become a variable), you can use ``(,(match:eqv '?) x)`.
<object>: Constant

Any other Scheme object is a pattern constant that matches only itself (up to eqv?).

Matching

Patterns can be compiled into matcher procedures that accept a datum and do something with the (possibly empty) set of bindings that make the datum match the pattern.

(matcher <pattern>)

Returns a procedure that accepts one object and returns an association list mapping the names of the variables in the pattern to pieces of the object such that the pattern and the object become equal? upon substituting those bindings into the pattern. If no such mapping exists, the procedure returns #f.
(for-each-matcher <pattern>)

Returns a procedure that, given an object and a procedure, applies the procedure it is given to each possible association list of bindings of variable names to pieces of the object that make the pattern match. This procedure does not return anything useful.
(all-results-matcher <pattern>)

Returns a procedure that, given an object, returns a (possibly empty) list of all association lists of bindings of variable names to pieces of the object that make the pattern match.

Rules

A rule is a pairing of a pattern and an expression to evaluate if the pattern matches (the body). The useful thing about rules is that the body expression has access to the bindings of the variables matched by the pattern.

(rule <pattern> <expression>): Rule macro

Returns a procedure that accepts one argument and tries to match the pattern against that argument. If the match succeeds, evaluates the expression in an environment extended with the bindings determined by the match and returns the result. If the match fails, returns the original input unchanged (up to eqv?).

In order to support conditions on the applicability of rules that are inconvenient to capture in the pattern, the body may return #f to force the rule application to backtrack back into the matcher (or fail).

(rule <pattern> <expression>): Rule macro (cont'd)

If the expression returns #f, the rule procedure interprets that particular match of the pattern as having failed after all, and evaluates the expression with the bindings from another match, if any. If the expression returns #f for all sets of bindings that cause the pattern to match, the rule procedure returns its input unchanged.

Unfortunately, this means that special measures are necessary to allow the body of a rule to cause the rule procedure to return #f.

(succeed <thing>): Procedure

A helper procedure to allow the body of a rule to cause its enclosing rule invocation to return anything, including #f.
(rule <pattern> <expression>): Rule macro (cont'd)

If the expression returns the result of calling succeed on an object, the rule procedure returns that object (even if the object is #f, which the rule procedure would otherwise interpret as a command to try a different match).

For purposes of term rewriting, a "rule firing" that didn't change the input is equivalent to the rule not having fired at all. In other circumstances, however, it is sometimes necessary to distinguish between a rule matching and intentionally returning its input vs a rule not matching at all. For this purpose, rule procedures actually accept an optional second argument, which, if supplied, acts as a token to return on failing to match (instead of the input).

(rule <pattern> <expression>): Rule macro (cont'd)

The returned rule procedure accepts an optional second argument. If supplied, this argument is returned (instead of the first argument) on failure to match the pattern (or on exhaustion of backtracking options).

Where there is a macro, there should generally be a procedure that does the same thing:

(make-rule <pattern> <procedure>): Rule constructor

Returns a rule procedure that matches its input against the pattern and calls the procedure with the resulting bindings as follows: every required formal parameter to the procedure is passed the binding of the pattern variable of the same name from the match. The procedure is otherwise treated the same way as the body expression of a rule made by the rule macro is treated: backtracking on #f, forcing return with succeed, etc.

Pattern Dispatch

A pattern-dispatch operator (like the factorial example in the Introduction) is a collection of rules, one of which is expected to match any datum that the operator may be given. The operator will attempt the rules in order, and return the first result if any rule matches. If no rule matches, a pattern-dispatch operator signals an error. This is a case where the distinction between a rule not matching and a rule matching and returning its input is significant.

(pattern-dispatch <rule> ...)

Returns a pattern-dispatch operator whose initial set of rules is given by the arguments. These rules will be tried left-to-right.
(attach-rule! <operator> <rule>)

Adds another rule to an existing pattern-dispatch operator. The new rule will be tried last.

Term Rewriting

Something like a peephole optimizer or a symbolic simplifier applies its rules to any sub-element of its input, replacing that part with the result of the rule; and keeps doing so until no rules apply anywhere within the input, in which case it returns the final result. Such a thing is called a term-rewriting system. Rules provides a collection of combinators for making term rewriting systems and similar operators out of rules.

Note that the results of all the procedures in this section look like rules, in the sense that they try to match something according to some pattern and return their input on failure, so these combinators nest.

(term-rewriting <rule> ...)

Returns a term-rewriting procedure that applies the given rules. The returned procedure accepts one argument, and applies any of its rules at any matching point that occurs inside the list structure of its argument, repeatedly replacing the match with the result of the rule, until no rules apply. Returns the final result. (Does not mutate its input unless the bodies of the rules do.) In particular, if no rules match, returns its input unchanged (up to eqv?). Of course, the rules in question should be arranged so as to ensure that this process terminates in a reasonable amount of time.

For purposes of determining substructure, the input is interpreted as an expression tree: to wit, an arbitrarily deep list of lists (as opposed to a tree of pairs). For example, given the input (* (+ a b) (+ c d)), the rules would be applied to *, +, a, b, (+ a b), (+ c d), the input itself, and any results (and subexpressions thereof) the rules may produce from such applications.
(rule-list <list of rules>)

Returns a procedure that tries each of its rules in order on its input (not subexpressions thereof) until one matches, and returns the result. Returns the input (up to eqv?) if no rules match.

Note: the returned procedure is slightly different from a pattern-dispatch operator, in that it does not error out on failure, but returns its input.
(in-order <list of rules>)

Returns a procedure that accepts one argument and applies each rule in the list to it once, in the order given, passing the results from one rule to the next (whether the rules match or not). The effect is actually the same as composing the rules as functions, in the proper order. Note: if none of the rules match, the net result is returning the input unchanged (up to eqv?).
(iterated <rule>)

Returns a procedure that repeatedly applies its rule to its input, and returns the final result. The input is not mutated (unless by the body of the rule). If the rule never matches, the procedure returns its input unchanged (up to eqv?).

Note: This is most useful with rules that are not idempotent, such as may arise as the outputs of the other combinators, like rule-list.
(on-subexpressions <rule>)

Returns a procedure that applies its rule to every point in the list structure of its input, bottom-up, including the input itself, and returns the final result. If the rule matches any subexpression, the rule's result is placed in the appropriate place before matching the expression it was a subexpression of. The input is not mutated (unless by the body of the rule). If the rule never matches, the procedure returns its input unchanged (up to eqv?). This is different from term-rewriting because it applies the rule only once at each point, whether it matches or not.
(iterated-on-subexpressions <rule>)

Like on-subexpressions, except the returned procedure iterates on each subexpression before trying a larger result. Note that not just the rule is iterated, but the rule is first reapplied to subexpressions of the result, because the rule can produce structure whose subexpressions might match the rule. If the system defined by the rule is confluent, this should produce the same result as (iterated (on-subexpressions <rule>)), but matches are attempted in a different order, leading to different performance characteristics (and potentially different end results if the rule is not confluent).
(top-down <rule>)

Like iterated-on-subexpressions, but also applies the rule repeatedly to the whole input before recurring to subexpressions.

Iteration patterns are hard to describe in words. If you are still confused about the rule application order of on-subexpressions, iterated-on-subexpressions, or top-down, they are defined quite concisely in term-rewriting.scm.

Simplifiers

Mostly by way of example, Rules includes several term-rewriting systems for simplifying albegraic and logical expressions, in simplifiers.scm. For instance,

(simplify-algebra
 '(+ (* 3 (+ x y 1))
     -3
     (* y (+ 1 2 -3) z)))
 ===> (+ (* 3 x) (* 3 y))

Extension

The pattern matching system of Rules is extensible, permitting the addition of custom matcher combinators and custom pattern syntax for them.

Pattern matchers in Rules nest because of an interface that allows a matcher for a compound (like a list) to combine matchers for the pieces as black boxes and expose the same interface. That's why they are called combinators.

Implementing Custom Matcher Combinators

To be precise, a matcher combinator in Rules is a procedure of three arguments: the datum, the dictionary, and the success continuation procedure. The datum is the portion of the data that the combinator is expected to match against, the dictionary is a data structure that represents the bindings made so far, and the success procedure represents the behavior of the rest of the matcher after this combinator. To wit, the success procedure accepts a dictionary (possibly augmented with any additional bindings this combinator chooses to make) and returns either #f to indicate that the rest of the matcher fails to match with those bindings, or a dictionary to indicate success (which should include bindings for all pattern variables occurring in the whole pattern).

The matcher combinator is expected to return #f if the matcher consisting of itself and its success procedure fails to match the given datum with the given dictionary, and a dictionary of bindings if it succeeds. (Matchers for data segments have a slightly different interface, below.) Giving a combinator access to the rest of the matcher like this enables guessing different possible bindings and intercepting failures in order to backtrack (see match:segment in patterns.scm).

For example, here is one way to make a matcher combinator for matching a pattern constant:

(define (constant-matcher pattern-constant)
  (lambda (data dictionary succeed)
    (and (eqv? data pattern-constant)
         (succeed dictionary))))

The returned procedure closes over the constant it is looking for. When it gets data, it checks that the data is eqv? to the constant. If not, the whole match from this point fails (because there is nothing the subsequent matchers can do about this datum being different from the desired constant). If the data is eqv? to the constant, this combinator defers completely to the sequel.

The dictionary is an associative structure for accessing previously made bindings and making new ones.

(dict:lookup <variable> <dictionary>)

Looks up the given variable (usually a symbol) in the given dictionary and returns the value cell (see dict:value) if found or #f if not. Does not directly return the value held in the value cell to be able to distinguish between no binding and a binding to #f.
(dict:value <value-cell>)

Returns the value held in the given value cell.
(dict:bind <variable> <object> <dictionary>)

Returns the new dictionary that results from adding to the given one a binding for the variable to the object. The input dictionary is not mutated.

Custom Combinators in Patterns

Any procedure that implements the interface of a matcher combinator can be used directly in a pattern. For example (note the quasiquote)

`(,(constant-matcher '+) (? x) (? y))  ; matches like '(+ (? x) (? y))

This fact is useful even without custom matcher combinators, to abstract over patterns (see, for example, simplifiers.scm).

The pattern compiler (that builds matcher combinators out of patterns) can also be extended, to recognize additional syntax for custom combinators:

(new-pattern-syntax! <predicate> <procedure>)

Adds a clause to the pattern compiler. The clause is applicable to any piece of syntax for which the given predicate returns a true value; if so, that piece of syntax is compiled to the combinator returned from invoking procedure, passing that syntax as its only argument. Note that if the predicate matches syntax intended to be compound, it is up to the procedure to compile its parts into submatcher combinators and compose them appropriately. See list-pattern->combinators in patterns.scm for an example.
(match:->combinators <pattern>)

Compiles the given pattern to a matcher combinator, respecting all syntax definitions given by new-pattern-syntax to date.

A Note on Segment Matching

Combinators that match sublists (rather than individual data items) necessarily have a somewhat different interface, because the number of items that the segment matcher consumes impacts the remaining data available for its success continuation to match.

The data that is passed to a segment matcher is always a list, and the segment matcher's success continuation accepts a second argument. The segment matcher is to match some prefix of the list, and pass the remainder in to its success continuation in addition to the (augmented) dictionary. For an example, see match:segment in patterns.scm. Note that in order for any enclosing compound combinators to be able to distinguish segment matchers from regular matchers (in order to pass them the appropriate arguments), the former must be marked by invoking the procedure segment-matcher! upon them.

(make-segment <list> <list>)

An abstraction for designating segments of lists without copying them (until needed). A segment is defined as all the elements of the first argument list, except those in the second, which must be a suffix thereof. Creating a segment is an O(1) operation. If a segment is placed in a dictionary (with dict:bind) then dict:value will retrieve it as a regular list (the requisite copying will be performed at most once).

Other Pattern Matching Systems

In general programming language discourse, the term "pattern matching" usually means something a little different from what's going on here. Typically, the allowable patterns are less general, allowing the matching to be implemented more efficiently, at the cost of expressiveness. Also typically, the patterns are embedded in some larger control construct, without allowing standalone matchers or rules to have an existence of their own. This obscures the essential semantic similarity of pattern dispatch with term rewriting; but may be appropriate in order to permit deep inspection of the patterns for high matching performance.

The examples I have in mind are

In Haskell, Scala, and presumably other members of the ML family, pattern matching is embedded into the structure of the language, essentially such that every function is a pattern-dispatch operator (except that further rules cannot be added to a defined operator after the fact). Patterns and rules do not have an independent existence, except insofar as a pattern-dispatch operator with exactly one rule can be thought of as being the same as a rule (which is not quite right, because they do not treat match failures gracefully).

The pattern matching in these languages is restricted relative to Rules in that all pattern variables must be distinct (obviating the need to check repeated ones for equality), there are no segment variables, and there is no notion of backtracking in the matcher (though there is an option for "rule bodies" to reject a match, in the form of guard clauses). On the other hand, user-defined product types are automatically added as additional patterns, giving smooth integration between construction and destructuring of algebraic data types.

User extensibility of the pattern system (aside from the automatic introduction of products) is given by view patterns in Haskell (and presumably similar constructs in other descendants of ML) and by extractor classes in Scala.
Prolog deeply integrates the notion of unification, which is like pattern matching except that the "data" can be a pattern also -- unification computes the most general common specializer of two patterns. If one of the inputs to the unification algorithm happens to have no variables in it, unification amounts to pattern matching. I do not actually know the relative expressiveness of the patterns in Prolog vs Rules. Prolog already has pervasive backtracking, so it is quite possible that the patterns admit multiple unifications, which may need to be searched.
Racket's match facility is very similar to the pattern matching in Rules, though instead of segment variables they have a concept of repeating subpatterns of lists. Again, patterns and rules appear only as clauses of variants of the match form and have no independent existence, so effectively can only be used in what amounts to anonymous, non-extensible pattern-dispatch operators.
Racket also ships with a term-rewriting library named redex. As far as I can tell, the clauses of match have no relationship to the rules used by redex.
My own pattern-case library is an implementation of ML-style pattern matching in MIT Scheme, and the same remarks about its relative expressiveness to Rules apply. The fact that I wrote two of these things tells you that I think there is room for different renditions of pattern matching in the same programming environment.

Developer Documentation

The developer documentation is the source code and the commentary therein.

Interesting stuff
- patterns.scm: Pattern matcher in the combinator style, and a compiler for it.
- rules.scm: Rules.
- pattern-dispatch.scm: Composition of rules into pattern-dispatch operators.
- term-rewriting.scm: Composition of rules into a term rewriting engine and a few useful variations on the theme.
- simplifiers.scm: Simplification of algebraic and logical expressions by means of term rewriting.
Support
- support/auto-compilation.scm: Automatically invoke the MIT Scheme compiler, if necessary and possible, to (re)compile files before loading them. This has nothing to do with Pattern Case, but I figured copying it in was easier than making an external dependency.
- support/eq-properties.scm: A generalization of Lisp property lists to any Scheme object (identifiable by eq?); used internally for tagging certain procedures as to the interface they expect.
- support/ghelper.scm: A predicate dispatch system, used to implement the pattern compiler.
- load.scm: Orchestrate the loading sequence. Nothing interesting to see here.
- Makefile: Run the test suite. Note that there is no "build" as such; source is automatically recompiled at loading time as needed.
- LICENSE: The AGPLv3, under which Pattern Case is licensed.
Test suite
- Run it with make test.
- The test/ directory contains the actual test suite.
- The testing/ directory is a git submodule pointed at the Test Manager framework that the test suite relies upon.

Portability

Rules is written in MIT Scheme with no particular portability considerations in mind. It is a language extension at heart, so the rule macro is quite important to its spirit. Rules should not be too difficult to port to any Scheme system that has the facilities to implement rule (notably a macro system permitting controlled non-hygiene). I expect Rules to run unmodified on any platform MIT Scheme supports.

Bugs

The procedures returned by the term-rewriting combinators do not obey exactly the same interface as rules, in that they do not accept the optional argument that allows the user of a rule to tell the difference between the rule failing to match and matching but returning identically the input. This could be viewed as a bug.

Unimplemented Features

More Matchers

There are plenty of additional matcher types that may be worth implementing. For example, something akin to the repetition operator of regular expressions, that accumulates the values from successive matches as lists of matched items. That was the point of making this machine extensible -- go nuts.

More Backtracking

In principle, the same mechanism used to control backtracking in the pattern matcher can be extended to the bodies of rules, so that said bodies can offer retractable substitutions that can be changed if they are found unacceptable later. For this system, I decided not to mess with that -- unlimited chronological backtracking leads to well known trouble, and I feel that such an extension would be better done by first embedding a general-purpose backtracking mechanism into the programming language (in which the pattern matchers can then be rewritten). If you feel that you want this, I hope the present system can serve as a useful example for writing your own.

Specificity Dispatch

In principle, pattern-dispatch operators can analyze the rules they are dispatching with and select the most specific of matching rules (rather than the first added) to apply. Implementing this in the present system is impeded by the fact that rules are opaque, so there is actually no way to examine two rules and determine whether one is more specific than another. That much could be fixed, but the extensibility of the pattern matcher to arbitrary user-supplied matchers, as well as the ability of user-supplied rule bodies to reject matches for arbitrarily complex reasons, makes specificity dispatch impossible in general (without requiring some kind of additional user-supplied information about the relationships of any new matchers and any restriction predicates to each other).

Better Performance

Though some attention has been given to making sure that at least common rules will have the asymptotic performace one would wish, further performance improvements are possible:

In principle, once there is only one segment variable left among the subpatterns of a list pattern, no search is necessary to determine how many elements of the list to match it with. At the moment this optimization is only applied in the common case that the segment variable in question is the last subpattern in the list.
If a segment variable is not used a the rule's body, much work could be saved by not copying it before evaluating said body. This would be very easy to implement in a lazy programming language, but in Scheme it would require a static dead-variable analysis of the body expression.
In principle, rule-list and pattern-dispatch could eliminate the work of matching common prefixes of multiple rules by using a trie structure to match all their rules at once. Implementing this is impeded in the present program by the fact that rules are opaque, so there is actually no way to know whether two rules would start with the same tests or not. That much could be fixed; but the fact that the pattern language allows user extension with arbitrary matchers further limits the ultimate applicability of this extension.
In principle, much work could be done to optimize the rule application order used by term-rewriting; especially by examining the rules and computing the circumstances under which applications of them can produce results upon which further rules may be applicable. In the present program this is impeded by the above-mentioned opacity of rules, and also by the fact that in principle the rule bodies are arbitrary Scheme expressions that can return anything.

Author

Alexey Radul, axch@mit.edu

History

The idea of compiling patterns to collections of combinator procedures goes at least as far back as Carl Hewitt's 1969 PhD thesis, though he did not implement it.

The progenitor of the current program was originally written by Gerald Jay Sussman in 1983 -- an appropriate source file had this to say:

This is a descendent of the infamous 6.001 rule interpreter, originally written by GJS for a lecture in the faculty course held at MIT in the summer of 1983, and subsequently used and tweaked from time to time. This subsystem has been a serious pain in the ass, because of its expressive limitations, but I have not had the guts to seriously improve it since its first appearance. -- GJS

January 2006. I have the guts now! The new matcher is based on combinators and is in matcher.scm. -- GJS

I myself got involved when I was a teaching assistant for Professor Sussman's Advanced Symbolic Programming course at MIT; my inspiration was to clean up all the internal and external interfaces, and understand what the essential pieces were and what they were good for. After a couple iterations between 2008 and 2010, I was able to produce a reasonably pretty version of this program, showcasing the relationships between patterns, rules, pattern dispatch, term rewriting, and simplification.

License

Rules is free software; you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

Rules is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU Affero General Public License along with Pattern Case; if not, see http://www.gnu.org/licenses/.

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README.md

README.md

Rules

Table of Contents

Introduction

Installation

Patterns

Examples

Concepts

Pattern Language

Matching

Rules

Pattern Dispatch

Term Rewriting

Simplifiers

Extension

Implementing Custom Matcher Combinators

Custom Combinators in Patterns

A Note on Segment Matching

Other Pattern Matching Systems

Developer Documentation

Portability

Bugs

Unimplemented Features

More Matchers

More Backtracking

Specificity Dispatch

Better Performance

Author

History

License

Files

README.md

Latest commit

History

README.md

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Rules

Table of Contents

Introduction

Installation

Patterns

Examples

Concepts

Pattern Language

Matching

Rules

Pattern Dispatch

Term Rewriting

Simplifiers

Extension

Implementing Custom Matcher Combinators

Custom Combinators in Patterns

A Note on Segment Matching

Other Pattern Matching Systems

Developer Documentation

Portability

Bugs

Unimplemented Features

More Matchers

More Backtracking

Specificity Dispatch

Better Performance

Author

History

License