Merge pull request #73 from JuliaSymbolics/s/doc-ctx

Document "contexts"

src/matchers.jl

@@ -29,8 +29,8 @@ Base.show(io::IO, s::Segment) = (print(io, "~~"); print(io, s.name))
 makesegment(s::Symbol, keys) = (push!(keys, s); Segment(s))
 
 """
-A wrapper for slot and segment predicates which allows them to
-take two arguments: the value and a Context
+A wrapper indicating that the function inside must be called with
+2 arguments. An expression, and the current context.
 """
 struct Contextual{F}
     f::F

src/rule_dsl.jl

@@ -40,7 +40,7 @@ function (r::Rule)(term, ctx=EmptyCtx())
 end
 
 """
-    `@rule LHS => RHS`
+    @rule LHS => RHS
 
 Creates a `Rule` object. A rule object is callable, and  takes an expression and rewrites
 it if it matches the LHS pattern to the RHS pattern, returns `nothing` otherwise.
@@ -141,6 +141,19 @@ sin((a + c))
 ```
 
 Predicate function gets an array of values if attached to a segment variable (`~~x`).
+
+**Context**:
+
+_In predicates_: Contextual predicates are functions wrapped in the `Contextual` type.
+The function is called with 2 arguments: the expression and a context object
+passed during a call to the Rule object (maybe done by passing a context to `simplify` or
+a `RuleSet` object).
+
+The function can use the inputs however it wants, and must return a boolean indicating
+whether the predicate holds or not.
+
+_In the consequent pattern_: Use `(@ctx)` to access the context object on the right hand side
+of an expression.
 """
 macro rule(expr)
     @assert expr.head == :call && expr.args[1] == :(=>)
@@ -206,11 +219,12 @@ end
 #### Rulesets
 
 """
-    RuleSet(rules::Vector{AbstractRules})(expr; depth=typemax(Int), applyall=false, recurse=true)
+    RuleSet(rules::Vector{AbstractRules}, context=EmptyCtx())(expr; depth=typemax(Int), applyall=false, recurse=true)
 
-`RuleSet` is an `AbstractRule` which applies the given `rules` throughout an `expr`. 
+`RuleSet` is an `AbstractRule` which applies the given `rules` throughout an `expr` with the
+context `context`.
 
-`RuleSet(rules)(expr)` Note that this only applies the rules in one pass, not until there are no
+Note that this only applies the rules in one pass, not until there are no
 changes to be applied. Use `SymbolicUtils.fixpoint(ruleset, expr)` to apply a RuleSet until there 
 are no changes.
 

src/simplify.jl

@@ -1,18 +1,39 @@
 ##### Numeric simplification
 
-default_rules(::EmptyCtx) = SIMPLIFY_RULES
 """
-    simplify(x, [rules=SIMPLIFY_RULES]; fixpoint=true, applyall=true, recurse=true)
+    default_rules(expr, context::T)::RuleSet
 
-Apply a `RuleSet` of rules provided in `rules`. By default
-these rules are `SymbolicUtils.SIMPLIFY_RULES`. If `fixpoint=true`
-repeatedly applies the set of rules until there are no changes.
+The `RuleSet` to be used by default for a given expression and the context.
+Julia packages defining their own context types should define this method.
+
+By default SymbolicUtils will try to apply appropriate rules for expressions
+of symtype Number.
+"""
+default_rules(x, ctx) = SIMPLIFY_RULES
+
+"""
+    simplify(x, ctx=EmptyCtx();
+        rules=default_rules(x, ctx),
+        fixpoint=true,
+        applyall=true,
+        recurse=true)
+
+Simplify an expression by applying `rules` until there are no changes.
+The second argument, the context is passed to every [`Contextual`](#Contextual)
+predicate and can be accessed as `(@ctx)` in the right hand side of `@rule` expression.
+
+By default the context is an `EmptyCtx()` -- which means there is no contextual information.
+Any arbitrary type can be used as a context, and packages defining their own contexts
+should define `default_rules(ctx::TheContextType)` to return a `RuleSet` that will
+be used by default while simplifying under that context.
+
+If `fixpoint=true` this will repeatedly apply the set of rules until there are no changes.
 Applies them once if `fixpoint=false`.
 
 The `applyall` and `recurse` keywords are forwarded to the enclosed
-`RuleSet`.
+`RuleSet`, they are mainly used for internal optimization.
 """
-function simplify(x, ctx=EmptyCtx(); rules=default_rules(ctx), fixpoint=true, applyall=true, recurse=true)
+function simplify(x, ctx=EmptyCtx(); rules=default_rules(x, ctx), fixpoint=true, applyall=true, recurse=true)
     if fixpoint
         SymbolicUtils.fixpoint(rules, x, ctx; recurse=recurse, applyall=recurse)
     else