updated documentation and test coverage

README.md

@@ -32,7 +32,9 @@ Interface for applying symbolic manipulation on [Julia expressions](https://docs
 * interface link communicates and interprets via various reduce output modes using `rcall` method;
 * high-level reduce-julia syntax parser-generator walks arbitrary expression to rewrite mathematical code;
 * import operators from REDUCE using code generation to apply to arbitrary computational expressions;
-* interactive `reduce>` REPL within the Julia terminal window activated by `}` key.
+* interactive `reduce>` REPL within the Julia terminal window activated by `}` key;
+* extended arithmetic operators `+`,`-`,`*`,`^`,`/`,`//` compute on `Symbol` and `Expr` types;
+* provides over 330 internal and external methods each supporting many argument types.
 
 ## Setup
 
@@ -53,31 +55,46 @@ View the documentation [stable](https://chakravala.github.io/Reduce.jl/stable) /
 
 Reduce expressions encapsulated into `RExpr` objects can be manipulated within julia using the standard syntax. Create an expression object either using the `RExpr("expression")` string constructor or `R"expression"`. Additionally, arbitrary julia expressions can also be parsed directly using the `RExpr(expr)` constructor. Internally `RExpr` objects are represented as an array that can be accessed by calling `*.str[n]` on the object.
 
-Sequences of reduce statements are automatically parsed into julia `quote` blocks using the `RExpr` constructor, which can `parse` back into a julia expression.
+When `Reduce` is used in Julia, all of the standard arithmetic operations are now extended to also work on `Symbol` and `Expr` types.
 ```Julia
-julia> :((x+im+π)^2; int(1/(1+x^3),x)) |> RExpr
-^(+(x,i,pi),2);
-int(/(1,+(1,^(x,3))),x);
+julia> 1-1/:n
+:((n - 1) // n)
 
-julia> rcall(ans,:expand) |> parse
-quote
- (((π + 2x) * π + x ^ 2) - 1) + 2 * (π + x) * im
- ((2 * sqrt(3) * atan((2x - 1) // sqrt(3)) - log((x ^ 2 - x) + 1)) + 2 * log(x + 1)) // 6
-end
-```
-Call `split(::RExpr)` to create a new `RExpr` object with all expressions split into separate array elements.
+julia> ans^-:n
+:(1 // ((n - 1) // n) ^ n)
 
+julia> limit(ans,:n,Inf)
+e = 2.7182818284590...
+```
+Julia abstract syntax trees are automatically converted into sequences of reduce statements that are in return parsed into julia `quote` blocks using the `RExpr` constructor.
 The `rcall` method is used to evaluate any type of expression.
 ```Julia
 julia> :(int(sin(im*x+pi)^2-1,x)) |> rcall
-:(-(((e ^ (4x) + 4 * e ^ (2x) * x) - 1)) // (8 * e ^ (2x)))
+:((1 - (e ^ (4x) + 4 * e ^ (2x) * x)) // (8 * e ^ (2x)))
+```
+However, there are often multiple equivalent ways of achieving the same result:
+```Julia
+julia> int(sin(im*:x+π)^2-1,:x)
+:((1 - (e ^ (4x) + 4 * e ^ (2x) * x)) // (8 * e ^ (2x)))
 ```
 The output of `rcall` will be the same as its input type.
 ```Julia
 julia> "int(sin(y)^2, y)" |> rcall
 "( - cos(y)*sin(y) + y)/2"
 ```
 Use `rcall(expr,switches...)` to evaluate `expr` using REDUCE mode `switches` like `:expand`, `:factor`, and `:latex`.
+```Julia
+julia> :((x+im+π)^2; int(1/(1+x^3),x)) |> RExpr
+^(+(x,i,pi),2);
+int(/(1,+(1,^(x,3))),x);
+
+julia> rcall(ans,:horner) |> parse
+quote
+ ((π + 2x) * π + 2 * (π + x) * im + x ^ 2) - 1
+ ((2 * sqrt(3) * atan((2x - 1) // sqrt(3)) - log((x ^ 2 - x) + 1)) + 2 * log(x + 1)) // 6
+end
+```
+Call `split(::RExpr)` to create a new `RExpr` object with all expressions internally split into separate array elements.
 
 Mathematical operators and REDUCE modes can be applied directly to `Expr` and `RExpr` objects.
 ```Julia
@@ -91,11 +108,23 @@ Although not all language features have been implemented yet, it is possible to
 julia> Expr(:for,:(i=2:34),:(product(i))) |> rcall
 :(@big_str "295232799039604140847618609643520000000")
 ```
+The `squash` function provides a way to reduce full program blocks into simplified functions,
+```Julia
+julia> Expr(:function,:(example(a,b)),quote
+ z = 3
+ target = z * :a * :b
+ z -= 1
+ target += z*(1-:a)*(1-:b)
+ end) |> squash |> factor
+:(function example(a, b)
+ (5b - 2) * a - 2 * (b - 1)
+ end)
+```
 
 ### Output mode
  Various output modes are supported. While in the REPL, the default `nat` output mode will be displayed for `RExpr` objects.
- ```Julia
- julia> :(sin(x*im) + cos(y*φ)) |> RExpr
+```Julia
+julia> :(sin(x*im) + cos(y*φ)) |> RExpr
 
  (sqrt(5) + 1)*y
 cos(-----------------) + sinh(x)*i
@@ -105,14 +134,14 @@ This same output can also be printed to the screen by calling `print(nat(r))` me
 
 It is possible to direclty convert a julia expression object to LaTeX code using the `latex` method.
 ```Julia
-julia> print(@latex sin(x*im) + cos(y*φ))
+julia> print(@latex sin(x) + cos(y*φ))
 \begin{displaymath}
-\cos \left(\left(\left(\sqrt {5}+1\right) y\right)/2\right)+\sinh \,x\: i
+\cos \left(\left(\left(\sqrt {5}+1\right) y\right)/2\right)+\sin \,x
 \end{displaymath}
 ```
-Internally, this command essentially expands to `rcall(:(sin(x*im) + cos(y*φ)),:latex) |> print`, which is equivalent.
+Internally, this command essentially expands to `rcall(:(sin(x) + cos(y*φ)),:latex) |> print`, which is equivalent.
 
-![latex-equation](https://latex.codecogs.com/svg.latex?\cos&space;\left(\left(\left(\sqrt&space;{5}+1\right)&space;y\right)/2\right)+\sinh&space;x\:&space;i)
+![latex-equation](https://latex.codecogs.com/svg.latex?\cos&space;\left(\left(\left(\sqrt&space;{5}+1\right)&space;y\right)/2\right)+\sin&space;x)
 
 In `IJulia` the display output of `RExpr` objects will be rendered LaTeX with the `rlfi` REDUCE package in `latex` mode.
 
@@ -145,6 +174,8 @@ Releases of `Reduce.jl` enable the general application of various REDUCE functio
 
 If the `reduce>` REPL is not appearing when `}` is pressed or the `Reduce.PSL` pipe is broken, the session can be restored by simply calling `Reduce.Reset()`, without requiring a restart of `julia` or reloading the package. This kills the currently running `redpsl` session and then re-initializes it for new use.
 
+Otherwise, questions can be asked on gitter/discourse or submit your issue or pull-request if you require additional features or noticed some unusual edge-case behavior.
+
 ### OhMyREPL Compatibility
 
 Reduce.jl is compatible with the [OhMyREPL.jl](https://github.com/KristofferC/OhMyREPL.jl) package.

docs/make.jl

@@ -23,7 +23,7 @@ deploydocs(
  branch = "gh-pages",
  latest = "master",
  osname = "linux",
- julia = "0.5",
+ julia = "0.6",
  deps = nothing,
  make = nothing,
 )

docs/src/index.md

@@ -36,6 +36,8 @@ Interface for applying symbolic manipulation on [Julia expressions](https://docs
 * high-level reduce-julia syntax parser-generator walks arbitrary expression to rewrite mathematical code;
 * import operators from REDUCE using code generation to apply to arbitrary computational expressions;
 * interactive `reduce>` REPL within the Julia terminal window activated by `}` key.
+* extended arithmetic operators `+`,`-`,`*`,`^`,`/`,`//` compute on `Symbol` and `Expr` types;
+* provides over 330 internal and external methods each supporting many argument types.
 
 ## Setup
 
@@ -69,31 +71,46 @@ Releases of `Reduce.jl` enable the general application of various REDUCE functio
 
 Reduce expressions encapsulated into `RExpr` objects can be manipulated within julia using the standard syntax. Create an expression object either using the `RExpr("expression")` string constructor or `R"expression"`. Additionally, arbitrary julia expressions can also be parsed directly using the `RExpr(expr)` constructor. Internally `RExpr` objects are represented as an array that can be accessed by calling `*.str[n]` on the object.
 
-Sequences of reduce statements are automatically parsed into julia `quote` blocks using the `RExpr` constructor, which can `parse` back into a julia expression.
+When `Reduce` is used in Julia, all of the standard arithmetic operations are now extended to also work on `Symbol` and `Expr` types.
 ```Julia
-julia> :((x+im+π)^2; int(1/(1+x^3),x)) |> RExpr
-^(+(x,i,pi),2);
-int(/(1,+(1,^(x,3))),x);
+julia> 1-1/:n
+:((n - 1) // n)
 
-julia> rcall(ans,:expand) |> parse
-quote
- (((π + 2x) * π + x ^ 2) - 1) + 2 * (π + x) * im
- ((2 * sqrt(3) * atan((2x - 1) // sqrt(3)) - log((x ^ 2 - x) + 1)) + 2 * log(x + 1)) // 6
-end
-```
-Call `split(::RExpr)` to create a new `RExpr` object with all expressions split into separate array elements.
+julia> ans^-:n
+:(1 // ((n - 1) // n) ^ n)
 
+julia> limit(ans,:n,Inf)
+e = 2.7182818284590...
+```
+Julia abstract syntax trees are automatically converted into sequences of reduce statements that are in return parsed into julia `quote` blocks using the `RExpr` constructor.
 The `rcall` method is used to evaluate any type of expression.
 ```Julia
 julia> :(int(sin(im*x+pi)^2-1,x)) |> rcall
-:(-(((e ^ (4x) + 4 * e ^ (2x) * x) - 1)) // (8 * e ^ (2x)))
+:((1 - (e ^ (4x) + 4 * e ^ (2x) * x)) // (8 * e ^ (2x)))
+```
+However, there are often multiple equivalent ways of achieving the same result:
+```Julia
+julia> int(sin(im*:x+π)^2-1,:x)
+:((1 - (e ^ (4x) + 4 * e ^ (2x) * x)) // (8 * e ^ (2x)))
 ```
 The output of `rcall` will be the same as its input type.
 ```Julia
 julia> "int(sin(y)^2, y)" |> rcall
 "( - cos(y)*sin(y) + y)/2"
 ```
 Use `rcall(expr,switches...)` to evaluate `expr` using REDUCE mode `switches` like `:expand`, `:factor`, and `:latex`.
+```Julia
+julia> :((x+im+π)^2; int(1/(1+x^3),x)) |> RExpr
+^(+(x,i,pi),2);
+int(/(1,+(1,^(x,3))),x);
+
+julia> rcall(ans,:horner) |> parse
+quote
+ ((π + 2x) * π + 2 * (π + x) * im + x ^ 2) - 1
+ ((2 * sqrt(3) * atan((2x - 1) // sqrt(3)) - log((x ^ 2 - x) + 1)) + 2 * log(x + 1)) // 6
+end
+```
+Call `split(::RExpr)` to create a new `RExpr` object with all expressions internally split into separate array elements.
 
 Mathematical operators and REDUCE modes can be applied directly to `Expr` and `RExpr` objects.
 ```Julia
@@ -107,28 +124,40 @@ Although not all language features have been implemented yet, it is possible to
 julia> Expr(:for,:(i=2:34),:(product(i))) |> rcall
 :(@big_str "295232799039604140847618609643520000000")
 ```
+The `squash` function provides a way to reduce full program blocks into simplified functions,
+```Julia
+julia> Expr(:function,:(example(a,b)),quote
+ z = 3
+ target = z * :a * :b
+ z -= 1
+ target += z*(1-:a)*(1-:b)
+ end) |> squash |> factor
+:(function example(a, b)
+ (5b - 2) * a - 2 * (b - 1)
+ end)
+```
 
 ### Output mode
 Various output modes are supported. While in the REPL, the default `nat` output mode will be displayed for `RExpr` objects.
 ```Julia
 julia> :(sin(x*im) + cos(y*φ)) |> RExpr
 
-  (sqrt(5) + 1)*y
- cos(-----------------) + sinh(x)*i
-  2
+ (sqrt(5) + 1)*y
+cos(-----------------) + sinh(x)*i
+ 2
 ```
 This same output can also be printed to the screen by calling `print(nat(r))` method.
 
 It is possible to direclty convert a julia expression object to LaTeX code using the `latex` method.
 ```Julia
-julia> print(@latex sin(x*im) + cos(y*φ))
+julia> print(@latex sin(x) + cos(y*φ))
 \begin{displaymath}
-\cos \left(\left(\left(\sqrt {5}+1\right) y\right)/2\right)+\sinh \,x\: i
+\cos \left(\left(\left(\sqrt {5}+1\right) y\right)/2\right)+\sin \,x
 \end{displaymath}
 ```
-Internally, this command essentially expands to `rcall(:(sin(x*im) + cos(y*φ)),:latex) |> print`, which is equivalent.
+Internally, this command essentially expands to `rcall(:(sin(x) + cos(y*φ)),:latex) |> print`, which is equivalent.
 
-![latex-equation](https://latex.codecogs.com/svg.latex?\cos&space;\left(\left(\left(\sqrt&space;{5}+1\right)&space;y\right)/2\right)+\sinh&space;x\:&space;i)
+![latex-equation](https://latex.codecogs.com/svg.latex?\cos&space;\left(\left(\left(\sqrt&space;{5}+1\right)&space;y\right)/2\right)+\sin&space;x)
 
 In `IJulia` the display output of `RExpr` objects will be rendered LaTeX with the `rlfi` REDUCE package in `latex` mode.
 
@@ -137,17 +166,19 @@ Similar to <kbd>?</kbd> help and <kbd>;</kbd> shell modes in Julia, `Reduce` pro
 ```Julia
 reduce> df(atan(golden_ratio*x),x);
 
-  2 2
-  sqrt(5)*x + sqrt(5) - x + 1
- -------------------------------
-  4 2
-  2*(x + 3*x + 1)
+ 2 2
+ sqrt(5)*x + sqrt(5) - x + 1
+-------------------------------
+ 4 2
+ 2*(x + 3*x + 1)
 ```
 
 ## Troubleshooting
 
 If the `reduce>` REPL is not appearing when `}` is pressed or the `Reduce.PSL` pipe is broken, the session can be restored by simply calling `Reduce.Reset()`, without requiring a restart of `julia` or reloading the package. This kills the currently running `redpsl` session and then re-initializes it for new use.
 
+Otherwise, questions can be asked on gitter/discourse or submit your issue or pull-request if you require additional features or noticed some unusual edge-case behavior.
+
 ### OhMyREPL Compatibility
 
 Reduce.jl is compatible with the [OhMyREPL.jl](https://github.com/KristofferC/OhMyREPL.jl) package.

docs/src/library.md

@@ -30,29 +30,41 @@ parse
 load_package
 ```
 
+```@docs
+sub
+```
+
+```@docs
+squash
+```
+
 ## Imported Operators
 
 Reduce `switch` modes callable as functions from Julia
-> :expand, :complex, :factor, :expandlog, :combinelog, :precise, :combineexpt, :rounded, :evallhseq, :nat, :latex
+> expand, complex, factor, horner, expandlog, combinelog, precise, combineexpt, rounded, evallhseq, nat, latex
 
-Calculus operators
-> :df, :int
+Reduce operators with multiple arguments
+> df, int, limit, sum, prod, +, -, ^, *, /, //
 
 Unary operators
-> :abs, :conj, :factorial, :floor, :max, :min, :round, :sign, :acos, :acosh, :acot, :acoth, :acsc, :acsch, :asec, :asech, :asin, :asinh, :atan, :atanh, :atan2, :cos, :cosh, :cot, :coth, :csc, :csch, :exp, :hypot, :log, :log10, :sec, :sech, :sin, :sinh, :sqrt, :tan, :tanh, :gamma, :factorize
+> abs, conj, factorial, floor, max, min, round, sign, acos, acosh, acot, acoth, acsc, acsch, asec, asech, asin, asinh, atan, atanh, atan2, cos, cosh, cot, coth, csc, csch, exp, hypot, log, log10, sec, sech, sin, sinh, sqrt, tan, tanh, gamma, factorize
 
-> :beta, :besseli, :besselj, :besselk, :bessely, :polygamma, :zeta
+> beta, besseli, besselj, besselk, bessely, polygamma, zeta
 
-> :ibeta, :igamma, :ln, :psi, :bernoulli, :continued_fraction, :ci, :dilog, :ei, :si, :airy_ai, :airy_aiprime, :airy_bi, :airy_biprime, :hanekl1, :hankel2, :kummerm, :kummeru, :lommel1, :lommel2, :struveh, :struvel, :whittakerm, :whittakeru, :solidharmonicy, :sphericalharmonicy
+> ibeta, igamma, ln, psi, bernoulli, continued_fraction, ci, dilog, ei, si, airy_ai, airy_aiprime, airy_bi, airy_biprime, hanekl1, hankel2, kummerm, kummeru, lommel1, lommel2, struveh, struvel, whittakerm, whittakeru, solidharmonicy, sphericalharmonicy
 
-> :ceiling, :fix, :impart, :repart, :nextprime, :euler, :fibonacci, :motzkin, :random, :random_new_seed
+> ceiling, fix, impart, repart, nextprime, euler, fibonacci, motzkin, random, random_new_seed
 
 ## Tools & Options
 
 ```@docs
 Reduce.parsegen
 ```
 
+```@docs
+Reduce.unfoldgen
+```
+
 ```@docs
 Reduce.linefilter
 ```
@@ -64,3 +76,19 @@ Reduce.Rational
 ```@docs
 Reduce.SubCall
 ```
+
+```@docs
+Reduce.SubHold
+```
+
+```@docs
+Reduce.SubFail
+```
+
+```@docs
+Reduce.ColCheck
+```
+
+```@docs
+Reduce.DisplayLog
+```

src/parser.jl

@@ -706,7 +706,7 @@ end
 """
  unfoldgen(::Symbol,::Symbol)
 
-Parser generator that outputs code to walk and manipulate REDUCE expressions
+Parser generator that outputs code to walk and manipulate Julia expressions
 """
 function unfoldgen(fun::Symbol,mode::Symbol)
  modefun = Symbol(:parse,"_",mode)

src/rexpr.jl

@@ -164,13 +164,23 @@ const repjlr = jl_to_r_utf
 const gexrjl = Regex("($(join(keys(r_to_jl),")|(")))")
 const gexjlr = Regex("($(join(keys(jl_to_r),")|(")))")
 
+"""
+ sub(::Union{Dict,Pair},expr)
+
+Make variable substitutions using Reduce's native sub command
+"""
 sub(syme::String,expr::RExpr) = "sub($syme,$expr)" |> rcall |> RExpr
 sub(syme::String,expr::T) where T = convert(T,sub(syme,RExpr(expr)))
 sub(s::Dict{String,String},expr) = sub(_syme(s),expr)
 sub(s::Dict{<:Any,<:Any},expr) = sub(Dict([=>(string.(RExpr.([b[1],b[2]]))...) for b ∈ collect(s)]...),expr)
 sub(s::Pair{<:Any,<:Any},expr) = sub(Dict(s),expr)
-sub(s::Array{Pair{<:Any,<:Any},1},expr) = sub(Dict(s...),expr)
+sub(s::Array{<:Pair{<:Any,<:Any},1},expr) = sub(Dict(s...),expr)
+
+"""
+ sub(T::DataType,expr::Expr)
 
+Make a substitution to conver numerical values to type T
+"""
 function sub(T::DataType,ixpr)
  if typeof(ixpr) == Expr
  expr = deepcopy(ixpr)
@@ -465,6 +475,11 @@ end
  end
 end=#
 
+"""
+ squash(expr)
+
+Reduces an entire program statement block using symbolic rewriting
+"""
 function squash(expr)
  typeof(expr) == Expr && if expr.head == :block
  return @eval $expr