Jonathan Harrop jdh30
jdh30
/ Simplify.mx
Last active
February 16, 2017 05:55
Symbolic simplification rules written in Mathematica's language
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| 0 + x_ := x | |
| x_ + 0 := x | |
| f_ + (g_ + h_) := f + g + h | |
| 0 x_ := 0 | |
| x_ 0 := 0 | |
| 1 x_ := x | |
| x_ 1 := x | |
| f_ (g_ h_) := f g h |
jdh30
/ Derivative
Last active
February 25, 2017 10:49
Rewrite rules for simple differentiation in Mathematica syntax
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| D[_, _] := 0 | |
| D[x_, x_] := 1 | |
| D[f_ + g_, x_] := D[f, x] + D[g, x] | |
| D[f_ - g_, x_] := D[f, x] - D[g, x] | |
| D[f_ g_, x_] := f D[g, x] + g D[f, x] | |
| D[f_ / g_, x_] := f D[1/g, x] + 1/g D[f, x] | |
| D[f_^g_, x_] := f^(g - 1) (g D[f, x] + f Log[f] D[g, x]) | |
| D[Log[f_], x_] := D[f, x] / f |
jdh30
/ derivative.ml
Last active
February 25, 2017 22:09
A symbolic derivative written in OCaml using pattern matching over code quotations
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| let d x = function | |
| | <:expr< $y$ >> when x=y -> <:expr< 1 >> | |
| | <:expr< $f$ + $g$ >> -> <:expr< $d f x$ + $d g x$ >> | |
| | <:expr< $f$ * $g$ >> -> <:expr< $f$ * $d g x$ + $g$ * $d f x$ >> | |
| | _ -> <:expr< 0 >> | |
jdh30
/ derivative.rw
Created
February 25, 2017 22:35
A symbolic derivative written in my own term rewrite language
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| D(x, y) -> 0 | |
| D(x, x) -> 1 | |
| D(f+g, x) -> D(f, x) + D(g, x) | |
| D(f*g, x) -> f*D(g, x) + g*D(f, x) |
jdh30
/ ReversePolishCalculator.fs
Created
March 25, 2017 13:58
Reverse polish calculator in F#, derived from this 35-line Racket metaprogramming example http://beautifulracket.com/stacker/source-listing.html
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| let (|Float|_|) s = | |
| let mutable x = 0.0 | |
| if System.Double.TryParse(s, &x) then Some x else None | |
| let binop f x y stack = | |
| let z = f x y | |
| printfn "%A" z | |
| z::stack | |
| let rec loop stack = |
jdh30
/ ReversePolishCompiler1.fs
Created
March 26, 2017 00:18
Reverse polish calculator compiler in F# using quotations, derived from this 35-line Racket example http://beautifulracket.com/stacker/source-listing.html Raw
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| let (|Float|_|) s = | |
| let mutable x = 0.0 | |
| if System.Double.TryParse(s, &x) then Some x else None | |
| let rec (|Parse|) = function | |
| | Float x::t -> <@ x @>, t | |
| | "+"::Parse(x, Parse(y, t)) -> <@ %x + %y @>, t | |
| | "*"::Parse(x, Parse(y, t)) -> <@ %x * %y @>, t | |
| let (Parse(f, _)) = stdin.ReadToEnd().Split '\n' |> List.ofSeq |> List.rev |
jdh30
/ ReversePolishCompiler2.fs
Created
March 26, 2017 00:34
Reverse polish compiler in F# using LLVM, derived from this 35-line Racket example http://beautifulracket.com/stacker/source-listing.html
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| let (|Int|_|) s = | |
| let mutable x = 0 | |
| if System.Int32.TryParse(s, &x) then Some x else None | |
| LLVM.NativeLibrary.LLVMDLL.Load() | |
| LLVM.Target.InitializeNative() | |
| let context = LLVM.Context.Global | |
| let i32 = LLVM.IntegerType.GetInt32 context |
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| open System.Collections.Generic | |
| /// Imperative depth-first search | |
| let dfs (V, E) = | |
| let visited = HashSet(HashIdentity.Structural) | |
| let stack = Stack[V] | |
| while stack.Count > 0 do | |
| let u = stack.Pop() | |
| if not(visited.Contains u) then | |
| for v in E u do |
jdh30
/ bf.bf
Created
April 6, 2017 01:03
BF interpreter written in BF from "A very short self-interpreter" https://arxiv.org/html/cs/0311032
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| >>>+[[-]>>[-]++>+>+++++++[<++++>>++<-]++>>+>+>+++++[> | |
| ++>++++++<<-]+>>>,<++[[>[->>]<[>>]<<-]<[<]<+>>[>]>[<+ | |
| >-[[<+>-]>]<[[[-]<]++<-[<+++++++++>[<->-]>>]>>]]<<]<] | |
| < | |
| [[<]>[[>]>>[>>]+[<<]<[<]<+>>-]>[>]+[->>]<<<<[[<<]<[<] | |
| +<<[+>+<<-[>-->+<<-[>+<[>>+<<-]]]>[<+>-]<]++>>-->[>]> | |
| >[>>]]<<[>>+<[[<]<]>[[<<]<[<]+[-<+>>-[<<+>++>-[<->[<< | |
| +>>-]]]<[>+<-]>]>[>]>]>[>>]>>]<<[>>+>>+>>]<<[->>>>>>> | |
| >]<<[>.>>>>>>>]<<[>->>>>>]<<[>,>>>]<<[>+>]<<[+<<]<] |
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| let timer = System.Diagnostics.Stopwatch.StartNew() | |
| type expr = | |
| | Int of int | |
| | Var of string | |
| | Add of expr * expr | |
| | Mul of expr * expr | |
| | Pow of expr * expr | |
| | Ln of expr |