github.com/fatlotus/mast

Mast: a Math AST for Golang

Because Go does not support operator overloading, most numerical libraries are messy to use. Mast is an attempt to write a domain-specific language for math, so that code can be written in a more simple way.

If it helps, think regular expressions, but for algebra.

// with Mast
mast.Eval("x = A' * b + c", &x, &A, &b, &c)

// without Mast
Transpose(&aT, &A)
Times(&Atb, &At, &b)
Plus(&x, &Atb, &c)

Parser

Mast mostly exists to create parsers for math-like languages. To use it, first create a *mast.Parser object, configuring the various operations and their precidence.

// A Parser configures the given operators in terms of precedence.
type Parser struct {
	// Define which operators appear in this language. These operators are
	// given in order of loosest to tightest (so addition/subtraction should
	// probably come before multiplication/division).
	Operators []Prec

	// Define which matching grouping operators are used.
	Groups []Group

	// If true, then "sin x" is legal and parses as "sin(x)" would. If false,
	// that is a syntax error.
	AdjacentIsApplication bool
}

Then you invoke the (p *mast.Parser).Parse(string) (*mast.Equation, error) function.

// Parses a single equation in the given source. On success, e is a
// parsed *Equation; iff not, error is non-nil and of type Unexpected{}.
func (p Parser) Parse(source string) (e *Equation, error) {

Example

Suppose we want to make a basic calculator parser. First, define which operations and grouping operators we want to support:

integers := &mast.Parser{
	// allow parentheses
	Groups: []Group{
		{"(", ")"},
	},
	
	// add plus, minux, multiply, divide, and modulo
	Operators: []Prec{
		{[]string{"+", "-"}, InfixLeft},
		{[]string{"*", "/", "%"}, InfixLeft},
		{[]string{"-", "+"}, Prefix},
	},
}

To parse a string using this language, invoke (p *mast.Parser) Parse(string) (*mast.Equation, error) with the source code to evaluate. For example, if we run:

tree, err := integers.Parse("y = (-a) * b + c")
fmt.Printf("tree: %v\n", tree)

then err will be nil and tree will be as follows:

tree := &Equation{
	Left: &Var{"y"},
	Right: &Binary{
		Op: "+",
		Left: &Binary{
			Op: "*",
			Left: &Unary{
				Op: "-",
				Elem: &Var{"a"},
			},
			Right: &Var{"b"},
		}
		Right: &Var{"c"}
	}
}

By iterating over the tree, your DSL can evaluate the mathematical expression while maintaining type integrity.

Evaluator

Mast includes a toy evaluator that handles matrices as [][]float64. To use it, invoke the Eval(code string, args ...interface{}) error function, passing pointers to the respective arguments.

// Evaluate the given expression with the given variables. Variables are
// assigned left to right based on first usage.
func Eval(code string, args ...interface{}) error {

Think %-arguments to fmt.Printf. To make setting up variables easier, arguments can be specified in three ways:

• a [][]float64 for an n x m matrix;
• a []float64 for an 1 x n column vector; or
• a float64, for a 1 x 1 scalar.

All other types panic.

Example

Suppose we want to compute a linear transform (multiplying a vector by a matrix, and adding a vector). First, we set up the variables to compute:

A := [][]float64{
	[]float64{1, 2},
}

x := []float64{3, 4}
// same as := [][]float64{[]float64{5}, []float64{6}}

b := 5.0
// same as := [][]float64{[]float64{5.0}} 

y := 0

Once those are set up, the computation is fairly easy.

if err := mast.Eval("y = A * x + b", &y, &A, &x, &b); err != nil {
	handleError(err)
	return
}

The result is then available in y.

License

This code is covered under the MIT license.

Copyright (c) 2016 Jeremy Archer

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.