Crate arithmetic_eval

Simple interpreter for ASTs produced by arithmetic-parser.

How it works

1. A Block of statements is compiled into an ExecutableModule. Internally, compilation processes the AST of the block and transforms it into a non-recusrive form. An ExecutableModule may require imports (such as NativeFns or constant Values), which can be taken from a VariableMap (e.g., an Environment).
2. ExecutableModule can then be executed, for the return value and/or for the changes at the top-level variable scope. There are two major variables influencing the execution outcome. An arithmetic is used to define arithmetic ops (+, unary and binary -, *, /, ^) and comparisons (==, !=, >, <, >=, <=). Imports may be redefined at this stage as well.

Type system

Values have 5 major types:

• Primitive values corresponding to literals in the parsed Block
• Boolean values
• Functions, which are further subdivided into native functions (defined in the Rust code) and interpreted ones (defined within a module)
• Tuples / arrays.
• Objects.

Besides these types, there is an auxiliary one: OpaqueRef, which represents a reference-counted native value, which can be returned from native functions or provided to them as an arg, but is otherwise opaque from the point of view of the interpreted code (cf. anyref in WASM).

Semantics

• All variables are immutable. Re-declaring a var shadows the previous declaration.
• Functions are first-class (in fact, a function is just a variant of the Value enum).
• Functions can capture variables (including other functions). All captures are by value.
• Arithmetic operations are defined on primitive values, tuples and objects. Ops on primitives are defined via an Arithmetic. With tuples and objects, operations are performed per element / field. Binary operations require tuples of the same size / objects of the same shape, or a tuple / object and a primitive value. As an example, (1, 2) + 3 and #{ x: 2, y: 3 } / #{ x: 4, y: 5 } are valid, but (1, 2) * (3, 4, 5) isn’t.
• Methods are considered syntactic sugar for functions, with the method receiver considered the first function argument. For example, (1, 2).map(sin) is equivalent to map((1, 2), sin).
• No type checks are performed before evaluation.
• Type annotations and type casts are completely ignored. This means that the interpreter may execute code that is incorrect with annotations (e.g., assignment of a tuple to a variable which is annotated to have a numeric type).

Value comparisons

Equality comparisons (==, !=) are defined on all types of values.

• For bool values, the comparisons work as expected.
• For functions, the equality is determined by the pointer (2 functions are equal iff they alias each other).
• OpaqueRefs either use the PartialEq impl of the underlying type or the pointer equality, depending on how the reference was created; see OpaqueRef docs for more details.
• Equality for primitive values is determined by the Arithmetic.
• Tuples are equal if they contain the same number of elements and elements are pairwise equal.
• Different types of values are always non-equal.

Order comparisons (>, <, >=, <=) are defined for primitive values only and use OrdArithmetic.

Tuples

• Tuples are created using a Tuple expression, e.g., (x, 1, 5).
• Indexing for tuples is performed via FieldAccess with a numeric field name: xs.0. Thus, the index is always a “compile-time” constant. An error is raised if the index is out of bounds or the receiver is not a tuple.
• Tuples can be destructured using a Destructure LHS of an assignment, e.g., (x, y, ...) = (1, 2, 3, 4). An error will be raised if the destructured value is not a tuple, or has an incompatible length.

Objects

• Objects can be created using object expressions, which are similar to ones in JavaScript. For example, #{ x: 1, y: (2, 3) } will create an object with two fields: x equal to 1 and y equal to (2, 3). Similar to Rust / modern JavaScript, shortcut field initialization is available: #{ x, y } will take vars x and y from the context.
• Object fields can be accessed via FieldAccess with a field name that is a valid variable name. No other values have such fields. An error will be raised if the object does not have the specified field.
• Objects can be destructured using an ObjectDestructure LHS of an assignment, e.g., { x, y } = obj. An error will be raised if the destructured value is not an object or does not have the specified fields. Destructuring is not exhaustive; i.e., the destructured object may have extra fields.
• Functional fields are permitted. Similar to Rust, to call a function field, it must be enclosed in parentheses: (obj.run)(arg0, arg1).

Crate features

• std. Enables support of types from std, such as the Error trait, and propagates to dependencies. Importantly, std is necessary for floating-point arithmetics.
• complex. Implements Number for floating-point complex numbers from the num-complex crate (i.e., Complex32 and Complex64). Enables complex number parsing in arithmetic-parser.
• bigint. Implements Number and a couple of other helpers for big integers from the num-bigint crate (i.e., BigInt and BigUint). Enables big integer parsing in arithmetic-parser.

Examples

use arithmetic_parser::grammars::{F32Grammar, Parse, Untyped};
use arithmetic_eval::{
    Assertions, Comparisons, Environment, Prelude, Value, VariableMap,
};

let program = r#"
    // The interpreter supports all parser features, including
    // function definitions, tuples and blocks.
    order = |x, y| (min(x, y), max(x, y));
    assert_eq(order(0.5, -1), (-1, 0.5));
    (_, M) = order(3^2, { x = 3; x + 5 });
    M
"#;
let program = Untyped::<F32Grammar>::parse_statements(program)?;

let mut env = Environment::new();
// Add some native functions to the environment.
env.extend(Prelude.iter());
env.extend(Assertions.iter());
env.extend(Comparisons.iter());

// To execute statements, we first compile them into a module.
let module = env.compile_module("test", &program)?;
// Then, the module can be run.
assert_eq!(module.run()?, Value::Prim(9.0));

Using objects:

let program = r#"
    minmax = |xs| xs.fold(#{ min: INF, max: -INF }, |acc, x| #{
         min: if(x < acc.min, x, acc.min),
         max: if(x > acc.max, x, acc.max),
    });
    assert_eq((3, 7, 2, 4).minmax().min, 2);
    assert_eq((5, -4, 6, 9, 1).minmax(), #{ min: -4, max: 9 });
"#;
let program = Untyped::<F32Grammar>::parse_statements(program)?;

let mut env = Environment::new();
env.extend(Prelude.iter());
env.extend(Assertions.iter());
let module = env.compile_module("minmax", &program)?;
module.run()?;

More complex examples are available in the examples directory of the crate.

Re-exports

pub use self::error::Error;
pub use self::error::ErrorKind;
pub use self::error::EvalResult;

Modules

arith	Arithmetic trait and its implementations.
error	Evaluation errors.
fns	Standard functions for the interpreter, and the tools to define new native functions.

Macros

wrap_fn	An alternative for wrap function which works for arguments / return results with non-'static lifetime.
wrap_fn_with_context	Analogue of wrap_fn macro that injects the CallContext as the first argument. This can be used to call functions within the implementation.

Structs

Assertions	Container for assertion functions: assert and assert_eq.
CallContext	Context for native function calls.
Comparisons	Container with the comparison functions: cmp, min and max.
Environment	Environment containing named Values.
ExecutableModule	Executable module together with its imports.
ExecutableModuleBuilder	Builder for an ExecutableModule.
IndexedId	Indexed module ID containing a prefix part (e.g., snippet).
InterpretedFn	Function defined within the interpreter.
ModuleImports	Imports of an ExecutableModule.
OpaqueRef	Opaque reference to a native value.
Prelude	Commonly used constants and functions from the fns module.
WildcardId	Module identifier that has a single possible value, which is displayed as *.
WithArithmetic	Container for an ExecutableModule together with an OrdArithmetic.

Enums

Function	Function definition. Functions can be either native (defined in the Rust code) or defined in the interpreter.
Value	Values produced by expressions during their interpretation.
ValueType	Possible high-level types of Values.

Traits

CompilerExt	Compiler extensions defined for some AST nodes, most notably, Block.
ModuleId	Identifier of an ExecutableModule. This is usually a “small” type, such as an integer or a string.
NativeFn	Function on zero or more Values.
Number	Marker trait for possible literals.
VariableMap	Encapsulates read access to named variables.

Type Definitions

SpannedValue

Value together with a span that has produced it.