functions

A function maps input values to output values. In Mech, functions are branch-based and support pattern matching, recursion, and kind annotations.

Syntax

Functions are defined with a signature, one or more guards, and a trailing ..

name(arg1, arg2, ...) -> 
  ├ pattern-1 -> expression-1
  ├ pattern-2 -> expression-2
  └ pattern-n -> expression-n.

A function call uses regular call syntax:

name(value1, value2)

The argument name can be added to the call for named arguments:

name(arg1: value1, arg2: value2)

Branches are matched from top to bottom.
The first matching branch is selected.
Function bodies are expressions.
Functions can call themselves recursively.
Calls are expressions, so they can be nested in formulas and broadcast over vectors/matrices.

power(x<u64>, n<u64>) -> <u64>

├ ( *, 0u64 ) ->1u64

└ ( x, n ) ->x*power(x, n-1u64)

.

power(2u64, 8u64)

factorial(n<u64>) -> <u64>

├0u64 ->1u64

└n ->n*factorial(n-1u64)

.

factorial(10u64)

fib(n<u64>) -> <u64>

├0u64 ->0u64

├1u64 ->1u64

└n ->fib(n-1u64)+fib(n-2u64)

.

fib(10u64)

Functions are nomally called with the following call syntax:

fxn-name(value1, value2, ...)

Some functions have named arguments, which allow arguments to be passed in any order. In this case, the call syntax is:

fxn-name(arg1: value1, arg2: value2, ...)

Function calls can also broadcast over vectors:

fib(n) -> 
  ├ 0u64 -> 0u64
  ├ 1u64 -> 1u64
  └ n -> fib(n - 1u64) + fib(n - 2u64).

xs := 0u64..=10u64
fib(xs)