Shorthand declaration of NSLayoutConstraint without visual format. (For those one-off cases where you don't want to use the visual format language.)

ConstraintPlayground.swift

import Cocoa

struct PartialConstraint {
    private let item:AnyObject
    private let attribute:NSLayoutAttribute
    private let multiplier:CGFloat?
    private let constant:CGFloat?
    
    private func constraintWith(partial:PartialConstraint, relation:NSLayoutRelation) -> NSLayoutConstraint {
        assert(multiplier == nil && constant == nil, "Cannot define multiplier or constant on LHS.")
        
        return NSLayoutConstraint(item: item, attribute: attribute, relatedBy: relation, toItem: partial.item, attribute: partial.attribute, multiplier: partial.multiplier ?? 1, constant: partial.constant ?? 0)
    }
    
    private func constraintWith(value:CGFloat, relation:NSLayoutRelation) -> NSLayoutConstraint {
        assert(multiplier == nil && constant == nil, "Cannot define multiplier or constant on LHS.")
        
        return NSLayoutConstraint(item: item, attribute: attribute, relatedBy: relation, toItem: nil, attribute: .NotAnAttribute, multiplier: 0, constant: value)
    }
}

func attr(item:AnyObject, attribute:NSLayoutAttribute) -> PartialConstraint {
    return PartialConstraint(item: item, attribute: attribute, multiplier: nil, constant: nil)
}

func == (lhs:PartialConstraint, rhs:PartialConstraint) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.Equal)
}

func >= (lhs:PartialConstraint, rhs:PartialConstraint) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.GreaterThanOrEqual)
}

func <= (lhs:PartialConstraint, rhs:PartialConstraint) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.LessThanOrEqual)
}

func == (lhs:PartialConstraint, rhs:CGFloat) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.Equal)
}

func >= (lhs:PartialConstraint, rhs:CGFloat) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.GreaterThanOrEqual)
}

func <= (lhs:PartialConstraint, rhs:CGFloat) -> NSLayoutConstraint {
    return lhs.constraintWith(rhs, relation:.LessThanOrEqual)
}

func * (lhs:PartialConstraint, rhs:CGFloat) -> PartialConstraint {
    assert(lhs.constant == nil, "Cannot assign multiplier after constant")
    return PartialConstraint(item: lhs.item, attribute: lhs.attribute, multiplier: (lhs.multiplier != nil ? lhs.multiplier! * rhs : rhs), constant: nil)
}

func * (lhs:CGFloat, rhs:PartialConstraint) -> PartialConstraint {
    return rhs * lhs
}

func / (lhs:PartialConstraint, rhs:CGFloat) -> PartialConstraint {
    return lhs * (1 / rhs)
}

func + (lhs:PartialConstraint, rhs:CGFloat) -> PartialConstraint {
    return PartialConstraint(item: lhs.item, attribute: lhs.attribute, multiplier: lhs.multiplier, constant: (lhs.constant != nil ? lhs.constant! + rhs : rhs))
}

func + (lhs:CGFloat, rhs:PartialConstraint) -> PartialConstraint {
    return rhs + lhs
}

func - (lhs:PartialConstraint, rhs:CGFloat) -> PartialConstraint {
    return lhs + (-rhs)
}

let view1 = NSView()
let view2 = NSView()
view1.addSubview(view2)

view1.addConstraint(attr(view2, .Width) == attr(view1, .Width) / 2 - 5)

println(view1.constraints)