… We present the spinal atomic λ -calculus, a typed λ -calculus with explicit sharing and … 5
Our result is the spinal atomic λ-calculus , a λ -calculus with a refined form of full laziness, spine …

… The atomic lambda-calculus implements full laziness, a standard notion of sharing where
only the skeleton of a term needs to be duplicated. Given a term t which needs to be duplicated…

… Before we formally introduce the spinal atomic λ-calculus, we provide some intuition. First
we show how we will represent the scope of an abstraction in our calculus. We represent …

… Similarly, we reserve the word atomic for a pre-atomic term that does not contain any β-redices.
Similarly to λ→, λ→-&T enjoys a number of highly desirable properties [4]. In particular, …

… based on some sugared form of the lambda calculus. Early examples are LISP, McCarthy et
… To determine the residuals of R in N, we attach an atomic label, say “a,” as the degree of R (…

… spine is left over with a closure as at the bottom of fig. 1 in its head. Should the arity of the
abstraction exceed the number of apply nodes along the spine, ie… an atomic subexpression eat …

… A homomorphism h from a signature Σ1 to a signature Σ2 maps atomic types of Σ1 to types
of Σ2, for functional types we have h(A → B) = h(A) → h(B). Moreover, it then maps terms in Λ(…

… Rename is self-dual, it binds atoms, and it is the inverse of α… The idea is that we shall exploit
Rename for renaming atoms … extends the simulation to spine evaluation strategy, which …

… Both concepts relate to the variable at the tip of the spine, which we … atomic, such that
each of f’s arguments args(f) is a variable, either addressing a function or a parameter. Non-atomic …

… This is because a TM transition (respectively, a cell of the TM tape), looks like an atomic unit
… of Closed CbN reduction is not an atomic operation from the complexity-theoretic point of …