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...] is the expression e with every free occurrence of the variable x replaced by y. The predicate isVal(e) holds iff e is a lambda abstraction or a constructor. A heap Γ is a partial map from variable names to expressions. The set domΓ := {x |(x 7→ e) ∈ Γ} contains all names bound in Γ, while thunksΓ := {x |(x 7→ e) ∈ Γ, ¬ isVal(e)} contains just those that are bound to thunks. Note that we consider heap-bound names to be free, i.e. domΓ ⊆ fvΓ. The proper treatment of names is the major technical hurdle when rigorously formalizing anything related to the lambda calculus. We employ Nominal Logic [27] here, so the lambda abstractions and let-bindings are proper equivalency classes, i.e. λx. x = λy. y. A configuration (Γ, e, S) consists of the heap Γ, the control e and the stack S. The stack is constructed from • the empty stack, [], • arguments, written $x·S and put on the stack during the evaluation of an application, • update markers, written #x·S and put on the stack during the evaluation of a variable’s right-hand-side, and • alternatives, written (e1 : e2)·S and put on the stack during the evaluation of the scrutinee of an if-then-else construct. Throughout this work we assume all con...

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...e the natural and denotational semantics given by Launchbury in the theorem prover Isabelle. • In doing so we are, to our knowledge, the first to use both the Nominal package (to handle name binding) =-=[11]-=- and the HOLCF [3] package (for the domain-theoretic aspects) in the same development. • We identify a problem in the original correctness proof, and find two ways to fix it: 1. We define an alternati...

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...pi1 and pi2 as pi1 + pi2. We denote the inverse permutation of pi as −pi. Application of permutations naturally extends to products, lists, functions and datatypes (nominal datatypes) as described in =-=[16]-=-. The smallest non-trivial permutation is called a swapping. We denote a swapping of atoms a and b as (a b), and define by: (a b) = λc. if a = c then b else if b = c then a else c 3 The source of the ...

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... ∥ R, and prove that this candidate relation is an IO-bisimulation. 5. Related Work We first discuss alternative approaches to the handling of binding and -conversion, starting from Nominal Isabelle =-=[28, 11, 30]-=-. This extension of the Isabelle proof assistant features nominal datatypes that represent -equivalence classes. It has been used successfully in a number of research efforts concerning formalization...