Logical relations for coherence of effect subtyping

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing

Categorical structure of continuation passing style

Laboratory for Foundations of Computer ScienceThis thesis attempts to make precise the structure inherent in Continuation Passing Style (CPS). We emphasize that CPS translates lambda-calculus into a very basic calculus that does not have functions as primitive. We give an abstract categorical presentation of continuation semantics by taking the continuation type constructor (cont in Standard ML of New Jersey) as primitive. This constructor on types extends to a contravariant functor on terms which is adjoint to itself on the left; restricted to the subcategory of those programs that do not manipulate the current continuation, it is adjoint to itself on the right. The motivating example of such a category is built from (equivalence classes of typing judgements for) continuation passing style (CPS) terms. The categorical approach suggests a notion of effect-free term as well as some operators for manipulating continuations. We use these for writing programs that illustrate our categorical approach and refute some conjectures about control effects. A call-by-value lambda-calculus with the control operator callcc can be interpreted. Arrow types are broken down into continuation types for argument/result-continuations pairs, reflecting the fact that CPS compiles functions into a special case of continuations. Variant translations are possible, among them lazy call-by-name, which can be derived by way of argument thunking, and a genuinely call-by-name transform. Specialising the semantics to the CPS term model allows a rational reconstruction of various CPS transforms

Semantics of Separation-Logic Typing and Higher-order Frame Rules for<br> Algol-like Languages

We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we provide simple sound rules for deriving higher-order frame rules, allowing for local reasoning

Relational Parametricity for Computational Effects

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc

Bounded Refinement Types

We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2) Floyd-Hoare logic within a state transformer monad equipped with combinators for branching and looping, and (3) using the above to implement a refined IO monad that tracks capabilities and resource usage. This leap in expressiveness comes via a translation to "ghost" functions, which lets us retain the automated and decidable SMT based checking and inference that makes refinement typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP 201

Interprocedural Type Specialization of JavaScript Programs Without Type Analysis

Dynamically typed programming languages such as Python and JavaScript defer type checking to run time. VM implementations can improve performance by eliminating redundant dynamic type checks. However, type inference analyses are often costly and involve tradeoffs between compilation time and resulting precision. This has lead to the creation of increasingly complex multi-tiered VM architectures. Lazy basic block versioning is a simple JIT compilation technique which effectively removes redundant type checks from critical code paths. This novel approach lazily generates type-specialized versions of basic blocks on-the-fly while propagating context-dependent type information. This approach does not require the use of costly program analyses, is not restricted by the precision limitations of traditional type analyses. This paper extends lazy basic block versioning to propagate type information interprocedurally, across function call boundaries. Our implementation in a JavaScript JIT compiler shows that across 26 benchmarks, interprocedural basic block versioning eliminates more type tag tests on average than what is achievable with static type analysis without resorting to code transformations. On average, 94.3% of type tag tests are eliminated, yielding speedups of up to 56%. We also show that our implementation is able to outperform Truffle/JS on several benchmarks, both in terms of execution time and compilation time.Comment: 10 pages, 10 figures, submitted to CGO 201

Interaction Trees: Representing Recursive and Impure Programs in Coq

"Interaction trees" (ITrees) are a general-purpose data structure for representing the behaviors of recursive programs that interact with their environments. A coinductive variant of "free monads," ITrees are built out of uninterpreted events and their continuations. They support compositional construction of interpreters from "event handlers", which give meaning to events by defining their semantics as monadic actions. ITrees are expressive enough to represent impure and potentially nonterminating, mutually recursive computations, while admitting a rich equational theory of equivalence up to weak bisimulation. In contrast to other approaches such as relationally specified operational semantics, ITrees are executable via code extraction, making them suitable for debugging, testing, and implementing software artifacts that are amenable to formal verification. We have implemented ITrees and their associated theory as a Coq library, mechanizing classic domain- and category-theoretic results about program semantics, iteration, monadic structures, and equational reasoning. Although the internals of the library rely heavily on coinductive proofs, the interface hides these details so that clients can use and reason about ITrees without explicit use of Coq's coinduction tactics. To showcase the utility of our theory, we prove the termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given in an ITree-based denotational semantics. Unlike previous results using operational techniques, our bisimulation proof follows straightforwardly by structural induction and elementary rewriting via an equational theory of combinators for control-flow graphs.Comment: 28 pages, 4 pages references, published at POPL 202