Functional programming with lambda-tree syntax

TL;DR

This paper introduces MLTS, a new functional programming language that employs lambda-tree syntax to handle bindings within data structures, ensuring bindings remain scoped and do not escape, with formal semantics and an implementation outline.

Contribution

The paper presents MLTS, a novel language that formalizes lambda-tree syntax with a logical semantics including nominal abstraction and nabla-quantifier, and extends core ML typing.

Findings

Formal semantics for MLTS using nominal abstraction and nabla-quantifier

A type system extending core ML typing for MLTS

An online interpreter demonstrating MLTS features

Abstract

We present the design of a new functional programming language, MLTS, that uses the lambda-tree syntax approach to encoding bindings appearing within data structures. In this approach, bindings never become free nor escape their scope: instead, binders in data structures are permitted to move to binders within programs. The design of MLTS includes additional sites within programs that directly support this movement of bindings. In order to formally define the language's operational semantics, we present an abstract syntax for MLTS and a natural semantics for its evaluation. We shall view such natural semantics as a logical theory within a rich logic that includes both *nominal abstraction* and the *nabla-quantifier*: as a result, the natural semantics specification of MLTS can be given a succinct and elegant presentation. We present a typing discipline that naturally extends the typing of core ML programs and we illustrate the features of MLTS by presenting several examples. An on-line interpreter for MLTS is briefly described.