The Perfect Lambda Syntax

Lambda-Grammars and the Syntax-Semantics Interface

Lambda: the ultimate syntax-semantics interface

Spreadsheets in accounting and Matlab in engineering are immensely popular because these glorified calculators let domain experts play : write down a problem in familiar terms and quickly try a number of solutions. Natural-language semanticists have a better tool. Not only does it compute grammar yields and truth values, it also infers types, normalizes terms, and displays truth conditions as f...

Mirror theory : syntactic representation in perfect syntax

In the better developed sciences it is the departures from symmetry rather than the symmetries that are typically taken to be in need of explanation. Mirror theory is an attempt to look at some of the central properties of syntactic representations in this spirit. The core hypothesis of this theory is that in syntactic representations complementation expresses morphological structure: x is the ...

Quantum Lambda Calculi with Classical Control: Syntax and Expressive Power

We study an untyped λ–calculus with quantum data and classical control. This work stems from previous proposals by Selinger and Valiron and by Van Tonder. We focus on syntax and expressiveness, rather than (denotational) semantics. We prove subject reduction, confluence and a standardization theorem. Moreover, we prove the computational equivalence of the proposed calculus with a suitable class...

Lambda-fold complete graph decompositions into perfect four-triple configurations