Call-by-Value Lambda Calculus as a Model of Computation in Coq
@article{Forster2018CallbyValueLC,
title={Call-by-Value Lambda Calculus as a Model of Computation in Coq},
author={Yannick Forster and Gert Smolka},
journal={Journal of Automated Reasoning},
year={2018},
volume={63},
pages={393-413}
}We formalise a (weak) call-by-value $$\lambda $$λ-calculus we call L in the constructive type theory of Coq and study it as a minimal functional programming language and as a model of computation. We show key results including (1) semantic properties of procedures are undecidable, (2) the class of total procedures is not recognisable, (3) a class is decidable if it is recognisable, corecognisable, and logically decidable, and (4) a class is recognisable if and only if it is enumerable. Most of…
7 Citations
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References
SHOWING 1-10 OF 33 REFERENCES
Weak Call-by-Value Lambda Calculus as a Model of Computation in Coq
- Computer ScienceITP
- 2017
A weak call-by-value \(\lambda \)-calculus is formalised in the constructive type theory of Coq and study it as a minimal functional programming language and as a model of computation.
Programming in the λ-Calculus: From Church to Scott and Back
- Computer ScienceThe Beauty of Functional Code
- 2013
This paper shows how to convert programs written in functional programming languages like Clean and Haskell to closed λ-expressions by using the Scott-encoding for Algebraic Data Types instead of the more common Church encoding to obtain an encoding that is better comprehensible and also more efficient.
Typing Total Recursive Functions in Coq
- Computer ScienceITP
- 2017
A (relatively) short mechanized proof that Coq types any recursive function which is provably total in Coq, and an unbounded minimization scheme for decidable predicates that can be used to reify a whole category of undecidable predicate.
Efficient Self-Interpretations in lambda Calculus
- Computer ScienceJ. Funct. Program.
- 1992
This work gives a compact representation schema for λ-terms, and shows how this leads to an exceedingly small and elegant self-interpreter and self-reducer, and gives a constructive proof for the second fixed point theorem for the representation schema.
(Leftmost-Outermost) Beta Reduction is Invariant, Indeed
- MathematicsLog. Methods Comput. Sci.
- 2016
The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties, and the first complete positive answer to this long-standing problem.
A Sorted Semantic Framework for Applied Process Calculi
- Computer Science, MathematicsLog. Methods Comput. Sci.
- 2016
This work extends previous work on psi-calculi with novel abstract patterns and pattern matching, and adds sorts to the data term language, giving sufficient criteria for subject reduction to hold, and proves standard congruence and structural properties of bisimulation.
Functional computation as concurrent computation
- Computer SciencePOPL '96
- 1996
It is proved that call- by-need complexity is dominated by call-by-value complexity, and the concurrent call-By-need model incorporates mutual recursion and can be extended to cyclic data structures by means of constraints.