# Normalization for fitch-style modal calculi

@article{Valliappan2022NormalizationFF, title={Normalization for fitch-style modal calculi}, author={Nachiappan Valliappan and Fabian Ruch and Carlos Tom{\'e} Corti{\~n}as}, journal={Proceedings of the ACM on Programming Languages}, year={2022}, volume={6}, pages={772 - 798} }

Fitch-style modal lambda calculi enable programming with necessity modalities in a typed lambda calculus by extending the typing context with a delimiting operator that is denoted by a lock. The addition of locks simplifies the formulation of typing rules for calculi that incorporate different modal axioms, but each variant demands different, tedious and seemingly ad hoc syntactic lemmas to prove normalization. In this work, we take a semantic approach to normalization, called normalization by…

## References

SHOWING 1-10 OF 42 REFERENCES

### Fitch-Style Modal Lambda Calculi

- PhilosophyFoSSaCS
- 2018

It is shown that Fitch-style modal deduction calculi have good computational properties for a variety of intuitionistic modal logics, and can be extended a la tense logic with the left adjoint of necessity, and are then complete for the categorical semantics.

### Recovering purity with comonads and capabilities

- Computer ScienceProc. ACM Program. Lang.
- 2020

This model formalises the intuition common to systems programmers that the ability to perform effects should be controlled via access to a permission or capability, and that a program is capability-safe if it performs no effects that it does not have a runtime capability for.

### Normalization by Evaluation for the Computational Lambda-Calculus

- Computer ScienceTLCA
- 2001

A suitable residualizing interpretation of base types, constants, and computational effects allows us to extract a syntactic normal form from a term's denotation, leading directly to a practical normalization algorithm.

### Typed Lambda Calculi and Applications

- Computer ScienceLecture Notes in Computer Science
- 2013

It is argued that thinking of non-linearity as the “limit” of linearity gives an interesting point of view on well-known properties of the Lambdacalculus and its relationship to computational complexity (through lambda-calculi whose normalization is time-bounded).

### Normalization by Evaluation for Call-By-Push-Value and Polarized Lambda Calculus

- Computer SciencePPDP
- 2019

We observe that normalization by evaluation for simply-typed lambda-calculus with weak coproducts can be carried out in a weak bi-cartesian closed category of presheaves equipped with a monad that…

### Dual-context calculi for modal logic

- Computer Science2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2017

The resulting systems are dual-context systems, in the style pioneered by Girard, Barber, Plotkin, Pfenning, Davies, and others, that derive natural deduction systems for the necessity fragment of various constructive modal logics by exploiting a pattern found in sequent calculi.

### A Formalised Proof of the Soundness and Completeness of a Simply Typed Lambda-Calculus with Explicit Substitutions

- Mathematics, Computer ScienceHigh. Order Symb. Comput.
- 2002

A simply-typed λ-calculus with explicit substitutions is presented and a fully formalised proof of its soundness and completeness with respect to Kripke models is given.

### Normalization by evaluation for typed lambda calculus with coproducts

- MathematicsProceedings 16th Annual IEEE Symposium on Logic in Computer Science
- 2001

This method is based on the semantic technique known as "normalization by evaluation", and involves inverting the interpretation of the syntax in a suitable sheaf model and extracting an appropriate unique normal form from this.

### An inverse of the evaluation functional for typed lambda -calculus

- Mathematics[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
- 1991

A functional p to e (procedure to expression) that inverts the evaluation functional for typed lambda -terms in any model of typedlambda -calculus containing some basic arithmetic is defined and is used to normalize (the lambda -representations of) natural deduction proofs of (higher order) arithmetic.

### Semantics for a Class of Intuitionistic Modal Calculi

- Philosophy
- 1980

A general criterion is proposed which enables us to define a rather large number of intuitionistic modal calculi and the idea that lies behind this criterion is that of presenting a uniform rule by means of which the authors can find the ‘intuitionistic analogues’ for some of the most usual classical modal systems.