An Algol-like language is a language that is based on ALGOL 60.
There is disagreement on what the "essence" of ALGOL 60 is. However, the currently prevailing view is that Algol-like languages are characterised by the following features:
This view was put forward by John Reynolds in an invited address to a symposium in tribute to Adriaan van Wijngaarden (1981). It survives in a manuscript known as "The Essence of ALGOL," which is reprinted in [O'Hearn and Tennent 1997]. Reynolds also introduced the Idealized Algol language in the same paper.
There are many reasons for which one might be interested in Algol-like languages. Sir Tony Hoare [Hoare 1974] said that ALGOL 60 was
a language so far ahead of its time that it was not only an improvement on its predecessors but also on nearly all its successors
Otherwise, there are multiple foundational reasons to consider Algol-like languages. In the words of O'Hearn and Tennent in the preface of their 1997 volumes:
In recent years there has been a remarkable convergence of interest in programming languages based on ALGOL 60. Researchers interested in the theory of procedural and object-oriented languages discovered that ALGOL 60 shows how to add procedures and object classes to simple imperative languages in a general and clean way. And, on the other hand, researchers interested in purely functional languages discovered that ALGOL 60 shows how to add imperative mechanisms to functional languages in a way that does not compromise their desirable properties.
Reynolds, John C. 1981. ‘The Essence of ALGOL’. In Algorithmic Languages: Proceedings of the International Symposium on Algorithmic Languages, edited by J. W. de Bakker and J. C. van Vliet, 345–72. Amsterdam: North-Holland.
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address = {Amsterdam},
title = {The {Essence} of {ALGOL}},
booktitle = {Algorithmic {Languages}: {Proceedings} of the {International} {Symposium} on {Algorithmic} {Languages}},
publisher = {North-Holland},
author = {Reynolds, John C.},
editor = {de Bakker, J. W. and van Vliet, J. C.},
year = {1981},
pages = {345--372},
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O’Hearn, Peter W., and Robert D. Tennent, eds. 1997. Algol-like Languages. Vol. 1. Boston, MA: Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4118-8.
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address = {Boston, MA},
title = {Algol-like {Languages}},
volume = {1},
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year = {1997},
doi = {10.1007/978-1-4612-4118-8}
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O’Hearn, Peter W., and Robert D. Tennent, eds. 1997. Algol-like Languages. Vol. 2. Boston, MA: Birkhäuser Boston. https://doi.org/10.1007/978-1-4757-3851-3.
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address = {Boston, MA},
title = {Algol-like {Languages}},
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publisher = {Birkhäuser Boston},
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year = {1997},
doi = {10.1007/978-1-4757-3851-3}
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