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Abstract / Description of output
One of the leading textbooks for formal methods is Software Foundations (SF), written by Benjamin Pierce in collaboration with others, and based onCoq. After five years using SF in the classroom, we came to the conclusion that Coq is not the best vehicle for this purpose, as too much of the course needs to focus on learning tactics for proof derivation, to the cost of learning programming language theory. Accordingly, we have written a new textbook, Programming Language Foundations in Agda (PLFA). PLFA covers much of the same ground as SF, although it is not a slavish imitation.
What did we learn from writing PLFA? First, that it is possible. One might expect that without proof tactics that the proofs become too long, but in fact proofs in PLFA are about the same length as those in SF. Proofs in Coq require an interactive environment to be understood, while proofs in Agda can be read on the page. Second, that constructive proofs of preservation and progress give immediate rise to a prototype evaluator. This fact is obvious in retrospect but it is not exploited in SF (which instead provides a separate normalise tactic) nor can we find it in the literature. Third, that using extrinsicallytyped terms is far less perspicuous than using intrinsicallytyped terms. SF uses the former presentation, while PLFA presents both; the former uses about 1.6 as many lines of Agda code as the latter, roughly the golden ratio.
The textbook is written as a literate Agda script, and can be found here: http://plfa.inf.ed.ac.uk
What did we learn from writing PLFA? First, that it is possible. One might expect that without proof tactics that the proofs become too long, but in fact proofs in PLFA are about the same length as those in SF. Proofs in Coq require an interactive environment to be understood, while proofs in Agda can be read on the page. Second, that constructive proofs of preservation and progress give immediate rise to a prototype evaluator. This fact is obvious in retrospect but it is not exploited in SF (which instead provides a separate normalise tactic) nor can we find it in the literature. Third, that using extrinsicallytyped terms is far less perspicuous than using intrinsicallytyped terms. SF uses the former presentation, while PLFA presents both; the former uses about 1.6 as many lines of Agda code as the latter, roughly the golden ratio.
The textbook is written as a literate Agda script, and can be found here: http://plfa.inf.ed.ac.uk
Original language  English 

Article number  102440 
Pages (fromto)  115 
Number of pages  15 
Journal  Science of Computer Programming 
Volume  194 
Early online date  24 Mar 2020 
DOIs  
Publication status  Published  1 Aug 2020 
Keywords / Materials (for Nontextual outputs)
 Agda
 Coq
 lambda calculus
 dependent types
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 1 Finished

From Data Types to Session Types  A Basis for Concurrency and Distribution
20/05/13 → 19/11/20
Project: Research