On proof theory with emphasis on natural deduction and sequent calculi:
Helmut Schwichtenberg, Constructive analysis with witnesses (2013) [pdf, pdf]
Helmut Schwichtenberg, Program Extraction in Constructive Analysis, in Logicism, Intuitionism, and Formalism, Synthese Library, 341 Springer (2009) [doi:10.1007/978-1-4020-8926-8_13]
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