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Call-by-name Forcing in Coq


This is a plugin for Coq v8.5 that implements the call-by-name forcing translation. The translation is described in this draft.


You need Coq v8.5 development files. The COQBIN environment variable should be pointing to the Coq binaries folder. Echoing make should be enough then.


The main features added by the plugin are the two following commands.

Forcing Translation

Forcing Translate foo using Obj Hom.

This translates the term foo in the forcing layer described by the Obj and Hom argument. Obj must have type Type and Hom must have type Obj -> Obj -> Type. The translation takes care of the Yoneda embedding so nothing more is expected. The translation currently works for global constants and inductive types.

All constants the term foo depends on must have been translated prior to the invocation of this command, otherwise it will fail.

Forcing Translate foo as id1 ... idn using Obj Hom.

Same as the above but allow to give a name to the translated constants. Without the provided name, the automatically generated constant is named fooᶠ. Note that the translation may generate several new constants, for instance in the inductive cases where in addition to the type, constructors are generated.

Forcing Implementation

Forcing Definition foo : type using Obj Hom.

This command starts the proof mode and let the user provide a term whose type is the forcing translation of type. When the proof is finished, an axiom foo is added to the environment and the term provided by the user is added as the forcing translation of foo.

Forcing Definition foo : type as id using Obj Hom.

Same as above but allows to give a name to the translated constant instead of the automatic fooᶠ.


A plugin for Coq that implements the call-by-name forcing translation



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