include Kernel.Reduction.ConvCheckerval are_convertible : Kernel.Reduction.convertibility_testare_convertible sg t1 t2 checks whether t1 and t2 are convertible or not in the signature sg.
val constraint_convertibility :
Kernel.Rule.constr ->
Kernel.Rule.rule_name ->
Kernel.Reduction.convertibility_testconstraint_convertibility cstr r sg [t1] [t2] checks wehther the [cstr] of the rule [r]
is satisfiable. Because constraints are checked once a term has matched the pattern,
satisfying a constraint comes back to check that two terms are convertible
val conversion_step :
Kernel.Signature.t ->
(Kernel.Term.term * Kernel.Term.term) ->
(Kernel.Term.term * Kernel.Term.term) list ->
(Kernel.Term.term * Kernel.Term.term) listconversion_step sg (l,r) lst returns a list lst' containing new convertibility obligations. Raise NotConvertible if the two terms are not convertible.
val reduction :
Kernel.Reduction.red_cfg ->
Kernel.Signature.t ->
Kernel.Term.term ->
Kernel.Term.termreduction cfg sg te reduces the term te following the configuration cfg and using the signature sg.
val whnf : Kernel.Signature.t -> Kernel.Term.term -> Kernel.Term.termwhnf sg t returns the Weak Head Normal Form of t.
Definition: a term is in weak-head-normal form if there is a reduction strategy such that all its reducts following this strategy (including itself) have the same 'shape' at the root.
The shape of a term could be computed like this:
let rec shape = function | Type -> Type | Kind -> Kind | Pi _ -> Pi | Lam _ -> Lam | DB (_,_,n) -> DB n | Const (_,m,v) -> Const m v | App(f,a0,args) -> App (shape f,List.length (a0::args))
Property: A (strongly normalizing) non weak-head-normal term can only have the form:
val snf : Kernel.Signature.t -> Kernel.Term.term -> Kernel.Term.termsng sg t returns the Strong Normal Form of t. This may loop whenever t is not strongly normalizing.