package dedukti

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module C : ConvChecker


include ConvChecker
val are_convertible : convertibility_test

are_convertible sg t1 t2 checks whether t1 and t2 are convertible or not in the signature sg.

val constraint_convertibility : Rule.constr -> Rule.rule_name -> convertibility_test

constraint_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 : Signature.t -> (Term.term * Term.term) -> (Term.term * Term.term) list -> (Term.term * Term.term) list

conversion_step sg (l,r) lst returns a list lst' containing new convertibility obligations. Raise NotConvertible if the two terms are not convertible.

val reduction : red_cfg -> Signature.t -> Term.term -> Term.term

reduction cfg sg te reduces the term te following the configuration cfg and using the signature sg.

whnf 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:

  • (x:A => b) a c_1..c_n, this is a beta-redex potentially with extra arguments.
  • or c a_1 .. a_n b_1 ..b_n with c a constant and c a'_1 .. a'_n is a gamma-redex where the (a'_i)s are reducts of (a_i)s.

sng sg t returns the Strong Normal Form of t. This may loop whenever t is not strongly normalizing.