lambdapi 2.0.0 · OCaml Package

Evaluation and conversion.

Preliminary remarks. We define the head-structure of a term t as:

λx:_,h if t=λx:a,u and h is the head-structure of u
Π if t=Πx:a,u
h _ if t=uv and h is the head-structure of u
? if t=?Mt1,..,tn (and ?M is not instantiated)
t itself otherwise (TYPE, KIND, x, f)

A term t is in head-normal form (hnf) if its head-structure is invariant by reduction.

A term t is in weak head-normal form (whnf) if it is an abstration or if it is in hnf. In particular, a term in head-normal form is in weak head-normal form.

A term t is in strong normal form (snf) if it cannot be reduced further.

val eta_equality : bool Timed.ref

Flag indicating whether eta-reduction should be used or not.

type stack = Term.term list

Abstract machine stack.

val tree_walk : 
  Term.problem ->
  Term.ctxt ->
  Term.dtree ->
  stack ->
  (Term.term * stack) option

tree_walk p tr ctx stk tries to apply a rewrite rule by matching the stack stk against the decision tree tr in context ctx. The resulting state of the abstract machine is returned in case of success. Even if matching fails, the stack stk may be imperatively updated since a reduction step taken in elements of the stack is preserved (this is done using TRef). Fresh metavariables generated by unification rules with extra pattern variables are added in p.

val whnf : ?rewrite:bool -> Term.ctxt -> Term.term -> Term.term

whnf ~rewrite c t computes a whnf of the term t in context c. User-defined rewrite rules are used only if ~rewrite = true.

val eq_modulo : Term.ctxt -> Term.term -> Term.term -> bool

eq_modulo c a b tests the convertibility of a and b in context c. WARNING: may have side effects in TRef's introduced by whnf.

val pure_eq_modulo : Term.ctxt -> Term.term -> Term.term -> bool

pure_eq_modulo c a b tests the convertibility of a and b in context c with no side effects.

val snf : Term.ctxt -> Term.term -> Term.term

snf c t computes the strong normal form of the term t in the context c. It unfolds variables defined in the context c.

val hnf : Term.ctxt -> Term.term -> Term.term

hnf t computes a head-normal form of the term t wrt beta-reduction, user-defined rewrite rules and variables defined in the context c.

val simplify : Term.term -> Term.term

simplify t computes a beta whnf of t belonging to the set S such that:

terms of S are in beta whnf normal format
if t is a product, then both its domain and codomain are in S.

val unfold_sym : Term.sym -> Term.term -> Term.term

If s is a non-opaque symbol having a definition, unfold_sym s t replaces in t all the occurrences of s by its definition.

type strategy =

| WHNF
(*
Reduce to weak head-normal form.
*)
| HNF
(*
Reduce to head-normal form.
*)
| SNF
(*
Reduce to strong normal form.
*)
| NONE
(*
Do nothing.
*)

Dedukti evaluation strategies.

type strat = {

strategy : strategy;
(*
Evaluation strategy.
*)
steps : int option;
(*
Max number of steps if given.
*)

}

val eval : strat -> Term.ctxt -> Term.term -> Term.term

eval s c t evaluates the term t in the context c according to strategy s.

package lambdapi