Role of

 - replace
 - replace_lifting
 - replace_lifting_csc
clarified with comments. None of this function is the inverse of subst :-)

diff --git a/components/tactics/proofEngineReduction.ml b/components/tactics/proofEngineReduction.ml
index c359313dd1e87e1ec88d1ef8684c46d6e48e3098..dbc98f722313e250ed0327c427c2aaaaffa9b280 100644 (file)
--- a/components/tactics/proofEngineReduction.ml
+++ b/components/tactics/proofEngineReduction.ml
@@ -122,7 +122,11 @@ let alpha_equivalence =
 
 exception WhatAndWithWhatDoNotHaveTheSameLength;;
 
-(* "textual" replacement of several subterms with other ones *)
+(* Replaces "textually" in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE NOT lifted when binders are
+   crossed. The terms in "with_what" ARE NOT lifted when binders are crossed.
+   Every free variable in "where" IS NOT lifted by nnn.
+*)
 let replace ~equality ~what ~with_what ~where =
   let find_image t =
    let rec find_image_aux =
@@ -182,8 +186,13 @@ let replace ~equality ~what ~with_what ~where =
     aux where
 ;;
 
-(* replaces in a term a term with another one. *)
-(* Lifting are performed as usual.             *)
+(* Replaces in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE lifted when binders are
+   crossed. The terms in "with_what" ARE lifted when binders are crossed.
+   Every free variable in "where" IS NOT lifted by nnn.
+   Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
+   inverse of subst up to the fact that free variables in "where" are NOT
+   lifted.  *)
 let replace_lifting ~equality ~what ~with_what ~where =
   let find_image what t =
    let rec find_image_aux =
@@ -278,8 +287,12 @@ let replace_lifting ~equality ~what ~with_what ~where =
   substaux 1 what where
 ;;
 
-(* replaces in a term a list of terms with other ones. *)
-(* Lifting are performed as usual.                     *)
+(* Replaces in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE NOT lifted when binders are
+   crossed. The terms in "with_what" ARE lifted when binders are crossed.
+   Every free variable in "where" IS lifted by nnn.
+   Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
+   inverse of subst up to the fact that "what" terms are NOT lifted. *)
 let replace_lifting_csc nnn ~equality ~what ~with_what ~where =
   let find_image t =
    let rec find_image_aux =

diff --git a/components/tactics/proofEngineReduction.mli b/components/tactics/proofEngineReduction.mli
index c0318bdfeb53be8562604f7595fabc77f8d136f5..39beb84aa8d8fc55913989f2a97a475ba07f563e 100644 (file)
--- a/components/tactics/proofEngineReduction.mli
+++ b/components/tactics/proofEngineReduction.mli
@@ -35,15 +35,36 @@ exception AlreadySimplified
 exception WhatAndWithWhatDoNotHaveTheSameLength;;
 
 val alpha_equivalence: Cic.term -> Cic.term -> bool
+
+(* Replaces "textually" in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE NOT lifted when binders are
+   crossed. The terms in "with_what" ARE NOT lifted when binders are crossed.
+   Every free variable in "where" IS NOT lifted by nnn. *)
 val replace :
   equality:('a -> Cic.term -> bool) ->
   what:'a list -> with_what:Cic.term list -> where:Cic.term -> Cic.term
+
+(* Replaces in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE lifted when binders are
+   crossed. The terms in "with_what" ARE lifted when binders are crossed.
+   Every free variable in "where" IS NOT lifted by nnn.
+   Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
+   inverse of subst up to the fact that free variables in "where" are NOT
+   lifted. *)
 val replace_lifting :
   equality:(Cic.term -> Cic.term -> bool) ->
   what:Cic.term list -> with_what:Cic.term list -> where:Cic.term -> Cic.term
+
+(* Replaces in "where" every term in "what" with the corresponding
+   term in "with_what". The terms in "what" ARE NOT lifted when binders are
+   crossed. The terms in "with_what" ARE lifted when binders are crossed.
+   Every free variable in "where" IS lifted by nnn.
+   Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the
+   inverse of subst up to the fact that "what" terms are NOT lifted. *)
 val replace_lifting_csc :
   int -> equality:(Cic.term -> Cic.term -> bool) ->
   what:Cic.term list -> with_what:Cic.term list -> where:Cic.term -> Cic.term
+
 val subst_inv :
   equality:(Cic.term -> Cic.term -> bool) ->
   what:Cic.term list -> int -> Cic.term -> Cic.term