Description

If there are nothing except blanks, newline characters between PAT₁ and PAT₂, reduces them to just one newline character.

Raw Input		Desired Output
=== PAT1 PAT2 === PAT 1 ... ... PAT 2 === PAT1 PAT2 === PAT1 ... ... ... PAT2 --- PAT1 PAT2 ---		=== PAT1 PAT2 === PAT 1 ... ... PAT 2 === PAT1 PAT2 === PAT1 ... ... ... PAT2 --- PAT1 PAT2 ---

Script and Comments

Script₁ [ 1] :top [ 2] /PAT1/!b [ 3] :loop [ 4] $q [ 5] N [ 6] /\n $/b loop [ 7] /\n PAT2[^\n]$/b matched [ 8] h [ 9] s/\n[^\n]$//p [10] x [11] s/^.\n// [12] b top [13] :matched [14] s/PAT1( \n )PAT2/PAT1\nPAT2/ [15] P [16] D
Comments -r If a line does not end with PAT₁ with optional trailing blanks, Step [2] prints it and then starts a new cycle. Otherwise, Step [5] appends the next line to PS. If the line appended by Step [5] is an empty one or consisting of only blanks, then sed jumps back to Step [3] to append the next line. a line begins with PAT₂ with optional leading blanks, then PS contains what we want to reduce; therefore, sed jumps to Step [13]. otherwise, there is nothing to reduce in PS up to the PAT₂ found. Note that there may be another PAT₁ behind it. So we use steps [8] thru [12] to: print all but the last line of PS, delete all but the last line, and then make jumps back to Step [1] to treat the last line of PS the same as a line read by a new cycle. Step [14] reduces the blanks and the empty lines between PAT₁ and PAT₂. Since there may exist another PAT₁ after the PAT₂ found, so we have to treat the last line of PS the same as a line read by a new cycle via Steps [14] and [15].
Script₂ [ 1] /PAT1/!b [ 2] :loop [ 3] $q [ 4] N [ 5] /\n $/b loop [ 6] /\n PAT2[^\n]$/b matched [ 7] h [ 8] s/\n[^\n]$//p [ 9] x [10] s/^.\n/\n/ [11] D [12] :matched [13] s/PAT1( \n )PAT2/PAT1\nPAT2/ [14] P [15] D	Comments The label :topof Script₁ is only referenced by Step [12]. This script removes it by replacing Steps [11] and [12] with Steps [10] and [11].