Writting grammar in prolog and can't get it to work correctly

Question

This is for a class assignment, but I can't figure out how to fix my problem. I wrote the following:

sentence(S0, S):- f(S0,S); t(S0, S1),n(S1, S2),t(S2, S).
f(S0, S):- termIf(S0, S1), pLeft(S1, S2), b(S2, S3), pRight(S3, S4), termThen(S4, S5), termBegin(S5, S6),sentence(S6, S7), termEnd(S7, S); termIf(S0, S1), pLeft(S1, S2), b(S2, S3), pRight(S3, S4), termThen(S4, S5),termBegin(S5, S6),sentence(S6, S7), termElse(S7, S8), sentence(S8, S9), termEnd(S9, S).
b(S0, S):- t(S0, S1), e(S1, S2), t(S2, S). 
termIf(S0, S) :- S0=[if|S].
termThen(S0, S):- S0=[then|S].
termBegin(S0, S):- S0=[begin|S].
termEnd(S0, S):- S0=[end|S].
termElse(S0, S):- S0=[else|S].
pLeft(S0, S):- S0=['('|S].
pRight(S0, S):- S0=[')'|S].
t(S0, S):- S0=[x|S].
t(S0, S):- S0=[y|S].
t(S0, S):- S0=[z|S].
t(S0, S):- S0=[1|S].
t(S0, S):- S0=[0|S].
e(S0, S):- S0=[>|S].
e(S0, S):- S0=[<|S].
n(S0, S):- S0=[+|S].
n(S0, S):- S0=[-|S].
n(S0, S):- S0=[=|S].

And I did a trace:

[trace] [5]  ?- sentence([if,'(', x, >, 0,')', then, begin, [x, =, 1], end], X).
   Call: (89) sentence([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
   Call: (90) f([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
   Call: (91) termIf([if, '(', x, >, 0, ')', then, begin|...], _67166) ? creep
   Call: (92) [if, '(', x, >, 0, ')', then, begin|...]=[if|_67158] ? creep
   Exit: (92) [if, '(', x, >, 0, ')', then, begin|...]=[if, '(', x, >, 0, ')', then, begin|...] ? creep
   Exit: (91) termIf([if, '(', x, >, 0, ')', then, begin|...], ['(', x, >, 0, ')', then, begin, [...|...]|...]) ? creep
   Call: (91) pLeft(['(', x, >, 0, ')', then, begin, [...|...]|...], _67348) ? creep
   Call: (92) ['(', x, >, 0, ')', then, begin, [...|...]|...]=['('|_67340] ? creep
   Exit: (92) ['(', x, >, 0, ')', then, begin, [...|...]|...]=['(', x, >, 0, ')', then, begin, [...|...]|...] ? creep
   Exit: (91) pLeft(['(', x, >, 0, ')', then, begin, [...|...]|...], [x, >, 0, ')', then, begin, [x|...], end]) ? creep
   Call: (91) b([x, >, 0, ')', then, begin, [x|...], end], _67530) ? creep
   Call: (92) t([x, >, 0, ')', then, begin, [x|...], end], _67574) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[x|_67566] ? creep
   Exit: (93) [x, >, 0, ')', then, begin, [x|...], end]=[x, >, 0, ')', then, begin, [x|...], end] ? creep
   Exit: (92) t([x, >, 0, ')', then, begin, [x|...], end], [>, 0, ')', then, begin, [x, =|...], end]) ? creep
   Call: (92) e([>, 0, ')', then, begin, [x, =|...], end], _67756) ? creep
   Call: (93) [>, 0, ')', then, begin, [x, =|...], end]=[>|_67748] ? creep
   Exit: (93) [>, 0, ')', then, begin, [x, =|...], end]=[>, 0, ')', then, begin, [x, =|...], end] ? creep
   Exit: (92) e([>, 0, ')', then, begin, [x, =|...], end], [0, ')', then, begin, [x, =, 1], end]) ? creep
   Call: (92) t([0, ')', then, begin, [x, =, 1], end], _67938) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[x|_67930] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[x|_67930] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _68076) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[y|_68068] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[y|_68068] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _68214) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[z|_68206] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[z|_68206] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _68352) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[1|_68344] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[1|_68344] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _68490) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[0|_68482] ? creep
   Exit: (93) [0, ')', then, begin, [x, =, 1], end]=[0, ')', then, begin, [x, =, 1], end] ? creep
   Exit: (92) t([0, ')', then, begin, [x, =, 1], end], [')', then, begin, [x, =, 1], end]) ? creep
   Exit: (91) b([x, >, 0, ')', then, begin, [x|...], end], [')', then, begin, [x, =, 1], end]) ? creep
   Call: (91) pRight([')', then, begin, [x, =, 1], end], _68716) ? creep
   Call: (92) [')', then, begin, [x, =, 1], end]=[')'|_68708] ? creep
   Exit: (92) [')', then, begin, [x, =, 1], end]=[')', then, begin, [x, =, 1], end] ? creep
   Exit: (91) pRight([')', then, begin, [x, =, 1], end], [then, begin, [x, =, 1], end]) ? creep
   Call: (91) termThen([then, begin, [x, =, 1], end], _68898) ? creep
   Call: (92) [then, begin, [x, =, 1], end]=[then|_68890] ? creep
   Exit: (92) [then, begin, [x, =, 1], end]=[then, begin, [x, =, 1], end] ? creep
   Exit: (91) termThen([then, begin, [x, =, 1], end], [begin, [x, =, 1], end]) ? creep
   Call: (91) termBegin([begin, [x, =, 1], end], _69080) ? creep
   Call: (92) [begin, [x, =, 1], end]=[begin|_69072] ? creep
   Exit: (92) [begin, [x, =, 1], end]=[begin, [x, =, 1], end] ? creep
   Exit: (91) termBegin([begin, [x, =, 1], end], [[x, =, 1], end]) ? creep
   Call: (91) sentence([[x, =, 1], end], _69262) ? creep
   Call: (92) f([[x, =, 1], end], _69306) ? creep
   Call: (93) termIf([[x, =, 1], end], _69350) ? creep
   Call: (94) [[x, =, 1], end]=[if|_69342] ? creep
   Fail: (94) [[x, =, 1], end]=[if|_69342] ? creep
   Fail: (93) termIf([[x, =, 1], end], _69488) ? creep
   Redo: (92) f([[x, =, 1], end], _69532) ? creep
   Call: (93) termIf([[x, =, 1], end], _69576) ? creep
   Call: (94) [[x, =, 1], end]=[if|_69568] ? creep
   Fail: (94) [[x, =, 1], end]=[if|_69568] ? creep
   Fail: (93) termIf([[x, =, 1], end], _69714) ? creep
   Fail: (92) f([[x, =, 1], end], _69758) ? creep
   Redo: (91) sentence([[x, =, 1], end], _69802) ? creep
   Call: (92) t([[x, =, 1], end], _69846) ? creep
   Call: (93) [[x, =, 1], end]=[x|_69838] ? creep
   Fail: (93) [[x, =, 1], end]=[x|_69838] ? creep
   Redo: (92) t([[x, =, 1], end], _69984) ? creep
   Call: (93) [[x, =, 1], end]=[y|_69976] ? creep
   Fail: (93) [[x, =, 1], end]=[y|_69976] ? creep
   Redo: (92) t([[x, =, 1], end], _70122) ? creep
   Call: (93) [[x, =, 1], end]=[z|_70114] ? creep
   Fail: (93) [[x, =, 1], end]=[z|_70114] ? creep
   Redo: (92) t([[x, =, 1], end], _70260) ? creep
 Call: (93) [[x, =, 1], end]=[1|_70252] ? creep
   Fail: (93) [[x, =, 1], end]=[1|_70252] ? creep
   Redo: (92) t([[x, =, 1], end], _70398) ? creep
   Call: (93) [[x, =, 1], end]=[0|_70390] ? creep
   Fail: (93) [[x, =, 1], end]=[0|_70390] ? creep
   Fail: (92) t([[x, =, 1], end], _70536) ? creep
   Fail: (91) sentence([[x, =, 1], end], _70580) ? creep
   Redo: (92) e([>, 0, ')', then, begin, [x, =|...], end], _70624) ? creep
   Call: (93) [>, 0, ')', then, begin, [x, =|...], end]=[<|_70616] ? creep
   Fail: (93) [>, 0, ')', then, begin, [x, =|...], end]=[<|_70616] ? creep
   Fail: (92) e([>, 0, ')', then, begin, [x, =|...], end], _70762) ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _70806) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[y|_70798] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[y|_70798] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _70944) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[z|_70936] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[z|_70936] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _71082) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[1|_71074] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[1|_71074] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _71220) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[0|_71212] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[0|_71212] ? creep
   Fail: (92) t([x, >, 0, ')', then, begin, [x|...], end], _71358) ? creep
   Fail: (91) b([x, >, 0, ')', then, begin, [x|...], end], _71402) ? creep
   Redo: (90) f([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
   Call: (91) termIf([if, '(', x, >, 0, ')', then, begin|...], _71490) ? creep
   Call: (92) [if, '(', x, >, 0, ')', then, begin|...]=[if|_71482] ? creep
   Exit: (92) [if, '(', x, >, 0, ')', then, begin|...]=[if, '(', x, >, 0, ')', then, begin|...] ? creep
   Exit: (91) termIf([if, '(', x, >, 0, ')', then, begin|...], ['(', x, >, 0, ')', then, begin, [...|...]|...]) ? creep
   Call: (91) pLeft(['(', x, >, 0, ')', then, begin, [...|...]|...], _71672) ? creep
   Call: (92) ['(', x, >, 0, ')', then, begin, [...|...]|...]=['('|_71664] ? creep
   Exit: (92) ['(', x, >, 0, ')', then, begin, [...|...]|...]=['(', x, >, 0, ')', then, begin, [...|...]|...] ? creep
   Exit: (91) pLeft(['(', x, >, 0, ')', then, begin, [...|...]|...], [x, >, 0, ')', then, begin, [x|...], end]) ? creep
   Call: (91) b([x, >, 0, ')', then, begin, [x|...], end], _71854) ? creep
   Call: (92) t([x, >, 0, ')', then, begin, [x|...], end], _71898) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[x|_71890] ? creep
   Exit: (93) [x, >, 0, ')', then, begin, [x|...], end]=[x, >, 0, ')', then, begin, [x|...], end] ? creep
   Exit: (92) t([x, >, 0, ')', then, begin, [x|...], end], [>, 0, ')', then, begin, [x, =|...], end]) ? creep
   Call: (92) e([>, 0, ')', then, begin, [x, =|...], end], _72080) ? creep
   Call: (93) [>, 0, ')', then, begin, [x, =|...], end]=[>|_72072] ? creep
   Exit: (93) [>, 0, ')', then, begin, [x, =|...], end]=[>, 0, ')', then, begin, [x, =|...], end] ? creep
   Exit: (92) e([>, 0, ')', then, begin, [x, =|...], end], [0, ')', then, begin, [x, =, 1], end]) ? creep
   Call: (92) t([0, ')', then, begin, [x, =, 1], end], _72262) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[x|_72254] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[x|_72254] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _72400) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[y|_72392] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[y|_72392] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _72538) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[z|_72530] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[z|_72530] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _72676) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[1|_72668] ? creep
   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[1|_72668] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _72814) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[0|_72806] ? creep
   Exit: (93) [0, ')', then, begin, [x, =, 1], end]=[0, ')', then, begin, [x, =, 1], end] ? creep
   Exit: (92) t([0, ')', then, begin, [x, =, 1], end], [')', then, begin, [x, =, 1], end]) ? creep
   Exit: (91) b([x, >, 0, ')', then, begin, [x|...], end], [')', then, begin, [x, =, 1], end]) ? creep
   Call: (91) pRight([')', then, begin, [x, =, 1], end], _73040) ? creep
   Call: (92) [')', then, begin, [x, =, 1], end]=[')'|_73032] ? creep
   Exit: (92) [')', then, begin, [x, =, 1], end]=[')', then, begin, [x, =, 1], end] ? creep
   Exit: (91) pRight([')', then, begin, [x, =, 1], end], [then, begin, [x, =, 1], end]) ? creep
   Call: (91) termThen([then, begin, [x, =, 1], end], _73222) ? creep
   Call: (92) [then, begin, [x, =, 1], end]=[then|_73214] ? creep
   Exit: (92) [then, begin, [x, =, 1], end]=[then, begin, [x, =, 1], end] ? creep
   Exit: (91) termThen([then, begin, [x, =, 1], end], [begin, [x, =, 1], end]) ? creep
   Call: (91) termBegin([begin, [x, =, 1], end], _73404) ? creep
   Call: (92) [begin, [x, =, 1], end]=[begin|_73396] ? creep
   Exit: (92) [begin, [x, =, 1], end]=[begin, [x, =, 1], end] ? creep
   Exit: (91) termBegin([begin, [x, =, 1], end], [[x, =, 1], end]) ? creep
   Call: (91) sentence([[x, =, 1], end], _73586) ? creep
   Call: (92) f([[x, =, 1], end], _73630)
Ԁ   Fail: (93) [0, ')', then, begin, [x, =, 1], end]=[1|_72668] ? creep
   Redo: (92) t([0, ')', then, begin, [x, =, 1], end], _72814) ? creep
   Call: (93) [0, ')', then, begin, [x, =, 1], end]=[0|_72806] ? creep
   Exit: (93) [0, ')', then, begin, [x, =, 1], end]=[0, ')', then, begin, [x, =, 1], end] ? creep
   Exit: (92) t([0, ')', then, begin, [x, =, 1], end], [')', then, begin, [x, =, 1], end]) ? creep
   Exit: (91) b([x, >, 0, ')', then, begin, [x|...], end], [')', then, begin, [x, =, 1], end]) ? creep
   Call: (91) pRight([')', then, begin, [x, =, 1], end], _73040) ? creep
   Call: (92) [')', then, begin, [x, =, 1], end]=[')'|_73032] ? creep
   Exit: (92) [')', then, begin, [x, =, 1], end]=[')', then, begin, [x, =, 1], end] ? creep
   Exit: (91) pRight([')', then, begin, [x, =, 1], end], [then, begin, [x, =, 1], end]) ? creep
   Call: (91) termThen([then, begin, [x, =, 1], end], _73222) ? creep
   Call: (92) [then, begin, [x, =, 1], end]=[then|_73214] ? creep
   Exit: (92) [then, begin, [x, =, 1], end]=[then, begin, [x, =, 1], end] ? creep
   Exit: (91) termThen([then, begin, [x, =, 1], end], [begin, [x, =, 1], end]) ? creep
   Call: (91) termBegin([begin, [x, =, 1], end], _73404) ? creep
   Call: (92) [begin, [x, =, 1], end]=[begin|_73396] ? creep
   Exit: (92) [begin, [x, =, 1], end]=[begin, [x, =, 1], end] ? creep
   Exit: (91) termBegin([begin, [x, =, 1], end], [[x, =, 1], end]) ? creep
   Call: (91) sentence([[x, =, 1], end], _73586) ? creep
   Call: (92) f([[x, =, 1], end], _73630) ? creep
   Call: (93) termIf([[x, =, 1], end], _73674) ? creep
   Call: (94) [[x, =, 1], end]=[if|_73666] ? creep
   Fail: (94) [[x, =, 1], end]=[if|_73666] ? creep
   Fail: (93) termIf([[x, =, 1], end], _73812) ? creep
   Redo: (92) f([[x, =, 1], end], _73856) ? creep
   Call: (93) termIf([[x, =, 1], end], _73900) ? creep
   Call: (94) [[x, =, 1], end]=[if|_73892] ? creep
   Fail: (94) [[x, =, 1], end]=[if|_73892] ? creep
   Fail: (93) termIf([[x, =, 1], end], _74038) ? creep
   Fail: (92) f([[x, =, 1], end], _74082) ? creep
   Redo: (91) sentence([[x, =, 1], end], _74126) ? creep
   Call: (92) t([[x, =, 1], end], _74170) ? creep
   Call: (93) [[x, =, 1], end]=[x|_74162] ? creep
   Fail: (93) [[x, =, 1], end]=[x|_74162] ? creep
   Redo: (92) t([[x, =, 1], end], _74308) ? creep
   Call: (93) [[x, =, 1], end]=[y|_74300] ? creep
   Fail: (93) [[x, =, 1], end]=[y|_74300] ? creep
   Redo: (92) t([[x, =, 1], end], _74446) ? creep
   Call: (93) [[x, =, 1], end]=[z|_74438] ? creep
   Fail: (93) [[x, =, 1], end]=[z|_74438] ? creep
   Redo: (92) t([[x, =, 1], end], _74584) ? creep
   Call: (93) [[x, =, 1], end]=[1|_74576] ? creep
   Fail: (93) [[x, =, 1], end]=[1|_74576] ? creep
   Redo: (92) t([[x, =, 1], end], _74722) ? creep
   Call: (93) [[x, =, 1], end]=[0|_74714] ? creep
   Fail: (93) [[x, =, 1], end]=[0|_74714] ? creep
   Fail: (92) t([[x, =, 1], end], _74860) ? creep
   Fail: (91) sentence([[x, =, 1], end], _74904) ? creep
   Redo: (92) e([>, 0, ')', then, begin, [x, =|...], end], _74948) ? creep
   Call: (93) [>, 0, ')', then, begin, [x, =|...], end]=[<|_74940] ? creep
   Fail: (93) [>, 0, ')', then, begin, [x, =|...], end]=[<|_74940] ? creep
   Fail: (92) e([>, 0, ')', then, begin, [x, =|...], end], _75086) ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _75130) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[y|_75122] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[y|_75122] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _75268) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[z|_75260] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[z|_75260] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _75406) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[1|_75398] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[1|_75398] ? creep
   Redo: (92) t([x, >, 0, ')', then, begin, [x|...], end], _75544) ? creep
   Call: (93) [x, >, 0, ')', then, begin, [x|...], end]=[0|_75536] ? creep
   Fail: (93) [x, >, 0, ')', then, begin, [x|...], end]=[0|_75536] ? creep
   Fail: (92) t([x, >, 0, ')', then, begin, [x|...], end], _75682) ? creep
   Fail: (91) b([x, >, 0, ')', then, begin, [x|...], end], _75726) ? creep
   Fail: (90) f([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
   Redo: (89) sentence([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
   Call: (90) t([if, '(', x, >, 0, ')', then, begin|...], _75858) ? creep
   Call: (91) [if, '(', x, >, 0, ')', then, begin|...]=[x|_75850] ? creep
   Fail: (91) [if, '(', x, >, 0, ')', then, begin|...]=[x|_75850] ? creep
   Redo: (90) t([if, '(', x, >, 0, ')', then, begin|...], _75996) ? creep
   Call: (91) [if, '(', x, >, 0, ')', then, begin|...]=[y|_75988] ? creep
   Fail: (91) [if, '(', x, >, 0, ')', then, begin|...]=[y|_75988] ? creep
   Redo: (90) t([if, '(', x, >, 0, ')', then, begin|...], _76134) ? creep
   Call: (91) [if, '(', x, >, 0, ')', then, begin|...]=[z|_76126]  
 Fail: (91) [if, '(', x, >, 0, ')', then, begin|...]=[z|_76126] ? creep
   Redo: (90) t([if, '(', x, >, 0, ')', then, begin|...], _76272) ? creep
   Call: (91) [if, '(', x, >, 0, ')', then, begin|...]=[1|_76264] ? creep
   Fail: (91) [if, '(', x, >, 0, ')', then, begin|...]=[1|_76264] ? creep
   Redo: (90) t([if, '(', x, >, 0, ')', then, begin|...], _76410) ? creep
   Call: (91) [if, '(', x, >, 0, ')', then, begin|...]=[0|_76402] ? creep
   Fail: (91) [if, '(', x, >, 0, ')', then, begin|...]=[0|_76402] ? creep
   Fail: (90) t([if, '(', x, >, 0, ')', then, begin|...], _76548) ? creep
   Fail: (89) sentence([if, '(', x, >, 0, ')', then, begin|...], _66584) ? creep
false

I think it is obviously failing when sentence is called but it is getting a [[x, =, 1], end] which it can't handle. I think the obvious answer is that [x, =, 1] is a first element of a list, but I can't figure out how to just pass that element to sentence so it will handle things correctly. I am very stumped.

Answer 1

How can you localize the error just by yourself? One possibility is to generalize your query. As long as your program is pure and monotonic the following holds:

if a generalized query fails, then also the more specialized query will fail

And thus, this generalization is relevant to the failure.

By replacing terms with _ I obtained the following still failing query (also, I translated your code into DCG-form)...

?- phrase(sentence,[if,'(', x, >, 0,')', then, begin, [x, =, 1], end]).
   false.

?- phrase(sentence,[_ ,  _, _, _, _,  _,    _,     _, [_|  _  ]|   _]).
   false.

sentence--> f ; t, n, t.

(plus the remaining rules as given by CapelliC)

From this generalization we see that there is no sentence that has as 9th element a list with at least one element.

Also note that you can now enumerate all sentences!

?- length(L,_), phrase(sentence,L).
   L = [x, +, x]
;  L = [x, +, y]
;  L = [x, +, z]
;  L = [x, +, 1]
;  L = [x, +, 0]
;  ... .

Answer 2

The problem, as noted by @jschimpf, is that we are mixing two description levels in the initial call. Lists are metadata, and this is more evident rewriting the grammar in DCG notation. Once corrected the original formulation (was sentence--> f; t,n,t.) the test ?- g. passes.

sentence--> f; [L], {phrase((t,n,t),L)}.
f--> termIf, pLeft, b, pRight, termThen, termBegin, sentence, termEnd.
f--> termIf, pLeft, b, pRight, termThen, termBegin, sentence, termElse, sentence, termEnd.
b--> t, e, t.
termIf--> [if].
termThen--> [then].
termBegin--> [begin].
termEnd--> [end].
termElse--> [else].
pLeft--> ['('].
pRight--> [')'].
t--> [x].
t--> [y].
t--> [z].
t--> [1].
t--> [0].
e--> [>].
e--> [<].
n--> [+].
n--> [-].
n--> [=].

g :- phrase(sentence, [if,'(', x, >, 0,')', then, begin, [x, =, 1], end]).

edit

Now we can fix the problem in the original code, where sentence/2 has the role that DCGs assign to phrase/2 :

sentence(S0,S):-
  S0=[H|T],
  (  \+is_list(H)
  -> f(S0,S)
  ;  t(H,S1),n(S1,S2),t(S2,[]),
     S=T
  ).

edit I have proposed what I think it's the more instructive correction of sentence/2, but we can avoid the 'impure' if/then/else construct, for instance

sentence(S0,S):-
  f(S0,S);S0=[H|S],H=[_|_],t(H,S1),n(S1,S2),t(S2,[]).

should work (untested...)

Answer 3

The code expects a flat list of terminals, but you have a nested [x,=,1] in there. What you wanted is

?- sentence([if, '(', x, >, 0, ')', then, begin, x, =, 1, end], X).
X = []
Yes (0.00s cpu, solution 1, maybe more)
No (0.00s cpu)